Final commit?

LaTeX/approach.tex

@@ -1,11 +1,10 @@
 \chapter{Algorithm Overview} \label{algorithm}
 
-	This thesis will attempt to develop an algorithm for the preliminary analysis of feasibility in
-	designing a low-thrust interplanetary mission to an outer planet by leveraging a monotonic basin
-	hopping algorithm. In this section, we will review the actual execution of the algorithm
-	developed. As an overview, the routine was designed to enable the determination of an optimized
-	spacecraft trajectory from the selection of some very basic mission parameters. Those parameters
-	include:
+	This thesis focuses on designing a low-thrust interplanetary mission to an outer planet by
+	leveraging a monotonic basin hopping algorithm. This section will review the actual execution of
+	the algorithm developed. As an overview, the routine is designed to enable the determination of
+	an optimal spacecraft trajectory that minimizes propellant usage and $C_3$ from the selection of
+	some very basic parameters. Those parameters include:
 
 	\begin{itemize}
 		\setlength\itemsep{-0.5em}
@@ -25,7 +24,7 @@
 	\end{itemize}
 
 	Which allows for an automated approach to optimization of the trajectory, while still providing
-	the mission designer with the flexibility to choose the particular flyby planets to investigate.
+	the designer with the flexibility to choose the particular flyby planets to investigate.
 
 	This is achieved via an optimal control problem in which the ``inner loop'' involves solving a
 	TPBVP to find the optimal solution given a suitable initial guess. Then an ``outer loop''
@@ -88,9 +87,13 @@
 		In this formulation the cost function $F$ is a user provided function of the input Guess.
 		The constraint function $G$ defines the following conditions that must be met:
 
+		\begin{spacing}{1.0}
 		\begin{itemize}
+			\setlength\itemsep{-0.5em}
 			\item For every phase other than the final:
+				\vspace{-0.5em}
 				\begin{itemize}
+				\setlength\itemsep{0em}
 					\item The minimum periapsis of the hyperbolic flyby arc must be above some
 						user-specified minimum safe altitude.
 					\item The magnitude of the incoming hyperbolic velocity must match the magnitude
@@ -99,16 +102,19 @@
 						at the end of the phase.
 				\end{itemize}
 			\item For the final phase:
+				\vspace{-0.5em}
 				\begin{itemize}
+				\setlength\itemsep{0em}
 					\item The spacecraft position must match the planet's position (within bounds)
 						at the end of the phase.
 					\item The final mass must be greater than the dry mass of the craft.
 				\end{itemize}
 		\end{itemize}
+		\end{spacing}
 
 		\begin{figure}[H]
 			\centering
-			\includegraphics[width=\textwidth]{flowcharts/nlp}
+			\includegraphics[width=\textwidth]{LaTeX/flowcharts/nlp}
 			\caption{A flowchart of the TPBVP Solution Approach}
 			\label{nlp}
 		\end{figure}
@@ -126,12 +132,11 @@
 			The following pseudo-code outlines the approach taken for the elliptical case. The
 			approach is quite similar when $a<0$:
 
-			% TODO: Some symbols here aren't recognized by the font
 			\begin{singlespacing}
 			\begin{verbatim}
 				i = 0
 				# First declare some useful variables from the state
-				sig0 = (position ⋅ velocity) / √(mu)
+				sig0 = dot(position, velocity) / √(mu)
 				a = 1 / ( 2/norm(position) - norm(velocity)^2/mu )
 				coeff = 1 - norm(position)/a
 
@@ -171,13 +176,13 @@
 
 			\begin{figure}[H]
 				\centering
-				\includegraphics[width=\textwidth]{fig/laguerre_plot}
+				\includegraphics[width=\textwidth]{LaTeX/fig/laguerre_plot}
 				\caption{Example of a natural trajectory propagated via the Laguerre-Conway
 				approach to solving Kepler's Problem}
 				\label{laguerre_plot}
 			\end{figure}
 
-		\subsection{Sims-Flanagan Propagator}
+		\subsection{Propagating with Sims-Flanagan Transcription}
 
 			Until this point, we've not yet discussed how best to model the low-thrust
 			trajectory arcs themselves. The Laguerre-Conway algorithm efficiently determines
@@ -197,7 +202,7 @@
 
 			\begin{figure}[H]
 				\centering
-				\includegraphics[width=\textwidth]{fig/spiral_plot}
+				\includegraphics[width=\textwidth]{LaTeX/fig/spiral_plot}
 				\caption{An example trajectory showing that classic continuous-thrust orbit
 				shapes, such as this orbit spiral, are easily achievable using a Sims-Flanagan
 				model}
@@ -221,16 +226,23 @@
 			and the mass flow rate (a function of the duty cycle percentage ($d$), thrust ($f$),
 			and the specific impulse of the thruster ($I_{sp}$), commonly used to measure
 			efficiency)\cite{sutton2016rocket}:
-
 			\begin{equation}
 				\Delta m = \Delta t \frac{f d}{I_{sp} g_0}
 			\end{equation}
-
 			Where $\Delta m$ is the fuel used in the sub-trajectory, $\Delta t$ is the time of
 			flight of the sub-trajectory, and $g_0$ is the standard gravity at the surface of
 			Earth. From knowledge of the mass flow rate, we can then decrement the mass
 			appropriately based on the magnitude of the thrust vector at each point.
 
+			In the implementation provided in this thesis, a Sims-Flanagan $n$ value of 20 was
+			chosen for each of the phases. This value, as tested by
+			Englander\cite{englander2012automated}, is sufficient for trajectories that maintain a
+			reasonably small number of solar revolutions. In the future, a more intelligent solution
+			could be to determine, roughly, the number of revolutions around the sun that the orbit
+			will likely take (perhaps by using the period of the orbit at the beginning of the
+			propagation and the time of flight), and scaling $n$ according to the number of
+			revolutions.
+
 		\subsection{Non-Linear Problem Solver}
 
 			Now that we have the basic building blocks of a continuous-thrust trajectory, we can
@@ -257,7 +269,7 @@
 						\item The $v_{\infty,in}$ vector representing excess velocity at the
 							planetary flyby (or completion of mission) at the end of the phase
 						\item The time of flight for the phase
-						\item The unit-thrust profile in a sun-fixed frame represented by a
+						\item The unit-thrust profile in a sun-centered frame represented by a
 							series of vectors with each element ranging from 0 to 1.
 					\end{itemize}
 			\end{itemize}
@@ -265,10 +277,9 @@
 
 			From this information, as can be seen in Figure~\ref{nlp}, we can formulate the mission
 			in terms of a non-linear programming problem. Specifically, the variables describing the
-			trajectory contained within the Guess object can be represented as an input vector,
-			$\vec{x}$, the cost function produced by an entire trajectory propagation as $F$, and
-			the constraints that the trajectory must satisfy as another function $\vec{G}$ such that
-			$\vec{G}(\vec{x}) = \vec{0}$.
+			trajectory from the free variable, $\vec{x}$, the cost function produced by an entire
+			trajectory propagation, $F$, and the constraints that the trajectory must satisfy as
+			another function $\vec{G}$ such that $\vec{G}(\vec{x}) = \vec{0}$.
 
 			This is a format that we can apply directly to the IPOPT solver, which Julia (the
 			programming language used) can utilize via bindings supplied by the SNOW.jl
@@ -318,7 +329,7 @@
 
 			\begin{figure}[H]
 				\centering
-				\includegraphics[width=\textwidth]{flowcharts/mbh}
+				\includegraphics[width=\textwidth]{LaTeX/flowcharts/mbh}
 				\caption{A flowchart visualizing the steps in the monotonic basin hopping
 				algorithm}
 				\label{mbh_flow}
@@ -326,12 +337,12 @@
 
 		\subsection{Random Trajectory Generation}\label{random_gen_section}
 
-			At a basic level, the algorithm needs to produce a guess (represented by all of the
-			values described in Section~\ref{inner_loop_section}) that contains random values within
-			reasonable bounds in the space. However, that still leaves the determination of which
-			distribution function to use for the random values over each of those variables, which
-			bounds to use, as well as the possibilities for any improvements to a purely random
-			search.
+			At a basic level, the algorithm needs to produce a guess for the free variable vector
+			(represented by all of the values described in Section~\ref{inner_loop_section}) that
+			contains random values within reasonable bounds in the space. However, that still leaves
+			the determination of which distribution function to use for the random values over each
+			of those variables, which bounds to use, as well as the possibilities for any
+			improvements to a purely random search.
 
 			Currently, the first value set for the mission guess is that of $n$, which is the
 			number of sub-trajectories that each arc will be broken into for the Sims-Flanagan
@@ -365,18 +376,18 @@
 			missions with more flybys.
 
 			Then, the internal components for each phase are generated. It is at this step, that
-			the mission guess generator splits the outputs into two separate outputs. The first
+			the trajectory guess generator splits the outputs into two separate outputs. The first
 			is meant to be truly random, as is generally used as input for a monotonic basin
 			hopping algorithm. The second utilizes a Lambert's solver to determine the
 			appropriate hyperbolic velocities (both in and out) at each flyby to generate a
-			natural trajectory arc. For this Lambert's case, the mission guess is simply seeded
+			natural trajectory arc. For this Lambert's case, the trajectory guess is simply seeded
 			with zero thrust controls and outputted to the monotonic basin hopper. The intention
 			here is that if the time of flights are randomly chosen so as to produce a
 			trajectory that is possible with a control in the vicinity of a natural trajectory,
 			we want to be sure to find that trajectory. More detail on how this is handled is
 			available in Section~\ref{mbh_subsection}.
 
-			However, for the truly random mission guess, there are still the $v_\infty$ values
+			However, for the truly random trajectory guess, there are still the $v_\infty$ values
 			and the initial thrust guesses to generate. For each of the phases, the incoming
 			excess hyperbolic velocity is calculated in much the same way that the launch
 			velocity was calculated. However, instead of multiplying the randomly generate unit
@@ -390,18 +401,12 @@
 			non-powered flyby.
 
 			From these two velocity vectors the turning angle, and thus the periapsis of the flyby,
-			can then be calculated by Equation~\ref{turning_angle_eq} and the following equation:
-
-			\begin{equation}
-				r_p = \frac{\mu}{\vec{v}_{\infty,in} \cdot \vec{v}_{\infty,out}} \cdot \left(
-				\frac{1}{\sin(\delta/2)} - 1 \right)
-			\end{equation}
-
-			If this radius of periapse is then found to be less than the minimum safe radius
-			(currently set to the radius of the planet plus 100 kilometers), then the process is
-			repeated with new random flyby velocities until a valid seed flyby is found. These
-			checks are also performed each time a mission is perturbed or generated by the NLP
-			solver.
+			can then be calculated by Equation~\ref{turning_angle_eq} and
+			Equation~\ref{periapsis_eq}. If this radius of periapse is then found to be less than
+			the minimum safe radius (currently set to the radius of the planet plus 100 kilometers),
+			then the process is repeated with new random flyby velocities until a valid seed flyby
+			is found. These checks are also performed each time a mission is perturbed or generated
+			by the NLP solver.
 
 			The final requirement then, is the thrust controls, which are actually quite simple.
 			Since the thrust is defined as a 3-vector of values between -1 and 1 representing some
@@ -438,15 +443,24 @@
 			generator produces two random missions as described in
 			Section~\ref{random_gen_section} that differ only in that one contains random flyby
 			velocities and control thrusts and the other contains Lambert's-solved flyby
-			velocities and zero control thrusts. For each of these guesses, the NLP solver is
-			called. If either of these mission guesses have converged onto a valid solution, the
-			lower loop, the ``drill loop'' is entered for the valid solution. After the
-			convergence checks and potentially drill loops are performed, if a valid solution
-			has been found, this solution is stored in an archive. If the solution found is
-			better than the current best solution in the archive (as determined by a
-			user-provided cost function of fuel usage, $C_3$ at launch, and $v-\infty$ at
-			arrival) then the new solution replaces the current best solution and the loop is
-			repeated. Taken by itself, the search loop should quickly generate enough random
+			velocities and zero control thrusts.
+
+			The choice of adding a ``Lambert's solution-seeded'' random mission is an attempt to
+			improve upon previous low-thrust MBH iterations by more intelligently choosing some of
+			the initial guesses. Because the majority of the initial guesses that are truly random
+			don't converge, this provides a greater number of valid initial guesses for the MBH
+			algorithm to use to find better trajectories. However, each MBH loop does then take
+			twice the time, which increases the amount of time required to truly traverse the entire
+			space.
+
+			For each of these guesses, the NLP solver is called. If either of these mission guesses
+			have converged onto a valid solution, the lower loop, the ``drill loop'' is entered for
+			the valid solution. After the convergence checks and potentially drill loops are
+			performed, if a valid solution has been found, this solution is stored in an archive. If
+			the solution found is better than the current best solution in the archive (as
+			determined by a user-provided cost function of fuel usage, $C_3$ at launch, and
+			$v-\infty$ at arrival) then the new solution replaces the current best solution and the
+			loop is repeated. Taken by itself, the search loop should quickly generate enough random
 			mission guesses to find all ``basins'' or areas in the solution space with valid
 			trajectories, but never attempts to more thoroughly explore the space around valid
 			solutions within these basins.
@@ -470,14 +484,11 @@
 			Because of this, the perturbation used in this implementation follows a
 			bi-directional, long-tailed Pareto distribution generated by the following
 			probability density function\cite{englander2014tuning}:
-
 			\begin{equation}
 				1 +
 				\left[ \frac{s}{\epsilon} \right] \cdot
 				\left[ \frac{\alpha - 1}{\frac{\epsilon}{\epsilon + r}^{-\alpha}} \right]
 			\end{equation}
-
-			\noindent
 			Where $s$ is a random array of signs (either plus one or minus one) with dimension
 			equal to the perturbed variable and bounds of -1 and 1, $r$ is a uniformly
 			distributed random array with dimension equal to the perturbed variable and bounds
@@ -496,4 +507,25 @@
 			iterations to perform without improvement in a row before ending the drill loop.
 			This process can be repeated essentially ''search patience`` number of times in
 			order to fully traverse all basins.
+			
+			It is worth validating whether the described Monotonic Basin Hopping algorithm
+			actually provides significant improvements in global cost-function minimization over
+			a single NLP-optimization run for the particular problem of low-thrust
+			interplanetary trajectories. Therefore, a simple sample Earth to Saturn trajectory
+			was selected and every single valid trajectory discovered by the MBH algorithm was
+			stored. In Figure~\ref{mbh_analysis}, the cost function values for each of these
+			valid trajectories is plotted in the order in which they were found. The line
+			indicates the minimum cost function discovered until that point in time. This
+			validates that the MBH, over sufficient number of iterations, will find optimal
+			values that the NLP optimization scheme could not discover on its own. It is also
+			worth noting that the ``basin drilling'' feature of the MBH scheme can be clearly
+			seen in the plot, where the algorithm continues to improve its own ``basin-best''
+			until it no longer can do so over a number of attempts.
+
+			\begin{figure}[H]
+				\centering
+				\includegraphics[width=\textwidth]{LaTeX/fig/mbh_analysis}
+				\caption{MBH cost function reduction over iterative updates}
+				\label{mbh_analysis}
+			\end{figure}
 

LaTeX/conclusion.tex

@@ -0,0 +1,40 @@
+\chapter{Conclusion} \label{conclusion}
+
+		This thesis explored an approach for automating the initial analysis and discovery of useful
+		interplanetary, low-thrust trajectories including the difficult task of optimizing the flyby
+		parameters. This makes the mission designer's job significantly simpler in that they can
+		simply explore a number of different flyby selection options in order to get a good
+		understanding of the mission scope and search space for a given spacecraft, launch window,
+		and target. The aim of this exploration was to examine whether a Monotonic Basin Hopping
+		algorithm utilizing an inner-loop NLP solver would be an appropriate choice for the
+		particular problem of low-thrust interplanetary trajectory optimization.
+
+		In performing this examination, two results were selected for further analysis. These
+		results are outlined in Table~\ref{results_table}. As can be seen in the table, both
+		resulting trajectories have trade-offs in mission length, launch energy, fuel usage, and
+		more. Each of these trajectories appear to be within the capabilities of existing launch
+		vehicles in terms of $C_3$.
+
+		In the course of producing this algorithm, a large number of improvement possibilities were
+		noted. This work was based, in large part, on the work of Jacob Englander in a number of
+		papers\cite{englander2014tuning}\cite{englander2017automated} \cite{englander2012automated}
+		in which they explored the hybrid optimal control problem of multi-objective low-thrust
+		interplanetary trajectories.
+
+		In light of this, there are a number of additional approaches that Englander took in
+		preparing their algorithm that were not implemented here in favor of reducing complexity and
+		time constraints. For instance, many of the Englander papers explore the concept of an outer
+		loop that utilizes a genetic algorithm to compare many different flyby planet choices
+		against each other.
+
+		Further improvements, in the name of performance stem from the field of computer science. An
+		evolutionary algorithm such as the one proposed by Englander would benefit from high levels
+		of parallelization. Therefore, it would be worth considering a GPU-accelerated or even
+		cluster-computing capable implementation of the monotonic basin hopping algorithm.
+
+		Finally, the monotonic basin hopping algorithm as currently written provides no guarantees
+		of actual global optimization. Generally optimization is achieved by running the algorithm
+		until it fails to produce newer, better trajectories for a sufficiently long time. But it
+		would be worth investigating the robustness of the NLP solver as well as the robustness of
+		the MBH algorithm basin drilling procedures in order to quantify the search granularity
+		needed to completely traverse the search space.

LaTeX/fig/thrust_angle.svg

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LaTeX/introduction.tex

@@ -1,16 +1,16 @@
 \chapter{Introduction}
 
 	Continuous low-thrust engines utilizing technologies such as Ion propulsion, Hall thrusters, and
-	others can be a powerful system in the enabling of long-range interplanetary missions with fuel
-	efficiencies unrivaled by those that employ only impulsive thrust systems. The challenge in
-	utilizing these systems, then, is the design of trajectories that effectively utilize this
-	technology. Continuous thrust propulsive systems tend to be particularly suited to missions
-	which require very high total change in velocity ($\Delta V$) values and take place over a
-	particularly long duration. Traditional impulsive thrusting techniques can achieve these changes
-	in velocity, but typically have a far lower specific impulse and, as such, are much less fuel
-	efficient, costing the mission valuable financial resources that could instead be used for
-	science. Because of their inherently high specific impulse (and thus efficiency), low-thrust
-	propagation systems are well-suited to interplanetary missions.
+	others enable long-range interplanetary missions with fuel efficiencies unrivaled by those that
+	employ only impulsive thrust systems. The challenge in utilizing these systems, then, is the
+	design of trajectories that effectively utilize this technology. Continuous thrust propulsive
+	systems tend to be particularly suited to missions which require very high total change in
+	velocity ($\Delta V$) values and take place over a particularly long duration. Traditional
+	impulsive thrusting techniques can achieve these changes in velocity, but typically have a far
+	lower specific impulse and, as such, are much less fuel efficient, costing the mission valuable
+	financial resources that could instead be used for science. Because of their inherently high
+	specific impulse (and thus efficiency), low-thrust propulsion systems are well-suited to
+	interplanetary missions.
 
 	The first attempt by NASA to use an electric ion-thruster for an interplanetary mission was the
 	Deep Space 1 mission\cite{brophy2002}. This mission was designed to test the ``new'' technology,
@@ -29,16 +29,15 @@
 	in October 2018 and is projected to perform a flyby of Earth, two of Venus, and six of
 	Mercury before inserting into an orbit around that planet.
 
-	A common theme in mission design is that there always exists a trade-off between efficiency
-	(particularly in terms of fuel use) and the time required to achieve the mission objective. Low
-	thrust systems in particular tend to produce mission profiles that sacrifice the rate of
-	convergence on the target state in order to achieve large increases in fuel efficiency. Often a
-	low-thrust mission profile in Earth orbit will require multiple orbital periods to achieve the
-	desired change in spacecraft state. Interplanetary missions, though, provide a particularly
-	useful case for continuous thrust technology. The trajectory arcs in interplanetary space are
-	generally much, much longer than orbital missions around the Earth. Because of this increase,
-	even a small continuous thrust is capable of producing large $\Delta V$ values over the course
-	of a single trajectory arc.
+	A common theme in mission design is that there is a trade-off between efficiency (particularly
+	in terms of fuel use) and the time required to achieve the mission objective. Low thrust systems
+	in particular tend to produce mission profiles that sacrifice the rate of convergence on the
+	target state in order to achieve large increases in fuel efficiency. Often a low-thrust transfer
+	in Earth orbit will require multiple orbital periods to achieve the desired change in spacecraft
+	state. Interplanetary missions, though, provide a particularly useful case for continuous thrust
+	technology. The trajectory arcs in interplanetary space are generally much, much longer than
+	orbital missions around the Earth. Because of this increase, even a small continuous thrust is
+	capable of producing large $\Delta V$ values over the course of a single trajectory arc.
 
 	Another technique often leveraged by interplanetary trajectory designers is the gravity assist.
 	Gravity assists utilize the inertia of a large planetary body to ``slingshot'' a spacecraft,
@@ -58,24 +57,22 @@
 	routine for producing unconstrained, globally optimal trajectories for realistic interplanetary
 	mission development that utilizes both planetary flybys and efficient low-thrust electric
 	propulsion techniques. Similar studies have also been performed by a number of researchers
-	including a team from JPL\cite{sims2006} as well as a Spanish team\cite{morante}, among several
-	others.
+	including a team from JPL\cite{sims2006}, among several others\cite{morante}.
 
-	This thesis will attempt to develop an algorithm for the optimization of low-thrust enabled
-	trajectories for initial feasibility analysis in mission design. The algorithm will utilize
-	a non-linear programming solver to directly optimize a set of control thrusts for the
-	user-provided flyby planets, for any provided cost function. A monotonic basin hopping algorithm
-	(MBH) will then be employed to traverse the search space in an effort to find additional local
-	optima. This approach differs from the work produced earlier by Englander and the other teams,
-	but is largely meant to explore the feasibility of such techniques and propose a few
-	enhancements. The approach defined in this thesis will then be used to investigate an example
-	mission to Saturn.
+	This thesis focuses on optimization of low-thrust enabled trajectories that use gravity assists.
+	The approach uses a non-linear programming solver to directly optimize a set of control thrusts
+	for the user-provided flyby planets, for any provided cost function. A monotonic basin hopping
+	algorithm (MBH) is then employed to traverse the search space in an effort to find additional
+	local optima. This approach differs from the work produced earlier by Englander and the other
+	teams, but is largely meant to explore the feasibility of such techniques and propose a few
+	enhancements. The approach defined in this thesis is then used to design low thrust trajectories
+	with gravity assits from the Earth to Saturn.
 
-	This thesis will explore these concepts in a number of different sections. Section
-	\ref{traj_dyn} will explore the basic dynamical principles of trajectory design, beginning the
-	with fundamental system dynamics, then exploring interplanetary system dynamics and gravity
-	flybys, and finally the dynamics that are specific to low-thrust enabled trajectories. Section
-	\ref{traj_optimization} will then discuss process of optimizing spacecraft trajectories in
-	general and the tool available for that. Section \ref{algorithm} will cover the implementation
-	details of the optimization algorithm developed for this paper. Finally, section \ref{results}
-	will explore the results of some hypothetical missions to Saturn.
+	This thesis is organized as follows: Section \ref{traj_dyn} will explore the basic dynamical
+	principles of trajectory design, beginning the with fundamental system dynamics, then exploring
+	interplanetary system dynamics and gravity flybys, and finally the dynamics that are specific to
+	low-thrust enabled trajectories. Section \ref{traj_optimization} will then discuss process of
+	optimizing spacecraft trajectories in general and the tool available for that. Section
+	\ref{algorithm} will cover the implementation details of the optimization algorithm developed
+	for this paper. Finally, section \ref{results} will explore the results of some hypothetical
+	missions to Saturn.

LaTeX/presentation.bib

@@ -0,0 +1,25 @@
+@misc{nasa_voyager,
+  title={Voyager - Mission Overview},
+  url={https://voyager.jpl.nasa.gov/mission/},
+  journal={NASA},
+  publisher={NASA}
+}
+
+@phdthesis{dhanasarCassini,
+  author = {Dhanasar, Mookesh},
+  year = {2005},
+  month = {12},
+  pages = {},
+  title = {A METHOD FOR THE DESIGN AND ANALYSIS OF DEEP SPACE NUCLEAR PROPULSION SYSTEMS}
+}
+
+@article{jehnBepi,
+  author = {Jehn, Rüdiger and García Yárnoz, Daniel and Schoenmaekers, Johannes and Companys, Vicente},
+  year = {2012},
+  month = {01},
+  pages = {1-9},
+  title = {Trajectory Design for BepiColombo Based on Navigation Requirements},
+  volume = {4},
+  journal = {Journal of Aerospace Engineering, Sciences and Applications},
+  doi = {10.7446/jaesa.0401.01}
+}

LaTeX/presentation.tex

@@ -0,0 +1,608 @@
+\documentclass{beamer}
+\usetheme{Antibes}
+
+\usepackage{xfrac}
+
+\definecolor{color1}{HTML}{3A4040}
+\definecolor{color2}{HTML}{F5F2F8}
+\definecolor{color3}{HTML}{C47B6E}
+\definecolor{color4}{HTML}{B6AD96}
+\definecolor{color5}{HTML}{B65D4E}
+
+\setbeamercolor*{structure}{bg=color3,fg=color3}
+\setbeamercolor*{palette primary}{fg=color1,bg=color4}
+\setbeamercolor*{palette secondary}{fg=color1,bg=color4}
+\setbeamercolor*{palette tertiary}{fg=color1,bg=color3}
+\setbeamercolor*{palette quaternary}{fg=color1,bg=color5}
+\setbeamercolor{alerted text}{fg=color1,bg=color3}
+\setbeamercolor{titlelike}{bg=color2,fg=color1}
+\setbeamercolor*{titlelike}{bg=color2,fg=color1}
+\setbeamercolor{frametitle}{bg=color1,fg=color2}
+\setbeamercolor{background canvas}{bg=color2,fg=color2}
+
+\title{Designing Optimal Low-Thrust Interplanetary Trajectories Utilizing Monotonic Basin Hopping}
+\author{Richard Connor Johnstone}
+\institute{University of Colorado -- Boulder}
+\date{\today}
+
+\begin{document}
+
+\begin{frame}
+	\titlepage
+\end{frame}
+
+\section{Introduction}
+
+	\subsection{Motivation}
+
+		% \begin{frame} \frametitle{Motivation}
+		% 	How can we leverage existing technologies and techniques to determine
+		% 	optimally-controlled trajectories to targets in interplanetary space?
+		% \end{frame}
+
+		\note{Today I'll be discussing my research in determining optimal trajectories
+		for interplanetary mission objectives. Numerous scientific and engineering advances have
+		been made possible by the recognition of optimal trajectories in interplanetary space.}
+
+		\begin{frame} \frametitle{Voyager}
+			\begin{figure}
+				\centering
+				\includegraphics[height=0.6\paperheight]{LaTeX/fig/voyager}
+				\caption{Voyager mission trajectory\cite{nasa_voyager}}
+			\end{figure}
+		\end{frame}
+
+		\note{For instance, the Voyagers I and II missions were launched in 1977 because of a
+		once-in-a-lifetime window in which the spacecraft were able to, on a single tour, visit all
+		four gas giant outer planets. These tours were only made possible because of the ability to
+		compute planetary ephemeris and map out a chain of gravity assists.}
+
+		\begin{frame} \frametitle{Bepi-Colombo}
+			\begin{figure}
+				\centering
+				\includegraphics[height=0.6\paperheight]{LaTeX/fig/bepicolombo}
+				\caption{Bepi-Colombo mission trajectory\cite{jehnBepi}}
+			\end{figure}
+		\end{frame}
+
+		\note{More recently, ESA has also been able to take advantage of gravity assists to send the
+		spacecraft Bepi-Colombo into a trajectory that rendezvous 6 times with Mercury. While this
+		mission did utilize a number of gravity assists, it also utilized another technology
+		well-suited to interplanetary travel: low-thrust electric propulsion systems}
+
+	\subsection{Context}
+
+		\begin{frame} \frametitle{Low Thrust Electric Propulsion}
+			Allows for some advantages in achieving more interesting mission objectives:
+			\begin{itemize}
+				\item Much higher thrusting efficiency (in terms of fuel usage) compared to high
+					thrust propulsive systems
+				\item Allows for a greater overall $\Delta V$ budget for a given mission
+			\end{itemize}
+
+			\pause
+			But requires some additional considerations:
+			\begin{itemize}
+				\item Requires significantly more time to achieve the same velocity change
+				\item Defines a new system dynamics control, which must be accounted for
+					continuously at each point in time, requiring additional computation for
+					optimization
+			\end{itemize}
+		\end{frame}
+
+		\note{Thanks to their ability to provide thrust extremely efficiently, these low-thrust
+		engines can be a powerful tool for enabling impressive scientific objectives, but they do
+		provide an additional layer of complexity for the mission designer, as their continuous
+		thrust nature changes the underlying system dynamics that would have been used to optimize a
+		mission such as Voyager, which did not employ low-thrust engines.}
+
+		\begin{frame} \frametitle{Problem Statement}
+			For a given low-thrust engine, spacecraft parameters, and planetary flyby selections,
+			what is the optimal control thrusting profile, launch conditions, and flyby parameters
+			to arrive at a target outer planet?
+		\end{frame}
+
+\section{Trajectory Optimization Background}
+
+	\subsection{System Dynamics}
+
+		\begin{frame} \frametitle{Dynamical Model: Two Body Problem}
+			\begin{columns}
+					\begin{column}{0.45\paperwidth}
+						Assumptions:
+						\begin{itemize}
+							\item There are only two bodies in the system
+							\item The only force acting between the two bodies is gravitational
+							\item The two masses are to be modeled as constant point masses
+						\end{itemize}
+					\end{column}
+					\begin{column}{0.45\paperwidth}
+						\begin{figure}
+							\centering
+							\includegraphics[width=0.45\paperwidth]{LaTeX/fig/2bp}
+						\end{figure}
+					\end{column}
+			\end{columns}
+		\end{frame}
+
+		\note{In order to understand how to optimize these trajectories, we'll first have to
+		understand the underlying system dynamics. I won't spend too long on this, as most of you
+		should have a good grasp on spacecraft dynamics, but we'll briefly analyse the most basic
+		model for spaceflight dynamics: the two body problem. This model requires us to make a
+		couple of basic assumptions. First that we are only concerned with the gravitational
+		influence between the nominative two bodies: the spacecraft and the planetary body around
+		which it is orbiting. Secondly, both of these bodies are modeled as point masses with
+		constant mass. This removes the need to account for non-uniform densities and asymmetry.}
+
+		\begin{frame} \frametitle{Dynamical Model: Two Body Problem}
+			\begin{columns}
+					\begin{column}{0.45\paperwidth}
+						\begin{align*}
+							m_2 \ddot{\vec{r}}_2 &= - \frac{G m_1 m_2}{r^2} \frac{\vec{r}}{\left| r \right|} \\
+							m_1 \ddot{\vec{r}}_1 &= \frac{G m_2 m_1}{r^2} \frac{\vec{r}}{\left| r \right|}
+						\end{align*}
+					\end{column}
+					\begin{column}{0.45\paperwidth}
+						\begin{figure}
+							\centering
+							\includegraphics[width=0.45\paperwidth]{LaTeX/fig/2bp}
+						\end{figure}
+					\end{column}
+			\end{columns}
+		\end{frame}
+
+		\note{From Newton's second law and the law of universal gravitation, we can then model this
+		force with this equation. Where...}
+
+		\begin{frame} \frametitle{Dynamical Model: Two Body Problem}
+			\begin{columns}
+					\begin{column}{0.45\paperwidth}
+						\begin{equation*}
+							\ddot{\vec{r}} = \ddot{\vec{r}}_2 - \ddot{\vec{r}}_1 =
+							- \frac{G \left( m_1 + m_2 \right)}{r^2} \frac{\vec{r}}{\left| r \right|}
+						\end{equation*}
+					\end{column}
+					\begin{column}{0.45\paperwidth}
+						\begin{figure}
+							\centering
+							\includegraphics[width=0.45\paperwidth]{LaTeX/fig/2bp}
+						\end{figure}
+					\end{column}
+			\end{columns}
+		\end{frame}
+
+		\note{Dividing by the mass, we can derive the acceleration...}
+
+		\begin{frame} \frametitle{Dynamical Model: Two Body Problem}
+			\begin{columns}
+					\begin{column}{0.45\paperwidth}
+						\begin{align*}
+							\mu &= G (m_1 + m_2) \approx G m_1 \\
+							\ddot{\vec{r}} &= - \frac{\mu}{r^2} \hat{r}
+						\end{align*}
+					\end{column}
+					\begin{column}{0.45\paperwidth}
+						\begin{figure}
+							\centering
+							\includegraphics[width=0.45\paperwidth]{LaTeX/fig/2bp}
+						\end{figure}
+					\end{column}
+			\end{columns}
+		\end{frame}
+
+		\note{Finally, we'll make the assumption that the mass of the spacecraft, is significantly
+		smaller than the mass of the planet. This allows us to represents the gravitational
+		parameter as a function of the planetary mass alone, rather than both combined. With this
+		assumption, we can model the system dynamics with this analytically solvable equation}
+
+		\begin{frame} \frametitle{Dynamical Model: Kepler's Laws}
+			\begin{itemize}
+				\item Each planet's orbit is an ellipse with the Sun at one of the foci.
+				\item The area swept out by the imaginary line connecting the primary and secondary
+					bodies increases linearly with respect to time.
+				\item The square of the orbital period is proportional to the cube of the semi-major
+					axis of the orbit, regardless of eccentricity.
+			\end{itemize}
+		\end{frame}
+
+		\note{In the early 1600s, Johannes Kepler determined three laws in order to describe the
+		motion of a satellite. These are:}
+
+		\begin{frame} \frametitle{Dynamical Model: Kepler's Laws}
+			\begin{equation*}
+				r = \frac{\sfrac{h^2}{\mu}}{1 + e \cos(\theta)}
+			\end{equation*}
+
+			\vspace{1em}
+
+			\begin{equation*}
+				\frac{\Delta t}{T} = \frac{E - e \sin E}{2 \pi}
+			\end{equation*}
+
+			\vspace{1em}
+
+			\begin{equation*}
+				T = 2 \pi \sqrt{\frac{a^3}{\mu}}
+			\end{equation*}
+		\end{frame}
+
+		\note{By utilizing these laws and some geometric properties of conic sections, we can
+		actually take them a step further, producing the following extremely useful equations for
+		representing spacecraft motion:}
+
+		\begin{frame} \frametitle{Dynamical Model: Kepler's Equation}
+			\begin{equation*}
+				\frac{\Delta t}{T} = \frac{E - e \sin E}{2 \pi}
+			\end{equation*}
+
+			\vspace{1em}
+
+			\begin{equation*}
+				T = 2 \pi \sqrt{\frac{a^3}{\mu}}
+			\end{equation*}
+
+			\vspace{1em}
+
+			\begin{equation*}
+				M = \sqrt{\frac{\mu}{a^3}} \Delta t = E - e \sin E
+			\end{equation*}
+		\end{frame}
+
+		\note{The second of these, which we'll take particular notice of, is considered Kepler's
+		equation. It provides a method for relating the time since periapsis of a satellite in an
+		orbit to the satellite's position along that orbit. The solution to this equatin can then be
+		used to solve for a spacecraft's position, which is very useful for direct optimization
+		methods.}
+
+		% \note{Finally, though, we'll need to actually solve Kepler's equation. For this purpose
+		% we'll use a generic root-finding method first proposed by Laguerre in the 19th century.
+		% Conway first explored its application on Kepler's equation in the 1980s and found it to be
+		% more robust at converging to a solution, with similar convergence speed, to the more common
+		% variations of the Newton-Raphson method}
+
+	\subsection{Interplanetary Trajectories}
+
+		\begin{frame} \frametitle{Interplanetary Trajectories: Patched Conics}
+			\begin{figure}[H]
+				\centering
+				\includegraphics[height=0.7\paperheight]{LaTeX/fig/patched_conics}
+			\end{figure}
+		\end{frame}
+
+		\note{Now that we have a grasp on the underlying system dynamics, we can consider the
+		additions needed for interplanetary travel specifically. To this end, we'll consider the
+		method of patched conics, a technique for reconciling the fact that the spacecraft will not
+		be under the influence of a single body, but actually a number of different bodies over the
+		course of its trajectory. To achieve this, we'll break the trajectory up into different
+		sub-trajectories, each governed by a distinct single body when the spacecraft is within the
+		sphere of influence of that particular body...}
+
+		\begin{frame} \frametitle{Interplanetary Trajectories: Gravity Assist}
+			\begin{figure}[H]
+				\centering
+				\includegraphics[height=0.7\paperheight]{LaTeX/fig/flyby}
+			\end{figure}
+		\end{frame}
+
+		\note{You'll notice, though, that the trajectories within the sphere of influence aren't
+		elliptical orbits. They're hyperbolic. Because of this fact, we can take advantage of the
+		gravity flyby effect. Because of the nature of the hyperbolic arc the spacecraft takes
+		around the planet, the spacecraft leaves in a different direction than it arrives. This
+		effect can be targeted up to a point, and a free "maneuver" can be achieved, changing the
+		direction of the spacecraft's motion relative to the Sun.}
+
+	\subsection{Low Thrust Trajectories}
+
+		\begin{frame} \frametitle{Low Thrust Trajectories: Sims-Flanagan Transcription}
+			\begin{columns}
+					\begin{column}{0.45\paperwidth}
+						\begin{itemize}
+							\item Each trajectory broken into $n$ segments
+							\item Impulsive thrust at the center of each one, assuming equal thrust
+								over the segment
+							\item Mass decremented over the duration of the segment
+						\end{itemize}
+					\end{column}
+					\begin{column}{0.45\paperwidth}
+						\begin{figure}
+							\centering
+							\includegraphics[width=0.45\paperwidth]{LaTeX/fig/sft}
+						\end{figure}
+					\end{column}
+			\end{columns}
+		\end{frame}
+
+		\note{We'll also need to discretize the low-thrust controls in order to apply a direct
+		optimization. This is achieved, in this thesis and many other implementations, with the
+		Sims-Flanagan transcription. The trajectory is broken up into a number of smaller
+		trajectories with a single impulsive thrust in the center of each. Effectively, this
+		allows...}
+
+		\begin{frame} \frametitle{Low Thrust Trajectories: Control Vector Description}
+			\begin{columns}
+					\begin{column}{0.45\paperwidth}
+						\begin{align*}
+							F_r &= F \cos(\beta) \sin (\alpha) \\
+							F_\theta &= F \cos(\beta) \cos (\alpha) \\
+							F_h &= F \sin(\beta)
+						\end{align*}
+					\end{column}
+					\begin{column}{0.45\paperwidth}
+						\begin{figure}
+							\centering
+							\includegraphics[width=0.45\paperwidth]{LaTeX/fig/thrust_angle}
+						\end{figure}
+					\end{column}
+			\end{columns}
+		\end{frame}
+
+		\note{Finally, in order to better understand the thrust control vector, we need a useful
+		frame. For this purpose, I use the r theta h frame in which the r axis is... This is useful
+		because the theta axis is aligned fairly close to the velocity direction. That allows for a
+		useful framework in which to analyze the control thrusts. Thrusts with a low alpha angle are
+		useful for raising the energy of the orbit, while other thrusts (either alpha around pi/2 or
+		high beta) are useful for steering controls.}
+
+\section{Algorithm Overview}
+
+	\subsection{Trajectory Composition}
+
+		\begin{frame} \frametitle{Input Description}
+			\footnotesize{
+			\begin{itemize}
+				\item \textbf<1>{Spacecraft dry mass in kilograms}
+				\item \textbf<1>{Total starting mass of the Spacecraft in kilograms}
+				\item \textbf<2>{Thruster Specific Impulse in seconds}
+				\item \textbf<2>{Thruster Maximum Thrusting Force in Newtons}
+				\item \textbf<2>{Thruster Duty Cycle Percentage}
+				\item \textbf<2>{Number of Thrusters on Spacecraft}
+				\item \textbf<3>{The Launch Window Boundaries}
+				\item \textbf<3>{The Latest Arrival Date}
+				\item \textbf<4>{A Maximum Acceptable $V_\infty$ at arrival in kilometers per
+					second}
+				\item \textbf<4>{A Maximum Acceptable $C_3$ at launch in kilometers per second
+					squared}
+				\item \textbf<4>{A cost function relating the mass usage, $v_\infty$ at arrival, and
+					$C_3$ at launch to a cost}
+				\item \textbf<5>{A list of flyby planets starting with Earth and ending with the
+					destination}
+			\end{itemize}
+			}
+		\end{frame}
+
+		\note{In order to fully understand the optimization algorithm, it makes sense to first
+		understand the variables that won't be optimized. These will represent the mission
+		parameters used as inputs to the algorithm. These first two will essentially size the
+		spacecraft that we'll be using. Then the next groups will define the thrusters, the launch
+		and arrival windows, the cost function to be used by the direct optimizer, and finally the
+		flybys that the spacecraft will leverage on its trajectory.}
+
+	\subsection{Inner Loop Implementation}
+
+		\begin{frame} \frametitle{Non-Linear Programming Approach - Definition}
+			A Non-Linear Programming Problem involves finding a solution that optimizes a function:
+
+			\begin{equation*}
+				f(\vec{x})
+			\end{equation*}
+
+			Subject to constraints:
+			\begin{align*}
+				\vec{g}(\vec{x}) &\le 0 \\
+				\vec{h}(\vec{x}) &= 0
+			\end{align*}
+
+		\end{frame}
+
+		\note{Now we'll treat the trajectory as a direct non-linear programming optimization
+		problem. This provides a general approach to determining a local optima to a scalar function
+		f of a vector-valued input, x, subject to constraints g and h, defined as can be seen here.}
+
+		\begin{frame} \frametitle{Non-Linear Programming Approach - Input Vector}
+			\begin{figure}
+				\centering
+				\includegraphics[height=0.7\paperheight]{LaTeX/flowcharts/nlp}
+			\end{figure}
+		\end{frame}
+
+		\note{So we need simply to define the function, constraints, and the input vector. Starting
+		with the input vector, we need to determine...}
+
+		\begin{frame} \frametitle{Non-Linear Programming Approach - Constraints}
+			\begin{itemize}
+				\item For every phase other than the final:
+					\begin{itemize}
+						\item The minimum periapsis of the hyperbolic flyby arc must be above some
+							user-specified minimum safe altitude.
+						\item The magnitude of the incoming hyperbolic velocity must match the magnitude
+							of the outgoing hyperbolic velocity.
+						\item The spacecraft position must match the planet's position (within bounds)
+							at the end of the phase.
+					\end{itemize}
+				\item For the final phase:
+					\begin{itemize}
+						\item The spacecraft position must match the planet's position (within bounds)
+							at the end of the phase.
+						\item The final mass must be greater than the dry mass of the craft.
+					\end{itemize}
+			\end{itemize}
+		\end{frame}
+
+		\note{And we can also determine a series of constraints...}
+
+		\begin{frame} \frametitle{Non-Linear Programming Approach - Cost Function}
+			\begin{equation*}
+				J(\vec{x}, m_{dry}, C_{3,max}) = 3 \left| \frac{m(\vec{x})}{m_{dry}} \right| +
+				\left| \frac{C_3(\vec{x})}{C_{3,max}} \right|
+			\end{equation*}
+		\end{frame}
+
+		\note{Finally, the cost function was designed to be user-specified. However, for the
+		implementation of this particular project, I utilized a combination of the normalized fuel
+		usage and launch c3. Now we have a fully-defined non-linear programming problem that can be
+		optimized using any direct method optimization scheme.}
+
+	\subsection{Outer Loop Implementation}
+
+		\begin{frame} \frametitle{Monotonic Basin Hopping}
+			\begin{figure}
+				\centering
+				\includegraphics[height=0.7\textheight]{LaTeX/flowcharts/mbh}
+			\end{figure}
+		\end{frame}
+
+		\note{Now we have a method for finding local optima in the vicinity of an input vector, but
+		what we're after is the global optima, meaning that we need a method for testing a variety
+		of input vectors, each of which could either fail to produce a valid trajectory after the
+		inner loop or produce a valid solution that may or may not be in a "basin", or collection of
+		nearby valid solutions with a single "regional" optimum. In order to approach this problem,
+		I've employed a Monotonic Basin Hopping algorithm. (Step through each of the steps)}
+
+		\begin{frame} \frametitle{Monotonic Basin Hopping - Perturbation PDF}
+			Pareto Distribution:
+			\begin{equation*}
+				1 +
+				\left[ \frac{s}{\epsilon} \right] \cdot
+				\left[ \frac{\alpha - 1}{\frac{\epsilon}{\epsilon + r}^{-\alpha}} \right]
+			\end{equation*}
+		\end{frame}
+
+\section{Sample Mission Analysis}
+
+	\subsection{Mission Scenario}
+
+		\begin{frame} \frametitle{Mission Scenario}
+			\begin{itemize}
+				\item Spacecraft starting mass: 3500 kg
+				\item Thruster Specific Impulse: 3200 s
+				\item Thruster Maximum Thrusting Force: 250 mN
+				\item Thruster Duty Cycle: 100\%
+				\item Number of Thrusters: 1
+				\item The Launch Window: 2023 and 2024
+				\item The Latest Arrival Date: December 31st, 2044
+				\item Maximum $C_3$ at launch: $100 \frac{\text{km}^2}{\text{s}^2}$
+			\end{itemize}
+		\end{frame}
+
+		\begin{frame} \frametitle{Flybys Analyzed}
+			\begin{itemize}
+				\item EJS
+				\item EMJS
+				\item EMMJS
+				\item EMS
+				\item ES
+				\item EVMJS
+				\item EVMS
+				\item EVVJS
+			\end{itemize}
+		\end{frame}
+
+	\subsection{Trajectory 1}
+
+		\begin{frame} \frametitle{Trajectory 1 - Earth → Mars → Saturn}
+			\begin{figure}
+				\includegraphics<1>[height=0.5\paperheight]{LaTeX/fig/EMS_plot}
+				\includegraphics<2>[height=0.5\paperheight]{LaTeX/fig/EMS_plot_noplanets}
+				\includegraphics<3>[height=0.5\paperheight]{LaTeX/fig/EMS_thrust_mag}
+				\includegraphics<4>[height=0.5\paperheight]{LaTeX/fig/EMS_thrust_components_vnb}
+			\end{figure}
+			\vspace{-1em}
+			\begin{table}\begin{tiny}
+				\begin{tabular}{ | c c c c c c | }
+					\hline
+					\bfseries Flyby Selection &
+					\bfseries Launch Date &
+					\bfseries Mission Length &
+					\bfseries Launch $C_3$ &
+					\bfseries Arrival $V_\infty$ &
+					\bfseries Fuel Usage \\
+					&  & (years) & $\left( \frac{km}{s} \right)^2$ & ($\frac{km}{s}$) & (kg) \\
+					\hline
+					EMS & 2024-06-27 & 7.9844 & 60.41025 & 5.816058 & 446.9227 \\
+					\hline
+				\end{tabular}
+			\end{tiny}\end{table}
+		\end{frame}
+
+	\subsection{Trajectory 2}
+
+		\begin{frame} \frametitle{Trajectory 2 - Earth → Mars → Jupiter → Saturn}
+			\begin{figure}
+				\includegraphics<1>[height=0.5\paperheight]{LaTeX/fig/EMJS_plot}
+				\includegraphics<2>[height=0.5\paperheight]{LaTeX/fig/EMJS_plot_noplanets}
+				\includegraphics<3>[height=0.5\paperheight]{LaTeX/fig/EMJS_thrust_mag}
+				\includegraphics<4>[height=0.5\paperheight]{LaTeX/fig/EMJS_thrust_components_vnb}
+			\end{figure}
+			\vspace{-1em}
+			\begin{table}\begin{tiny}
+				\begin{tabular}{ | c c c c c c | }
+					\hline
+					\bfseries Flyby Selection &
+					\bfseries Launch Date &
+					\bfseries Mission Length &
+					\bfseries Launch $C_3$ &
+					\bfseries Arrival $V_\infty$ &
+					\bfseries Fuel Usage \\
+					&  & (years) & $\left( \frac{km}{s} \right)^2$ & ($\frac{km}{s}$) & (kg) \\
+					\hline
+					EMJS & 2023-11-08 & 14.1072 & 40.43862 & 3.477395 & 530.6683 \\
+					\hline
+				\end{tabular}
+			\end{tiny}\end{table}
+		\end{frame}
+
+	\subsection{Results Analysis}
+
+		\begin{frame} \frametitle{Results Review}
+			\begin{table}\begin{tiny}
+				\begin{tabular}{ | c c c c c c | }
+					\hline
+					\bfseries Flyby Selection &
+					\bfseries Launch Date &
+					\bfseries Mission Length &
+					\bfseries Launch $C_3$ &
+					\bfseries Arrival $V_\infty$ &
+					\bfseries Fuel Usage \\
+					&  & (years) & $\left( \frac{km}{s} \right)^2$ & ($\frac{km}{s}$) & (kg) \\
+					\hline
+					EMS & 2024-06-27 & 7.9844 & 60.41025 & 5.816058 & 446.9227 \\
+					EMJS & 2023-11-08 & 14.1072 & 40.43862 & 3.477395 & 530.6683 \\
+					\hline
+				\end{tabular}
+			\end{tiny}\end{table}
+		\end{frame}
+
+\section{Conclusion}
+
+	\begin{frame} \frametitle{Conclusion}
+		\begin{itemize}
+			\item Validation of direct approach to optimizing interplanetary, low-thrust
+				trajectories as non-linear programming problems
+			\item Validation of Monotonic Basin Hopping algorithm for finding global optima in the
+				same scenario
+			\item Application in a realistic sample mission revealed two effective trajectory
+				possibilities
+		\end{itemize}
+	\end{frame}
+
+	\begin{frame} \frametitle{Future Work}
+		\begin{itemize}
+			\item Outer loop which chooses optimal flyby trajectories for increased automation
+			\item Parallelization would be effective for this problem
+			\item Better quantification of search space ``coverage'' by the monotonic basin hopping
+				algorithm
+		\end{itemize}
+	\end{frame}
+
+	\begin{frame}
+		\begin{center}
+		\begin{Huge}
+			Thank You!
+		\end{Huge}
+		\end{center}
+	\end{frame}
+
+	\bibliographystyle{plain}
+	\bibliography{LaTeX/presentation}
+
+\end{document}

LaTeX/results.tex

@@ -1,56 +1,29 @@
-\chapter{Results Analysis} \label{results}
+\chapter{Application: Designing a Trajectory To Saturn} \label{results}
 
-	The algorithm described in this thesis is quite flexible in its design and could be used as
-	a tool for a mission designer on a variety of different mission types. However, to consider
-	a relatively simple but representative mission design objective, a sample mission to Saturn
-	was investigated.
+	To consider a relatively simple but representative mission design objective, a sample mission to
+	Saturn was investigated.
 
-	Ultimately, two optimized trajectories were selected. The results of those trajectories can
-	be found in Table~\ref{results_table} below:
+	\section{Mission Scenario}
 
-	\begin{table}[h!]
-	\begin{small}
-	\centering
-	\begin{tabular}{ | c c c c c c | }
-		\hline
-		\bfseries Flyby Selection &
-		\bfseries Launch Date &
-		\bfseries Mission Length &
-		\bfseries Launch $C_3$ &
-		\bfseries Arrival $V_\infty$ &
-		\bfseries Fuel Usage \\
-		&  & (years) & $\left( \frac{km}{s} \right)^2$ & ($\frac{km}{s}$) & (kg) \\
-		\hline
-		EMS & 2024-06-27 & 7.9844 & 60.41025 & 5.816058 & 446.9227 \\
-		EMJS & 2023-11-08 & 14.1072 & 40.43862 & 3.477395 & 530.6683 \\
-		\hline
-	\end{tabular}
-	\end{small}
-	\caption{Comparison of the two most optimal trajectories}
-	\label{results_table}
-	\end{table}
-
-	\section{Mission Constraints}
-
-		The sample mission was defined to represent a general case for a near-future low-thrust
-		trajectory to Saturn. No constraints were placed on the flyby planets, but a number of
+		The sample mission is defined to represent a general case for a near-future low-thrust
+		trajectory to Saturn. No constraints are placed on the flyby planets, but a number of
 		constraints were placed on the algorithm to represent a realistic mission scenario. 
 
 		The first choice required by the application is one not necessarily designable to the
-		initial mission designer (though not necessarily fixed in the design either) and is that
-		of the spacecraft parameters. The application accepts as input a spacecraft object
-		containing: the dry mass of the craft, the fuel mass at launch, the number of onboard
-		thrusters, and the specific impulse, maximum thrust and duty cycle of each thruster.
+		initial mission designer (though not necessarily fixed in the design either) and is that of
+		the spacecraft parameters. The application accepts as input a spacecraft object containing:
+		the dry mass of the spacecraft, the fuel mass at launch, the number of onboard thrusters,
+		and the specific impulse, maximum thrust and duty cycle of each thruster.
 
-		For this mission, the spacecraft was chosen to have a dry mass of only 200 kilograms for
-		a fuel mass of 3300 kilograms. This was chosen in order to have an overall mass roughly
-		in the same zone as that of the Cassini spacecraft, which launched with 5712 kilograms
-		of total mass, with the fuel accounting for 2978 of those kilograms\cite{cassini}. The
-		dry mass of the craft was chosen to be extremely low in order to allow for a variety of
-		''successful`` missions in which the craft didn't run out of fuel. That way, the
-		delivered dry mass to Saturn could be thought of as a metric of success, without
-		discounting mission that may have delivered just under whatever more realistic dry mass
-		one might set, in case those missions are in the vicinity of actually valid missions.
+		For this mission, the spacecraft was chosen to have a dry mass of only 200 kilograms for a
+		fuel mass of 3300 kilograms. This was chosen in order to have an overall mass roughly in the
+		same zone as that of the Cassini spacecraft, which launched with 5712 kilograms of total
+		mass, with the fuel accounting for 2978 of those kilograms\cite{cassini}. The dry mass of
+		the spacecraft was chosen to be extremely low in order to allow for a variety of
+		``successful'' missions in which the spacecraft didn't run out of fuel. That way, the
+		delivered dry mass to Saturn could be thought of as a metric of success, without discounting
+		mission that may have delivered just under whatever more realistic dry mass one might set,
+		in case those missions are in the vicinity of actually valid missions.
 
 		The thruster was chosen to have a specific impulse of 3200 seconds, a maximum thrust of
 		250 millinewtons, and a 100\% duty cycle. This puts the thruster roughly in line with
@@ -91,7 +64,17 @@
 			used by the mass at launch and the $C_3$ number is determined by dividing the $C_3$
 			at launch by the maximum allowed. These two numbers are then weighted, with the fuel
 			usage value getting a weight of three and the launch energy value getting a weight
-			of one. The values are summed and returned as the cost value.
+			of one. The values are summed and returned as the cost value, represented as the value
+			$J$ below:
+
+			\begin{equation}
+				J(\vec{x}, m_{dry}, C_{3,max}) = 3 \left| \frac{h(\vec{x})}{m_{dry}} \right| +
+				\left| \frac{k(\vec{x})}{C_{3,max}} \right|
+			\end{equation}
+
+			\noindent
+			Where $h(\vec{x})$ represents the total fuel mass used during the trajectory and
+			$k(\vec{x})$ represents the launch $C_3$ of the initial phase.
 
 		\subsection{Flybys Analyzed}
 
@@ -102,9 +85,12 @@
 			the mission.
 
 			For this particular mission scenario, the following flyby profiles were
-			investigated:
+			investigated (E: Earth, M: Mars, V: Venus, J: Jupiter, S: Saturn). These flyby choices
+			were initially sampled randomly, but as patterns were noticed during the previous runs,
+			certain trajectories were chosen to investigate phases that seemed promising.
 
 			\begin{itemize}
+				\setlength\itemsep{-0.5em}
 				\item EJS
 				\item EMJS
 				\item EMMJS
@@ -115,6 +101,77 @@
 				\item EVVJS
 			\end{itemize}
 
+			For each of these trajectories, the optimization algorithm was run. During the MBH phase
+			of the optimization algorithm, anytime a new ``basin best'' mission was discovered, it
+			was recorded. The resultant cost function values of each of those discovered missions
+			can be found in the table below:
+
+			\begin{longtable}{
+					|
+					>{\centering}p{0.75in}
+					>{\centering}p{1.25in}
+					>{\centering}p{1.1in}
+					>{\centering}p{1in}
+					>{\centering}p{0.8in}
+					>{\centering\arraybackslash}p{0.8in}
+					|
+				}
+				\hline
+				\bfseries Flyby Selection &
+				\bfseries Cost Function Value &
+				\bfseries Mass Delivered (kg) &
+				\bfseries Time of Flight (years) &
+				\bfseries Launch $C_3$ ($\frac{\text{km}^2}{\text{s}^2}$) &
+				\bfseries Arrival $V_\infty$ Norm \\
+				\hline
+				\endhead
+				ES & 0.555 & 3423.49 & 5.945 & 97.89 & 0.009 \\
+				ES & 0.5551 & 3422.41 & 5.945 & 97.73 & 0.0 \\
+				ES & 0.5553 & 3425.31 & 5.897 & 98.26 & 0.0 \\
+				ES & 0.561 & 3403.47 & 5.945 & 95.65 & 0.0 \\
+				ES & 0.5612 & 3406.47 & 5.894 & 96.22 & 0.002 \\
+				EMS & 0.648 & 3130.77 & 8.451 & 66.3 & 6.391 \\
+				EMJS & 0.6601 & 2962.65 & 14.107 & 39.91 & 3.636 \\
+				EMS & 0.6883 & 3004.49 & 9.229 & 52.71 & 4.245 \\
+				EMS & 0.697 & 3037.04 & 7.984 & 60.04 & 6.021 \\
+				EMJS & 0.7458 & 2837.9 & 14.036 & 35.65 & 4.816 \\
+				EMJS & 0.7975 & 1905.95 & 12.99 & 16.92 & 2.686 \\
+				EMJS & 0.8037 & 2652.62 & 13.793 & 15.48 & 3.209 \\
+				EMJS & 0.8251 & 2760.39 & 13.857 & 38.23 & 3.818 \\
+				EMMJS & 0.9115 & 2528.08 & 15.853 & 15.68 & 3.189 \\
+				EMJS & 0.9415 & 2484.97 & 16.33 & 14.29 & 2.021 \\
+				EMJS & 0.9614 & 2511.65 & 15.756 & 22.85 & 3.393 \\
+				EMS & 1.0297 & 1655.14 & 10.412 & 3.18 & 4.529 \\
+				EJS & 1.1285 & 1734.51 & 15.725 & 41.98 & 2.595 \\
+				ES & 1.2317 & 1639.1 & 9.248 & 39.72 & 5.785 \\
+				EVMS & 1.326 & 2241.72 & 8.87 & 49.49 & 4.977 \\
+				EMS & 1.3288 & 1400.47 & 7.843 & 1.87 & 5.634 \\
+				EMS & 1.3378 & 2705.69 & 15.848 & 131.39 & 5.151 \\
+				EMJS & 1.3953 & 1904.96 & 13.813 & 5.62 & 5.146 \\
+				EVMS & 1.4152 & 1963.98 & 11.315 & 19.72 & 9.117 \\
+				EVMS & 1.4596 & 1963.09 & 11.885 & 28.45 & 6.7 \\
+				EVMS & 1.4665 & 1915.47 & 11.691 & 21.67 & 8.919 \\
+				EVMS & 1.5221 & 1966.29 & 12.002 & 41.49 & 7.085 \\
+				EVMS & 1.5923 & 1811.71 & 7.612 & 29.05 & 8.892 \\
+				EVMJS & 1.6694 & 2324.68 & 14.203 & 132.4 & 5.346 \\
+				EMS & 1.7029 & 1652.8 & 12.064 & 23.93 & 8.898 \\
+				EMJS & 1.7044 & 1687.48 & 17.45 & 30.16 & 6.148 \\
+				EMS & 1.7811 & 1504.33 & 18.067 & 14.1 & 3.195 \\
+				EVVJS & 2.0106 & 1362.61 & 14.71 & 35.72 & 6.315 \\
+				EMJS & 2.1595 & 1026.4 & 17.548 & 7.86 & 7.977 \\
+				EJS & 2.1622 & 1543.52 & 12.96 & 97.03 & 9.42 \\
+				EMJS & 2.2217 & 2055.3 & 21.583 & 196.67 & 2.074 \\
+				EMMJS & 2.3843 & 730.68 & 14.754 & 2.12 & 6.915 \\
+				EMJS & 2.4246 & 1470.46 & 24.186 & 136.99 & 1.749 \\
+				EMMJS & 2.4645 & 971.97 & 16.935 & 59.53 & 7.34 \\
+				EVVJS & 2.4926 & 908.6 & 15.287 & 54.28 & 3.942 \\
+				EMJS & 2.4948 & 872.56 & 12.943 & 48.55 & 8.548 \\
+				EVMS & 2.7112 & 726.4 & 12.263 & 66.76 & 9.478 \\
+				EMJS & 2.7681 & 496.32 & 16.0 & 38.71 & 10.348 \\
+				\hline
+				\caption{Table of resultant cost function values for every discovered mission}\label{cost_fn_table}\\
+			\end{longtable}
+
 	\section{Faster, Less Efficient Trajectory}
 
 		In order to showcase the flexibility of the optimization algorithm (and the chosen cost
@@ -128,21 +185,24 @@
 		contrast to the usual dichotomy of low-thrust travel. The cost function used for this
 		analysis did not include the time of flight as a component of the overall cost, and yet
 		this trajectory still managed to be the lowest cost trajectory of all trajectories found
-		by the algorithm.
+		by the algorithm, meaning that it has merit for both a flyby mission as well as a capture
+		mission.
 
-		The mission begins in late June of 2024 and proceeds first to an initial gravity assist
-		with Mars after three and one half years to rendezvous in mid-December 2027.
-		Unfortunately, the launch energy required to effectively used the gravity assist with
-		Mars at this time is quite high. The $C_3$ value was found to be $60.4102$ kilometers
-		per second squared. However, for this phase, the thrust magnitudes are quite low,
-		raising slowly only as the spacecraft approaches Mars, allowing for a nearly-natural
-		trajectory to Mars rendezvous. Note also that the in-plane thrust direction was neither
-		zero nor $\pi$, implying that these thrusts were steering thrusts rather than
-		momentum-increasing thrusts.
+		The mission begins in late June of 2024 and proceeds first to an initial gravity assist with
+		Mars after three and one half years to rendezvous in mid-December 2027. Unfortunately, the
+		launch energy required to effectively use the gravity assist with Mars at this time is
+		quite high. The $C_3$ value was found to be $60.4102 \frac{\text{km}^2}{\text{s}^2}$. While
+		not as low as some of the other missions found to be very optimal, it should be noted that
+		missions with this $C_3$ and launch mass are still quite feasible.
+
+		However, for this phase, the thrust magnitudes are quite low, raising slowly only as the
+		spacecraft approaches Mars, allowing for a nearly-natural trajectory to Mars rendezvous.
+		Note also that the in-plane thrust angle was neither zero nor $\pi$, implying that these
+		thrusts were steering thrusts rather than momentum-increasing thrusts.
 
 		\begin{figure}[H]
 			\centering
-			\includegraphics[width=0.9\textwidth]{fig/EMS_plot}
+			\includegraphics[width=0.9\textwidth]{LaTeX/fig/EMS_plot}
 			\caption{Depictions of the faster Earth-Mars-Saturn trajectory found by the
 			algorithm to be most efficient; planetary ephemeris arcs are shown during the phase
 			in which the spacecraft approached them}
@@ -151,39 +211,39 @@
 
 		\begin{figure}[H]
 			\centering
-			\includegraphics[width=0.9\textwidth]{fig/EMS_plot_noplanets}
+			\includegraphics[width=0.9\textwidth]{LaTeX/fig/EMS_plot_noplanets}
 			\caption{Another depiction of the EMS trajectory, without the planetary ephemeris
 			arcs}
 			\label{ems_nop}
 		\end{figure}
 
 		The second and final leg of this trip exits the Mars flyby and, initially burns quite
-		heavily along the velocity vector in order to increase it's semi-major axis. After an
-		initial period of thrusting, though, the spacecraft effectively coasts with minor
-		adjustments until its rendezvous with Saturn just four and a half years later in June of
-		2032. The arrival $v_\infty$ is not particularly small, at $5.816058$ kilometers per
-		second, but this is to be expected as the arrival excess velocity was not considered as
-		a part of the cost function. If capture was not the final intention of the mission, this
-		may be of little concern. Otherwise, the low fuel usage of $446.92$ kilograms for a
-		$3500$ kilogram launch mass leaves much margin for a large impulsive thrust to enter
-		into a capture orbit at Saturn.
+		heavily along the velocity vector in order to increase its semi-major axis. After an initial
+		period of thrusting, though, the spacecraft effectively coasts with minor adjustments until
+		its rendezvous with Saturn just four and a half years later in June of 2032. The arrival
+		$v_\infty$ is not particularly small, at $5.816058 \frac{\text{km}}{\text{s}}$, but this is
+		to be expected as the arrival excess velocity was not considered as a part of the cost
+		function. If capture was not the final intention of the mission, this may be of little
+		concern. Otherwise, the low fuel usage of $446.92$ kilograms for a $3500$ kilogram launch
+		mass leaves much margin for a large impulsive thrust to enter into a capture orbit at
+		Saturn.
 
 		\begin{figure}[H]
 			\centering
-			\includegraphics[width=0.9\textwidth]{fig/EMS_thrust_mag}
+			\includegraphics[width=0.9\textwidth]{LaTeX/fig/EMS_thrust_mag}
 			\caption{The magnitude of the unit thrust vector over time for the EMS trajectory}
 			\label{ems_mag}
 		\end{figure}
 
 		\begin{figure}[H]
 			\centering
-			\includegraphics[width=0.9\textwidth]{fig/EMS_thrust_components}
+			\includegraphics[width=0.9\textwidth]{LaTeX/fig/EMS_thrust_components}
 			\caption{The inertial x, y, and z components of the unit thrust vector over time for
 			the EMS trajectory}
 			\label{ems_components}
 		\end{figure}
 
-		In this case the algorithm effectively realized that a higher-powered launch from
+		In this case the algorithm effectively discovered that a higher-powered launch from
 		the Earth, then a natural coasting arc to Mars flyby would provide the spacecraft with
 		enough velocity that a short but efficient powered-arc to Saturn was possible with
 		effective thrusting. It also determined that the most effective way to achieve this
@@ -202,12 +262,11 @@
 
 	\section{Slower, More Efficient Trajectory}
 
-		Next we'll analyze the nominally second-best trajectory. While the cost function
-		provided to the algorithm can be a useful tool for narrowing down the field of search
-		results, it can also be very useful to explore options that may or may not be of similar
-		"efficiency" in terms of the cost function, but beneficial for other reasons. By
-		outputting many different optimal trajectories, the MBH algorithm can allow for this
-		type of mission design flexibility.
+		Next we'll analyze the nominally second-best trajectory. While the cost function provided to
+		the algorithm can be a useful tool for narrowing down the field of search results, it can
+		also be very useful to explore options that may or may not have quite as small of a cost
+		function value, but beneficial for other reasons. By outputting many different optimal
+		trajectories, the MBH algorithm can allow for this type of mission design flexibility.
 
 		To highlight the flexibility, a second trajectory has been selected, which has nearly
 		equal value by the cost function, coming in slightly lower. However, this trajectory
@@ -227,7 +286,7 @@
 
 		\begin{figure}[H]
 			\centering
-			\includegraphics[width=0.9\textwidth]{fig/EMJS_plot}
+			\includegraphics[width=0.9\textwidth]{LaTeX/fig/EMJS_plot}
 			\caption{Depictions of the slower Earth-Mars-Jupiter-Saturn trajectory found by the
 			algorithm to be the second most efficient; planetary ephemeris arcs are shown during
 			the phase in which the spacecraft approached them}
@@ -236,7 +295,7 @@
 
 		\begin{figure}[H]
 			\centering
-			\includegraphics[width=0.9\textwidth]{fig/EMJS_plot_noplanets}
+			\includegraphics[width=0.9\textwidth]{LaTeX/fig/EMJS_plot_noplanets}
 			\caption{Another depiction of the EMJS trajectory, without the planetary ephemeris
 			arcs}
 			\label{emjs_nop}
@@ -251,14 +310,14 @@
 
 		\begin{figure}[H]
 			\centering
-			\includegraphics[width=0.9\textwidth]{fig/EMJS_thrust_mag}
+			\includegraphics[width=0.9\textwidth]{LaTeX/fig/EMJS_thrust_mag}
 			\caption{The magnitude of the unit thrust vector over time for the EMJS trajectory}
 			\label{emjs_mag}
 		\end{figure}
 
 		\begin{figure}[H]
 			\centering
-			\includegraphics[width=0.9\textwidth]{fig/EMJS_thrust_components}
+			\includegraphics[width=0.9\textwidth]{LaTeX/fig/EMJS_thrust_components}
 			\caption{The inertial x, y, and z components of the unit thrust vector over time for
 			the EMJS trajectory}
 			\label{emjs_components}
@@ -276,81 +335,51 @@
 		While the fuel use is also slightly higher at $530.668$ kilograms, plenty of payload
 		mass is still capable of delivery into the vicinity of Saturn. Also, it should be noted
 		that the incoming excess hyperbolic velocity at arrival to Saturn is significantly
-		lower, at only $3.4774$ kilometers per second, meaning that less of the delivered
+		lower, at only $3.4774\frac{\text{km}}{\text{s}}$, meaning that less of the delivered
 		payload mass would need to be taken up by impulsive thrusters and fuel for Saturn orbit
 		capture, should the mission designer desire this.
 
-		Also, as mentioned before, the launch energy requirements are quite a bit lower. Having
-		a second mission trajectory capable of launching on a smaller vehicle could be valuable
-		to a mission designer presenting possibilities. According to an analysis of the Delta IV
-		and Atlas V launch configurations\cite{c3capabilities} in Figure~\ref{c3}, this
+	\section{Final Trajectory Analysis}
+
+		Ultimately, two optimized trajectories were selected to be excellent candidates for further
+		consideration. The resultant flyby selection, launch and arrival dates, and relevant cost
+		function input of those trajectories can be found in Table~\ref{results_table} below:
+
+		\begin{table}[h!]
+		\begin{small}
+		\centering
+		\begin{tabular}{ | c c c c c c | }
+			\hline
+			\bfseries Flyby Selection &
+			\bfseries Launch Date &
+			\bfseries Mission Length &
+			\bfseries Launch $C_3$ &
+			\bfseries Arrival $V_\infty$ &
+			\bfseries Fuel Usage \\
+			&  & (years) & $\left( \frac{km}{s} \right)^2$ & ($\frac{km}{s}$) & (kg) \\
+			\hline
+			EMS & 2024-06-27 & 7.9844 & 60.41025 & 5.816058 & 446.9227 \\
+			EMJS & 2023-11-08 & 14.1072 & 40.43862 & 3.477395 & 530.6683 \\
+			\hline
+		\end{tabular}
+		\end{small}
+		\caption{Comparison of the two most optimal trajectories}
+		\label{results_table}
+		\end{table}
+
+		As mentioned before, the launch energy requirements of the second trajectory are quite a bit
+		lower. Having a second mission trajectory capable of launching on a smaller vehicle could be
+		valuable to a mission designer presenting possibilities. According to an analysis of the
+		Delta IV and Atlas V launch configurations\cite{c3capabilities} in Figure~\ref{c3}, this
 		reduction of $C_3$ from around 60 to around 40 brings the sample mission to just within
-		range of both the Delta IV Heavy and the Atlas V in its largest configuration, neither
-		of which are possible for the other result, meaning that either different launch
-		vehicles must be found or mission specifications must change.
+		range of both the Delta IV Heavy and the Atlas V in its largest configuration, neither of
+		which are possible for the other result, meaning that either different launch vehicles must
+		be found or mission specifications must change.
 
 		\begin{figure}[H]
 			\centering
-			\includegraphics[width=\textwidth]{fig/c3}
+			\includegraphics[width=\textwidth]{LaTeX/fig/c3}
 			\caption{Plot of Delta IV and Atlas V launch vehicle capabilities as they relate to
-			payload mass}
+			payload mass \cite{c3capabilities} from Vardaxis, et al, 2007 }
 			\label{c3}
 		\end{figure}
-
-\chapter{Conclusion} \label{conclusion}
-
-	\section{Overview of Results}
-
-		A mission designer's job is quite a difficult one and it can be very useful to have
-		tools to automate some of the more complex analysis. This paper attempted to explore one
-		such tool, meant for automating the initial analysis and discovery of useful
-		interplanetary, low-thrust trajectories including the difficult task of optimizing the
-		flyby parameters. This makes the mission designer's job significantly simpler in that
-		they can simply explore a number of different flyby selection options in order to get a
-		good understanding of the mission scope and search space for a given spacecraft, launch
-		window, and target.
-
-		In performing this examination, two results were selected for further analysis. These
-		results are outlined in Table~\ref{results_table}. As can be seen in the table, both
-		resulting trajectories have trade-offs in mission length, launch energy, fuel usage, and
-		more. However, both results should be considered very useful low-thrust trajectories in
-		comparison to other missions that have launched on similar interplanetary trajectories,
-		using both impulsive and low-thrust arcs with planetary flybys. Each of these missions
-		should be feasible or nearly feasible (feasible with some modifications) using existing
-		launch vehicle and certainly even larger missions should be reasonable with advances in
-		launch capabilities currently being explored.
-
-	\section{Recommendations for Future Work}\label{improvement_section}
-
-		In the course of producing this algorithm, a large number of improvement possibilities
-		were noted. This work was based, in large part, on the work of Jacob Englander in a
-		number of papers\cite{englander2014tuning}\cite{englander2017automated}
-		\cite{englander2012automated} in which he explored the hybrid optimal control problem of
-		multi-objective low-thrust interplanetary trajectories.
-
-		In light of this, there are a number of additional approaches that Englander took in
-		preparing his algorithm that were not implemented here in favor of reducing complexity
-		and time constraints. For instance, many of the Englander papers explore the concept of
-		an outer loop that utilizes a genetic algorithm to compare many different flyby planet
-		choice against each other. This would create a truly automated approach to low-thrust
-		interplanetary mission planning. However, a requirement of this approach is that the
-		monotonic basin hopping algorithm algorithm must converge on optimal solutions very
-		quickly. Englander typically runs his for 20 minutes each for evolutionary fitness
-		evaluation, which is over an order of magnitude faster than the implementation in this
-		paper to achieve satisfactory results.
-
-		Further improvements to performance stem from the field of computer science. An
-		evolutionary algorithm such as the one proposed by Englander would benefit from high
-		levels of parallelization. Therefore, it would be worth considering a GPU-accelerated or
-		even cluster-computing capable implementation of the monotonic basin hopping algorithm.
-		These cluster computing concepts scale very well with new cloud infrastructures such as
-		that provided by AWS or DigitalOcean.
-
-		Finally, the monotonic basin hopping algorithm as currently written provides no
-		guarantees of actual global optimization. Generally optimization is achieved by running
-		the algorithm until it fails to produce newer, better trajectories for a sufficiently
-		long time. But it would be worth investigating the robustness of the NLP solver as well
-		as the robustness of the MBH algorithm basin drilling procedures in order to quantify
-		the search granularity needed to completely traverse the search space. From this
-		information, a new MBH algorithm could be written that is guaranteed to explore the
-		entire space.

LaTeX/thesis.tex

@@ -1,4 +1,4 @@
-\documentclass[defaultstyle,11pt]{thesis}
+\documentclass[defaultstyle,11pt]{LaTeX/thesis}
 
 \usepackage{graphicx}
 \usepackage{amssymb}
@@ -7,6 +7,9 @@
 \usepackage{amsfonts}
 \usepackage{float}
 \usepackage{xfrac}
+\usepackage{adjustbox}
+\usepackage{longtable}
+\usepackage{array}
 
 \title{Designing Optimal Low-Thrust Interplanetary Trajectories Utilizing Monotonic Basin Hopping}
 \author{Richard C.}{Johnstone}
@@ -20,33 +23,48 @@
 
 \abstract{  \OnePageChapter
 
-	There are a variety of approaches to finding and optimizing low-thrust trajectories in
-	interplanetary space. This thesis analyzes one such approach, namely the application of a
-	Monotonic Basin Hopping (MBH) algorithm to a series of Sims-Flanagan transcribed trajectory arcs
-	and its applications in a multiple-shooting non-linear solver for the purpose of finding valid
-	low-thrust trajectories between planets given poor initial conditions. These valid arcs are then
-	fed into the MBH algorithm, which combines them in order to find and optimize interplanetary
-	trajectories, given a set of flyby planets. This allows for a fairly rapid searching of a very
-	large solution space of low-thrust profiles via a medium fidelity inner-loop solver and a
-	well-suited optimization routine. The trajectories found by this method can then be optimized
-	further by feeding the solutions back, once again, into the non-linear solver, this time
-	allowing the solver to perform optimization.
+	Much work has been performed recently to utilize the increasingly viable technology of
+	low-thrust electric propulsion systems on missions of interplanetary scope. This thesis analyzes
+	a technique for designing trajectories for spacecraft with a low-thrust propulsion system that
+	also use natural gravity flybys for missions to the outer planets. Often, the goal is to find
+	feasible solutions that also minimize propellant mass requirements. First, locally optimal
+	solutions are constructed by using an interior-point linesearch algorithm, along with multiple
+	shooting techniques for optimization. Then, Monotonic Basin Hopping is utilized to traverse the
+	search space, improve the local optima determined by the internal optimizer, and determine the
+	global optima. This approach allows for a medium-fidelity, fully automated global optimization
+	of the low thrust controls and flyby parameters for a given target destination. As an
+	application of this method, two sample trajectories to Saturn are analyzed.
 
 }
 
 \dedication[Dedication]{
-	Dedicated to some people.
+	\begin{center}
+		I'd like to dedicate this work to anyone with an interest in space.
+
+		We're all exploring this together.
+	\end{center}
 }
 
 \acknowledgements{	\OnePageChapter
-	This will be an acknowledgement.
+	I owe just about everything that I am today to the circumstances that I grew up in and in no
+	area of my life is that more apparent than in my loving family. I'd like to thank them for
+	providing me with the emotional support I needed to grow confident in my own abilities and the
+	logistical support I needed to nurture my curiosities.
+
+	I'd also like to thank my girlfriend, Rachael, for supporting me through this process. This has
+	not been an easy time for me, and I owe a lot to your support this past year.
+
+	Finally, I'd like to give a huge thanks to Dr. Bosanac, who provided me with the structure I
+	needed to stay on track, the motivation I needed to really get the most out of this paper, and
+	the guidance I needed to finish this up. It's no exxageration to say that this thesis wouldn't be
+	written to anywhere near the level of quality it was without you.
 }
 
 \emptyLoT
 
 \begin{document}
 
-	\input macros.tex
+	\input LaTeX/macros.tex
 
 	\input LaTeX/introduction.tex
 
@@ -58,10 +76,10 @@
 
 	\input LaTeX/results.tex
 
+	\input LaTeX/conclusion.tex
+
 	\bibliographystyle{plain}
 	\nocite{*}
-	\bibliography{thesis}
-
-	\appendix
+	\bibliography{LaTeX/thesis}
 
 \end{document}

LaTeX/trajectory_design.tex

@@ -16,56 +16,49 @@
 			very high-fidelity force models that account for aerodynamic pressure, solar radiation
 			pressure, multi-body effects, and other forces may be too time intensive for a
 			particular application. Initial surveys of the solution space often don't require such
-			complex models in order to gain valuable insight.
+			complex models in order to gain valuable preliminary insight.
 
-			Therefore, a common approach (and the one utilized in this implementation) is to first
-			use a lower-fidelity dynamical model that captures only the gravitational force due to
-			the primary body around which the spacecraft is orbiting. This approach can provide an
+			A common approach (and the one utilized in this implementation) is to first use a
+			lower-fidelity dynamical model that captures only the gravitational force due to the
+			primary body around which the spacecraft is orbiting. This approach can provide an
 			excellent low-to-medium fidelity model that is useful as an underlying model in an
 			algorithm for quickly categorizing a search space for initial mission feasibility
 			explorations.
 
 			In order to explore the Two Body Problem, we must first examine the full set of
 			assumptions associated with the force model\cite{vallado2001fundamentals}. Firstly, we
-			are only concerned with the nominative two bodies: the spacecraft and the planetary body
-			around which it is orbiting. Secondly, both of these bodies are modeled as point masses
-			with constant mass. This removes the need to account for non-uniform densities and
-			asymmetry. Finally, for convenience in notation at the end, we'll also assume that the
-			mass of the spacecraft ($m_2$) is much much smaller than the mass of the planetary body
-			($m_1$) and enough so as to be considered negligible. The only force acting on this
-			system is then the force of gravity that the primary body enacts upon the secondary.
-
+			are only concerned with the gravitational influence between the nominative two bodies:
+			the spacecraft and the planetary body around which it is orbiting. Secondly, both of
+			these bodies are modeled as point masses with constant mass. This removes the need to
+			account for non-uniform densities and asymmetry. Finally, for convenience in notation at
+			the end, we'll also assume that the mass of the spacecraft ($m_2$) is much much smaller
+			than the mass of the planetary body ($m_1$) and enough so as to be considered
+			negligible.
 			\begin{figure}[H]
 				\centering
-				\includegraphics[width=0.65\textwidth]{fig/2bp}
+				\includegraphics[width=0.65\textwidth]{LaTeX/fig/2bp}
 				\caption{Figure representing the positions of the bodies relative to each other and
 				the center of mass in the two body problem}
 				\label{2bp_fig}
 			\end{figure}
-
 			Under these assumptions, the force acting on the body due to the law of universal
 			gravitation is:
-
 			\begin{align}
 				F_2 &= - \frac{G m_1 m_2}{r^2} \frac{\vec{r}}{\left| r \right|} \\
 				F_1 &= \frac{G m_2 m_1}{r^2} \frac{\vec{r}}{\left| r \right|}
 			\end{align}
-
 			And by Newton's second law (force is the product of mass and acceleration), we can
 			derive the following differential equations for $r_1$ and $r_2$:
-
 			\begin{align}
 				m_2 \ddot{\vec{r}}_2 &= - \frac{G m_1 m_2}{r^2} \frac{\vec{r}}{\left| r \right|} \\
 				m_1 \ddot{\vec{r}}_1 &= \frac{G m_2 m_1}{r^2} \frac{\vec{r}}{\left| r \right|}
 			\end{align}
-
 			Where $\vec{r}$ is the position of the spacecraft relative to the primary body,
 			$\vec{r}_1$ is the position of the primary body relative to the origin of the inertial
 			frame, and $\vec{r}_2$ is the position of the spacecraft relative to the center of the
 			inertial frame. $G$ is the universal gravitational parameter, $m_1$ is the mass of the
 			planetary body, and $m_2$ is the mass of the spacecraft. From these equations, we can
 			then determine the acceleration of the spacecraft relative to the planet:
-
 			\begin{equation}
 				\ddot{\vec{r}} = \ddot{\vec{r}}_2 - \ddot{\vec{r}}_1 =
 				- \frac{G \left( m_1 + m_2 \right)}{r^2} \frac{\vec{r}}{\left| r \right|}
@@ -76,66 +69,19 @@
 			negligible $m_2$ term. We can also introduce, for convenience, a gravitational parameter
 			$\mu$ which represents the gravity constant for the system about the center of motion
 			($\mu = G (m_1 + m_2) \approx G m_1$). Doing so and simplifying produces:
-
 			\begin{equation}
 				\ddot{\vec{r}} = - \frac{\mu}{r^2} \hat{r}
 			\end{equation}
 
-			We may also wish to utilize the total orbital energy for a spacecraft within this model.
-			Since the spacecraft is acting only under the gravitational influence of the planet and
-			no other forces, we can define the total specific mechanical energy as:
-
-
-			We may also wish to utilize the total orbital energy for a spacecraft within this model.
-			Since the spacecraft is acting only under the gravitational influence of the planet and
-			no other forces, we can define the total specific mechanical energy as:
-
-
-			We may also wish to utilize the total orbital energy for a spacecraft within this model.
-			Since the spacecraft is acting only under the gravitational influence of the planet and
-			no other forces, we can define the total specific mechanical energy as:
-
-
-			We may also wish to utilize the total orbital energy for a spacecraft within this model.
-			Since the spacecraft is acting only under the gravitational influence of the planet and
-			no other forces, we can define the total specific mechanical energy as:
-
-
-			We may also wish to utilize the total orbital energy for a spacecraft within this model.
-			Since the spacecraft is acting only under the gravitational influence of the planet and
-			no other forces, we can define the total specific mechanical energy as:
-
-
-			We may also wish to utilize the total orbital energy for a spacecraft within this model.
-			Since the spacecraft is acting only under the gravitational influence of the planet and
-			no other forces, we can define the total specific mechanical energy as:
-
-
-			We may also wish to utilize the total orbital energy for a spacecraft within this model.
-			Since the spacecraft is acting only under the gravitational influence of the planet and
-			no other forces, we can define the total specific mechanical energy as:
-
-
-			We may also wish to utilize the total orbital energy for a spacecraft within this model.
-			Since the spacecraft is acting only under the gravitational influence of the planet and
-			no other forces, we can define the total specific mechanical energy as:
-
-
-			We may also wish to utilize the total orbital energy for a spacecraft within this model.
 			Since the spacecraft is acting only under the gravitational influence of the planet and
 			no other forces, we can define the total specific mechanical energy as
 			\cite{vallado2001fundamentals}:
-
 			\begin{equation} \label{energy}
 				\xi = \frac{v^2}{2} - \frac{\mu}{r}
 			\end{equation}
-
-			\noindent
 			Where the first term represents the kinetic energy of the spacecraft and the second term
 			represents the gravitational potential energy.
 
-		\subsection{Kepler's Laws}
-
 			Now that we've fully qualified the forces acting within the Two Body Problem, we can concern
 			ourselves with more practical applications of it as a force model. It should be noted,
 			firstly, that the spacecraft's position and velocity (given an initial position and velocity
@@ -144,6 +90,8 @@
 			one-dimensional equations (one for each component of the three-dimensional space) and
 			three unknowns (the three components of the second derivative of the position).
 
+		\subsection{Kepler's Laws}
+
 			In the early 1600s, Johannes Kepler produced just such a solution, by taking advantages of
 			what is also known as ``Kepler's Laws'' which are\cite{murray1999solar}:
 
@@ -152,68 +100,61 @@
 					expanded to any orbit by re-wording as ``all orbital paths follow a conic section
 					(circle, ellipse, parabola, or hyperbola) with a primary mass at one of the foci''.
 
-					Specifically the path of the orbit follows the trajectory equation:
-
+					The conic trajectory equation explains this observation and offers a description
+					of the path as:
 					\begin{equation}
 						r = \frac{\sfrac{h^2}{\mu}}{1 + e \cos(\theta)}
 					\end{equation}
-
-					Where $h$ is the angular momentum of the satellite, $e$ is the
+					where $h$ is the angular momentum of the satellite, $e$ is the
 					eccentricity of the orbit, and $\theta$ is the true anomaly, or simply
-					the angular distance the satellite has traversed along the orbit path.
+					the angular distance the satellite has traversed along the orbit path from
+					periapsis.
 
 				\item The area swept out by the imaginary line connecting the primary and secondary
 					bodies increases linearly with respect to time. This implies that the magnitude of the
 					orbital speed is not constant. For the moment, we'll just take this
 					value to be a constant:
-
 					\begin{equation}\label{swept}
 						\frac{\Delta t}{T} = \frac{k}{\pi a b}
 					\end{equation}
-
-					Where $k$ is the constant value, $a$ and $b$ are the semi-major and
+					where $k$ is the constant value, $a$ and $b$ are the semi-major and
 					semi-minor axis of the conic section, and $T$ is the period. In the
 					following section, we'll derive the value for $k$.
 
 				\item The square of the orbital period is proportional to the cube of the semi-major
-					axis of the orbit, regardless of eccentricity. Specifically, the relationship is:
-
+					axis of the orbit, regardless of eccentricity. For an elliptical orbit this
+					observation connects to the following known expression for the orbit period:
 					\begin{equation}
 						T = 2 \pi \sqrt{\frac{a^3}{\mu}}
 					\end{equation}
-
-					Where $T$ is the period and $a$ is the semi-major axis.
+					where $T$ is the period and $a$ is the semi-major axis.
 			\end{enumerate}
 
 		\subsection{Kepler's Equation}
 
 			Kepler was able to produce an equation to represent the angular displacement of an
 			orbiting body around a primary body as a function of time, which we'll derive now for
-			the elliptical case\cite{vallado2001fundamentals}. Since the total area of an ellipse is
-			the product of $\pi$, the semi-major axis, and the semi-minor axis ($\pi a b$), we can
-			relate (by Kepler's second law) the area swept out by an orbit as a function of time, as
-			we did in Equation~\ref{swept}. This leaves just one unknown variable $k$, which we can
-			determine through use of the geometric auxiliary circle, which is a circle with radius
-			equal to the ellipse's semi-major axis and center directly between the two foci, as in
-			Figure~\ref{aux_circ}.
+			the elliptical case\cite{vallado2001fundamentals}. Because the total area of an ellipse
+			is the product of $\pi$, the semi-major axis, and the semi-minor axis ($\pi a b$), we
+			can relate (by Kepler's second law) the area swept out by an orbit as a function of
+			time, as we did in Equation~\ref{swept}. This leaves just one unknown variable $k$,
+			which we can determine through use of the geometric auxiliary circle, which is a circle
+			with radius equal to the ellipse's semi-major axis and center directly between the two
+			foci, as in Figure~\ref{aux_circ}.
 
 			\begin{figure}[H]
 				\centering
-				\includegraphics[width=0.8\textwidth]{fig/kepler}
-				\caption{Geometric Representation of Auxiliary Circle}\label{aux_circ}
+				\includegraphics[width=0.8\textwidth]{LaTeX/fig/kepler}
+				\caption{Geometric representation of auxiliary circle}\label{aux_circ}
 			\end{figure}
 
 			In order to find the area swept by the spacecraft\cite{vallado2001fundamentals}, $k$, we
 			can take advantage of the fact that that area is the triangle $k_1$ subtracted from the
 			elliptical segment $PCB$:
-
 			\begin{equation}\label{areas_eq}
 				k = area(seg_{PCB}) - area(k_1)
 			\end{equation}
-
-			\noindent
 			Where the area of the triangle $k_1$ can be found easily using geometric formulae:
-
 			\begin{align}
 				area(k_1) &= \frac{1}{2} \left( ae - a \cos E \right) \left( \frac{b}{a} a \sin E \right) \\
 									&= \frac{ab}{2} \left(e \sin E - \cos E \sin E \right)
@@ -225,7 +166,6 @@
 			can find the area for the elliptical segment $PCB$ by first finding the circular segment
 			$POB'$, subtracting the triangle $COB'$, then applying the fact that an ellipse is
 			merely a vertical scaling of a circle by the amount $\frac{b}{a}$.
-
 			\begin{align}
 				area(PCB) &= \frac{b}{a} \left( area(POB') - area(COB') \right) \\
 				&= \frac{b}{a} \left( \frac{a^2 E}{2} - \frac{1}{2} \left( a \cos E \right)
@@ -233,29 +173,22 @@
 				&= \frac{abE}{2} - \frac{ab}{2} \left( \cos E \sin E \right) \\
 				&= \frac{ab}{2} \left( E - \cos E \sin E \right)
 			\end{align}
-
 			By substituting the two areas back into Equation~\ref{areas_eq} we can get the $k$ area
 			swept out by the spacecraft:
-
 			\begin{equation}
 				k = \frac{ab}{2} \left( E - e \sin E \right)
 			\end{equation}
-
 			Which we can then substitute back into the equation for the swept area as a function of
 			time (Equation~\ref{swept}) for period of time since the spacecraft left periapsis:
-
 			\begin{equation}
 				\frac{\Delta t}{T} = \frac{t_2 - t_{peri}}{T} = \frac{E - e \sin E}{2 \pi}
 			\end{equation}
-
 			Which is, effectively, Kepler's equation. It is commonly known by a different form:
-
 			\begin{equation}
 				M = \sqrt{\frac{\mu}{a^3}} \Delta t = E - e \sin E
 			\end{equation}
-
-			Where we've defined the mean anomaly as $M$ and used the fact that $T =
-			\sqrt{\frac{a^3}{\mu}}$. This provides us a useful relationship between Eccentric Anomaly
+			where we've defined the mean anomaly as $M$ and used the fact that $T =
+			\sqrt{\frac{a^3}{\mu}}$. This provides us a useful relationship between eccentric anomaly
 			($E$) which can be related to spacecraft position, and time, but we still need a useful
 			algorithm for solving this equation in order to use this equation to propagate a
 			spacecraft.
@@ -263,77 +196,57 @@
 	\subsection{LaGuerre-Conway Algorithm}\label{laguerre}
 
 		For this thesis, the algorithm used to solve Kepler's equation was the general numeric
-		root-finding scheme first developed by LaGuerre in the 1800s and first applied to
-		Kepler's equation by Bruce Conway in 1985\cite{laguerre_conway}. In his paper, Conway
-		makes a compelling argument for utilizing the less common LaGuerre method over higher
-		order Newton or Newton-Raphson methods.
-
-		The Newton-Raphson methods, while found to generally have quite impressive convergence
-		rates (generally successfully solving Kepler's equation correctly within 5 iterations),
-		were prone to failures in convergence given certain specific initial conditions.
-		Therefore LaGuerre's algorithm is proposed as an alternative.
-
-		The algorithm can be relatively easily derived by examining the polynomial equation with
-		$m$ roots:
+		root-finding scheme first developed by LaGuerre in the 1800s and first applied to Kepler's
+		equation by Bruce Conway in 1985\cite{laguerre_conway}. In his paper, Conway makes a
+		compelling argument for utilizing the less common LaGuerre method over higher order Newton
+		or Newton-Raphson methods. The Newton-Raphson methods, while found to generally have quite
+		impressive convergence rates (generally successfully solving Kepler's equation correctly
+		within 5 iterations), were prone to failures in convergence given certain specific initial
+		conditions. Therefore LaGuerre's algorithm is proposed as an alternative.
 
+		The algorithm can be derived by examining the polynomial equation with $m$ roots:
 		\begin{equation}
 			g(x) = (x - x_1) (x - x_2) ... ( x - x_m)
 		\end{equation}
-
-		\noindent
 		We can then generate some useful convenience functions as:
-
 		\begin{align}
 			\ln|g(x)| &= \ln|(x - x_1)| + \ln|(x - x_2)| + ... + \ln|( x - x_m)| \\
 			\frac{d\ln|g(x)|}{dx} &= \frac{1}{x - x_1} + \frac{1}{x - x_2} + ... + \frac{1}{x -
 			x_m} = G_1(x)
 		\end{align}
-
 		and
-
 		\begin{align}
 			\frac{-d^2\ln|g(x)|}{dx^2} &= \frac{1}{(x - x_1)^2} + \frac{1}{(x - x_2)^2} + ... +
 			\frac{1}{(x - x_m)^2} = G_2(x)
 		\end{align}
-
 		Now we define the targeted root as $x_1$ and make the approximation that all of the
 		other roots are equidistant from the targeted root, which means:
-
 		\begin{equation}
 			x - x_i = b, i=2,3,...,m
 		\end{equation}
-
-		\noindent
 		We can then rewrite $G_1$ and $G_2$ as:
-
 		\begin{align}
 			G_1 &= \frac{1}{a} + \frac{n-1}{b} \\
 			G_2 &= \frac{1}{a^2} + \frac{n-1}{b^2}
 		\end{align}
-
-		\noindent
 		Which may be solved for $a$ in terms of $G_1$, $G_2$:
-
 		\begin{equation}
 			a = \frac{n}{G_1 \pm \sqrt{(n-1)(nG_2 - G_1^2)}}
 		\end{equation}
-
-		\noindent
 		With corresponding iteration function:
-
 		\begin{equation}
 			x_{i+1} = x_i - \frac{n g(x_i)}{g'(x_i) \pm \sqrt{(n-1)^2 f'(x_i)^2 - n (n-1) f(x_i)
 			f''(x_i)}}
 		\end{equation}
 
 		This iteration scheme can be shown to be globally convergent, regardless of the initial
-		guess. More relevantly, Conway also showed that the application of this method to
-		Kepler's equation was shown to converge with similar speed to many of the best common
-		higher order Newton-Raphson solvers. However, LaGuerre's method was also found to be
-		incredibly robust, converging to the correct value for every one of Conway's 500,000
-		tests. Because of this robustness, it is very useful for propagating spacecraft states.
+		guess. Conway also showed that the application of this method to Kepler's equation was shown
+		to converge with similar speed to many of the best common higher order Newton-Raphson
+		solvers. However, LaGuerre's method was also found to be incredibly robust, converging to
+		the correct value for every one of Conway's 500,000 tests. Because of this robustness, it is
+		useful for solving Kepler's equation.
 
-	\section{Interplanetary Considerations}\label{interplanetary}
+	\section{Interplanetary Trajectories}\label{interplanetary}
 
 		In interplanetary travel, the primary body most responsible for gravitational forces might
 		be a number of different bodies, dependent on the phase of the mission. In fact, at some
@@ -378,21 +291,22 @@
 
 			\begin{figure}[H]
 				\centering
-				\includegraphics[width=0.8\textwidth]{fig/patched_conics}
+				\includegraphics[width=0.8\textwidth]{LaTeX/fig/patched_conics}
 				\caption{Patched Conics Example Figure}
 				\label{patched_conics_fig}
 			\end{figure}
 
 			This effectively breaks the trajectory into a series of arcs each governed by a distinct
 			Two-Body problem patched together by distinct transition points. These transition points
-			occur along the spheres of influence of the planets nearest to the spacecraft.
+			occur along the spheres of influence of the planets nearest to the spacecraft. A
+			conceptual example of this process, labeled the method of patched conics, appears in
+			Figure~\ref{patched_conics_fig}.
 
 			Therefore, we must understand how to convert our spacecraft's state from the Sun frame
 			to the planetary frame as it crosses this boundary. An elliptical orbit about the sun
 			will have enough orbital energy to represent a hyperbolic orbit around the planet. So we
 			first need to determine the velocity of the spacecraft relative to the planet as it
 			crosses the SOI, which we can determine by subtraction \cite{vallado2001fundamentals}:
-
 			\begin{equation}
 				\vec{v}_{sc/p} = \vec{v}_{sc/sun} - \vec{v}_{planet/sun}
 			\end{equation}
@@ -400,24 +314,21 @@
 			Since the orbit around the planet is hyperbolic, in order to characterize the hyperbola
 			we must determine the velocity of the spacecraft when it has infinite distance relative
 			to the planet. Since this never occurs, a further approximation is made that the
-			velocity that the spacecraft has (relative to the planet) as it crosses the SOI can be
-			modeled as the $\vec{v}_\infty$ of that hyperbolic arc.
+			velocity of the spacecraft (relative to the planet) as it crosses the SOI can be modeled
+			as the $\vec{v}_\infty$ of that hyperbolic arc.
 
 			As an example, we may wish to determine the velocity relative to the planet that the
 			spacecraft has at the periapsis of its hyperbolic trajectory during the flyby. This
-			could be useful, perhaps, for sizing the $\Delta V<$ required during the insertion stage
+			could be useful, perhaps, for sizing the $\Delta V$ required during the insertion stage
 			of the mission if the spacecraft is intended to be captured into an elliptical orbit
 			around its target planet. For a given incoming hyperbolic $\vec{v}_\infty$, we can first
 			determine the specific mechanical energy of the hyperbola at infinite distance by using
 			Equation~\ref{energy}:
-
 			\begin{equation}
 				\xi = \frac{v^2}{2} - \frac{\mu}{r} = \frac{v_\infty^2}{2}
 			\end{equation}
-
 			We can then leverage the conservation of energy to determine the velocity at a
 			particular point, $r_{ins}$:
-
 			\begin{align}
 				\xi_{ins} &= \frac{v_{ins}^2}{2} - \frac{\mu}{r_{ins}} \\
 				\xi_{ins} &= \xi_\infty = \frac{v_\infty^2}{2} \\
@@ -426,31 +337,29 @@
 
 		\subsection{Launch Considerations}
 
-			Generally speaking, an interplanetary mission begins with launch. For a satellite of
-			given size, a certain amount of orbital energy can be imparted to the satellite by the
-			launch vehicle. In practice, this value, for a particular mission, is actually
-			determined as a parameter of the mission trajectory to be optimized. The excess velocity
-			at infinity of the hyperbolic orbit of the spacecraft that leaves the Earth can be used
-			to derive the launch energy. This is usually qualified as the quantity $C_3$, which is
-			actually double the kinetic orbital energy with respect to the Sun, or simply the square
-			of the excess hyperbolic velocity at infinity\cite{wie1998space}.
+			For a satellite of given size, a certain amount of orbital energy can be imparted to the
+			satellite by the launch vehicle. In practice, this value, for a particular mission, is
+			actually determined as a parameter of the mission trajectory to be optimized. The excess
+			velocity at infinity of the hyperbolic orbit of the spacecraft that leaves the Earth can
+			be used to derive the launch energy. This is usually qualified as the quantity $C_3$,
+			which is actually double the kinetic orbital energy with respect to the Sun, or simply
+			the square of the excess hyperbolic velocity at infinity\cite{wie1998space}.
 
 			This algorithm will assume that the initial trajectory at the beginning of the mission
 			will be some hyperbolic orbit with velocity enough to leave the Earth. That initial
-			$v_\infty$ will be used as a tunable parameter in the NLP solver. This allows the
-			mission designer to include the launch $C_3$ in the cost function and, hopefully,
+			$v_\infty$ will be used as a tunable parameter in the optimization routine. This allows
+			the mission designer to include the launch $C_3$ in the cost function and, hopefully,
 			determine the mission trajectory that includes the least initial launch energy. This can
 			then be fed back into a mass-$C_3$ curve for prospective launch providers to determine
 			what the maximum mass any launch provider is capable of imparting that specific $C_3$
 			to.
 
-			A similar approach is taken at the end of the mission. This algorithm doesn't attempt to
-			exactly match the velocity of the planet at the end of the mission. Instead, the excess
-			hyperbolic velocity is also treated as a parameter that can be minimized by the cost
-			function. If a mission is to then end in insertion, a portion of the mass budget can
-			then be used for an impulsive thrust engine, which can provide a final insertion burn at
-			the end of the mission. This approach also allows flexibility for missions that might
-			end in a flyby rather than insertion.
+			A similar approach is taken at the end of the trajectory. This algorithm doesn't attempt
+			to exactly match the velocity of the planet. Instead, the excess hyperbolic velocity is
+			also treated as a parameter that can be minimized by the cost function. If a trajectory
+			is to then end in insertion, a portion of the mass budget can then be used for an
+			impulsive thrust engine, which can provide a final insertion burn. This approach also
+			allows flexibility for missions that might end in a flyby rather than insertion.
 
 		\subsection{Gravity Assist Maneuvers}
 
@@ -480,8 +389,8 @@
 
 			\begin{figure}[H]
 				\centering
-				\includegraphics[width=0.8\textwidth]{fig/flyby}
-				\caption{Visualization of velocity changes during a gravity assist}
+				\includegraphics[width=0.8\textwidth]{LaTeX/fig/flyby}
+				\caption{Velocity changes during a gravity assist}
 				\label{grav_assist_fig}
 			\end{figure}
 
@@ -491,7 +400,7 @@
 			turning angle of this bend. In doing so, one can effectively achieve a (restricted) free
 			impulsive thrust event.
 
-		\subsection{Flyby Periapsis}
+		\subsection{Flyby Periapsis Altitude}
 
 			Now that we understand gravity assists, the natural question is then how to leverage
 			them for achieving certain velocity changes\cite{cho2017b}. But first, we must consider
@@ -500,7 +409,6 @@
 			mentioned in the previous section, given an excess hyperbolic velocity entering the
 			planet's sphere of influence ($\vec{v}_{\infty, in}$) and a target excess hyperbolic
 			velocity as the spacecraft leaves the sphere of influence ($\vec{v}_{\infty, out}$):
-
 			\begin{equation}\label{turning_angle_eq}
 				\delta = \arccos \left( \frac{\vec{v}_{\infty,in} \cdot
 				\vec{v}_{\infty,out}}{|\vec{v}_{\infty,in}| |\vec{v}_{\infty,out}|} \right)
@@ -510,12 +418,10 @@
 			that we must target in order to achieve the required turning angle. The periapsis of the
 			flyby, however, can provide a useful check on what turning angles are possible for a
 			given flyby, since the periapsis:
-
-			\begin{equation}
+			\begin{equation}\label{periapsis_eq}
 				r_p = \frac{\mu}{v_\infty^2} \left[ \frac{1}{\sin\left(\frac{\delta}{2}\right)} - 1 \right]
 			\end{equation}
-
-			Cannot be lower than some safe value that accounts for the radius of the planet and
+			cannot be lower than some safe value that accounts for the radius of the planet and
 			perhaps its atmosphere if applicable.
 
 		\subsection{Multiple Gravity Assist Techniques}
@@ -543,19 +449,21 @@
 				here for its robustness given any initial guess \cite{battin1984elegant}.
 
 				Firstly, some geometric considerations must be accounted for. For any initial
-				position, $\vec{r}_0$, and final position, $\vec{r}_f$, and time of flight $\Delta
+				position, $\vec{r}_1$, and final position, $\vec{r}_2$, and time of flight $\Delta
 				t$, there are actually two separate transfer orbits that can connect the two points
-				with paths that traverse less than one full orbit. For each of these, there are
+				with paths that traverse less than one full orbit. Therefore, there are
 				actually then two trajectories that can connect the points
 				\cite{vallado2001fundamentals}. The first of the two will have a $\Delta \theta$ of
 				less than 180 degrees, which we classify as a Type I trajectory, and the second will
 				have a $\Delta \theta$ of greater than 180 degrees, which we call a Type II
 				trajectory. They will also differ in their direction of motion (clockwise or
-				counter-clockwise about the focus). This can be seen in Figure~\ref{type1type2}.
+				counter-clockwise about the focus). This can be seen in Figure~\ref{type1type2},
+				where both of the Lambert's solutions are presented for sample points in an orbit
+				around the Sun.
 
 				\begin{figure}[H]
 					\centering
-					\includegraphics[width=0.8\textwidth]{fig/lamberts}
+					\includegraphics[width=0.8\textwidth]{LaTeX/fig/lamberts}
 					\caption{Visualization of the possible solutions to Lambert's Problem}
 					\label{type1type2}
 				\end{figure}
@@ -563,20 +471,16 @@
 				The iteration used in this thesis will start by first calculating the change in true
 				anomaly, $\Delta \theta$, as well as the cosine of this value, which can be found
 				by:
-
 				\begin{align}
 					\cos (\Delta \theta) &= \frac{\vec{r}_1 \cdot \vec{r}_2}{|\vec{r}_1| |\vec{r}_2|} \\
 					\Delta \theta &= \arctan(y_2/x_2) - \arctan(y_1/x_1)
 				\end{align}
-
 				The direction of motion is then chosen such that counter-clockwise orbits are
 				considered, as travelling in the same direction as the planets is generally more
 				efficient. Next, the variable $A$ is defined:
-
 				\begin{equation}
 					A = DM \sqrt{|r_1| |r_2| (1 - \cos(\Delta \theta))}
 				\end{equation}
-
 				A is independent of $\psi$, and therefore won't need updating as the iteration
 				proceeds. Then $\psi$ is initialized to any number within its bounds
 				($[-4\pi,4\pi^2]$), arbitrarily set to 0, representing a parabolic arc as a starting
@@ -587,7 +491,6 @@
 				time of flight matches the expected value to within a provided tolerance. In order
 				to calculate the time of flight at each step, we must first calculate some useful
 				coefficients:
-
 				\begin{equation}\label{loop_start}
 					c_2 = \begin{cases}
 						\frac{1-\cos(\sqrt{\psi})}{\psi} \quad &\text{if} \, \psi > 10^{-6} \\
@@ -595,31 +498,24 @@
 						1/2 \quad &\text{if} \, 10^{-6} > \psi > -10^{-6}
 					\end{cases}
 				\end{equation}
-
 				\begin{equation}
 					c_3 = \begin{cases}
-						\frac{\sqrt{\psi} - \sin sqrt{\psi}}{\psi^{3/2}} \quad &\text{if} \, \psi > 10^{-6} \\
+						\frac{\sqrt{\psi} - \sin \sqrt{\psi}}{\psi^{3/2}} \quad &\text{if} \, \psi > 10^{-6} \\
 						\frac{\sinh\sqrt{-\psi} - \sqrt{-\psi}}{(-\psi)^{3/2}} \quad &\text{if} \, \psi < -10^{-6} \\
 						1/6 \quad &\text{if} \, 10^{-6} > \psi > -10^{-6}
 					\end{cases}
 				\end{equation}
-
-				\noindent
 				Where the conditions of this piecewise function represent the elliptical,
 				hyperbolic, and parabolic cases, respectively. Once we have these, we can calculate
 				another variable, $y$:
-
 				\begin{equation}
 					y = |r_1| + |r_2| + \frac{A (c_3 \psi - 1)}{\sqrt{c_2}}
 				\end{equation}
-
 				We can then finally calculate the variable $\chi$, and from that, the time of
 				flight:
-
 				\begin{equation}
-					\chi = sqrt{\frac{y}{c_2}}
+					\chi = \sqrt{\frac{y}{c_2}}
 				\end{equation}
-
 				\begin{equation}
 					\Delta t = \frac{c_3 \chi^3 + A \sqrt{y}}{\sqrt{c_2}}
 				\end{equation}
@@ -632,22 +528,17 @@
 
 				The resulting $f$ and $g$ functions (and the derivative of $g$, $\dot{g}$) can then
 				be calculated:
-
 				\begin{align}
 					f &= 1 - \frac{y}{|r_1|} \\
 					g &= A \sqrt{\frac{y}{\mu}} \\
 					\dot{g} &= 1 - \frac{y}{|r_2|}
 				\end{align}
-
 				And from these, we can calculate the velocities of the transfer points as:
-
 				\begin{align}
 					\vec{v}_1 &= \frac{\vec{r}_1 - f \vec{r}_2}{g} \\
 					\vec{v}_2 &= \frac{\dot{g} \vec{r}_2 - \vec{r}_1}{g}
 				\end{align}
-
-				\noindent
-				Fully constraining the connecting orbit.
+				Fully describing the connecting path with the specified flight time.
 
 			\subsubsection{Planetary Ephemeris}
 
@@ -660,8 +551,8 @@
 
 				The primary use of SPICE in this thesis, however, was to determine the planetary
 				ephemeris at a known epoch. Using the NAIF0012 and DE430 kernels, ephemeris in the
-				ecliptic plane J2000 frame could be easily determined for a given epoch, provided as
-				a decimal Julian Day since the J2000 epoch.
+				International Celestial Reference Frame could be easily determined for a given
+				epoch, provided as a decimal Julian Day since the J2000 epoch.
 
 			\subsubsection{Porkchop Plots}
 
@@ -681,24 +572,17 @@
 				Using porkchop plots such as the one in Figure~\ref{porkchop}, mission designers can
 				quickly visualize which natural trajectories are possible between planets. Using the
 				fact that incoming and outgoing $v_\infty$ magnitudes must be the same for a flyby,
-				a savvy mission designer can even begin to work out what combinations of flybys
-				might be possible for a given timeline, spacecraft state, and planet selection.
+				a mission designer can even begin to work out what combinations of flybys might be
+				possible for a given timeline, spacecraft state, and planet selection.
 
-				%TODO: Create my own porkchop plot
 				\begin{figure}[H]
 					\centering
-					\includegraphics[width=\textwidth]{fig/porkchop}
+					\includegraphics[width=\textwidth]{LaTeX/fig/porkchop}
 					\caption{A sample porkchop plot of an Earth-Mars transfer}
 					\label{porkchop}
 				\end{figure}
 
-				However, this is an impulsive thrust-centered approach. The solution to Lambert's
-				problem assumes a natural trajectory. A natural trajectory is unnecessary when the
-				trajectory can be modified by a continuous thrust profile along the arc. Therefore,
-				for the hybrid problem of optimizing both flyby selection and thrust profiles,
-				porkchop plots are less helpful, and an algorithmic approach is preferred.
-
-	\section{Low Thrust Considerations} \label{low_thrust}
+	\section{Modeling Low Thrust Control} \label{low_thrust}
 
 		In this section, we'll discuss the intricacies of continuous low-thrust trajectories in
 		particular. There are many methods for optimizing such profiles and we'll briefly discuss
@@ -706,7 +590,7 @@
 		as introduce the concept of a control law and the notation used in this thesis for modelling
 		low-thrust trajectories more simply.
 
-		\subsection{Specific Impulse}
+		\subsection{Engine Model}
 
 			The primary advantage of continuous thrust methods over their impulsive counterparts is
 			in their fuel-efficiency in generating changes in velocity. Put specifically, all
@@ -718,45 +602,34 @@
 			This efficiency is often captured in a single variable called specific impulse, often
 			denoted as $I_{sp}$. We can derive the specific impulse by starting with the rocket
 			thrust equation\cite{sutton2016rocket}:
-
 			\begin{equation}
 				F = \dot{m} v_e + \Delta p A_e
 			\end{equation}
-
-			\noindent
 			Where $F$ is the thrust imparted, $\dot{m}$ is the fuel mass rate, $v_e$ is the exhaust
 			velocity of the fuel, $\Delta p$ is the change in pressure across the exhaust opening,
 			and $A_e$ is the area of the exhaust opening. We can then define a new variable
 			$v_{eq}$, such that the thrust equation becomes:
-
 			\begin{align}
-				v_{eq} &= v_e - \frac{\Delta p A_e}{\dot{m}} \\
+				v_{eq} &= v_e + \frac{\Delta p A_e}{\dot{m}} \\
 				F &= \dot{m} v_{eq} \label{isp_1}
 			\end{align}
-
-			\noindent
 			And we can then take the integral of this value with respect to time to find the total
 			impulse, dividing by the weight of the fuel to derive the specific impulse:
-
 			\begin{align}
 				I &= \int F dt = \int \dot{m} v_{eq} dt = m_e v_{eq} \\
 				I_{sp} &= \frac{I}{m_e g_0} = \frac{m_e v_{eq}}{m_e g_0} = \frac{v_{eq}}{g_0}
 			\end{align}
-
 			Plugging Equation~\ref{isp_1} into the previous equation we can derive the following
 			formula for $I_{sp}$:
-
 			\begin{equation} \label{isp_real}
 				I_{sp} = \frac{F}{\dot{m} g_0}
 			\end{equation}
-
-			\noindent
 			Which is generally taken to be a value with units of seconds and effectively represents
 			the efficiency with which a thruster converts mass to thrust.
 
 		\subsection{Sims-Flanagan Transcription}
 
-			this thesis chose to use a model well suited for modeling low-thrust paths: the
+			In this thesis the following approach is used for modeling low-thrust paths: the
 			Sims-Flanagan transcription (SFT)\cite{sims1999preliminary}. The SFT allows for
 			flexibility in the trade-off between fidelity and performance, which makes it very
 			useful for this sort of preliminary analysis.
@@ -769,7 +642,7 @@
 
 			\begin{figure}[H]
 				\centering
-				\includegraphics[width=0.6\textwidth]{fig/sft}
+				\includegraphics[width=0.6\textwidth]{LaTeX/fig/sft}
 				\caption{Example of an orbit raising using the Sims-Flanagan Transcription with 7
 				Sub-Trajectories}
 				\label{sft_fig}
@@ -792,7 +665,7 @@
 			continuous low-thrust trajectory within the Two-Body Problem, with only
 			linearly-increasing computation time\cite{sims1999preliminary}.
 
-		\subsection{Low-Thrust Control Laws}
+		\subsection{Low-Thrust Control Vector Description}
 
 			In determining a low-thrust arc, a number of variables must be accounted for and,
 			ideally, optimized. Generally speaking, this means that a control law must be determined
@@ -805,24 +678,23 @@
 			The methods for determining this direction varies greatly depending on the particular
 			control law chosen for that mission. Often, this process involves first determining a
 			useful frame to think about the kinematics of the spacecraft. In this case, we'll use a
-			frame often used in these low-thrust control laws: the spacecraft $\hat{R} \hat{\theta}
-			\hat{H}$ frame. In this frame, the $\hat{R}$ direction is the radial direction from the
-			center of the primary to the center of the spacecraft. The $\hat{H}$ hat is
-			perpendicular to this, in the direction of orbital momentum (out-of-plane) and the
-			$\hat{\theta}$ direction completes the right-handed orthonormal frame.
+			frame often used in these low-thrust control laws: the spacecraft-centered $\hat{R}
+			\hat{\theta} \hat{H}$ frame. In this frame, the $\hat{R}$ direction is the radial
+			direction from the center of the primary to the center of the spacecraft. The $\hat{H}$
+			hat is perpendicular to this, in the direction of orbital momentum (out-of-plane) and
+			the $\hat{\theta}$ direction completes the right-handed orthonormal triad.
 
 			This frame is useful because, for a given orbit, especially a nearly circular one, the
 			$\hat{\theta}$ direction is nearly aligned with the velocity direction for that orbit at
 			that moment. This allows us to define a set of two angles, which we'll call $\alpha$ and
 			$\beta$, to represent the in and out of plane pointing direction of the thrusters. This
-			convention is useful because a $(0,0)$ set represents a thrust force more or less
-			directly in line with the direction of the velocity, a commonly useful thrusting
-			direction for most effectively increasing (or decreasing if negative) the angular
-			momentum and orbital energy of the trajectory.
+			convention is useful because, in a near-circular path, a $(0,0)$ set represents a thrust
+			force more or less directly in line with the direction of the velocity, a commonly
+			useful thrusting direction for most effectively increasing (or decreasing if negative)
+			the angular momentum and orbital energy of the trajectory.
 
 			Using these conventions, we can then redefine our thrust vector in terms of the $\alpha$
 			and $\beta$ angles in the chosen frame:
-
 			\begin{align}
 				F_r &= F \cos(\beta) \sin (\alpha) \\
 				F_\theta &= F \cos(\beta) \cos (\alpha) \\
@@ -831,12 +703,12 @@
 
 		\subsubsection{Thrust Magnitude}
 
-			However, there is actually another variable that can be varied by the majority of
-			electric thrusters. Either by controlling the input power of the thruster or the duty
-			cycle, the thrust magnitude can also be varied, limited by the maximum thrust available
-			to the thruster. Not all control laws allow for this fine-tuned control of the thruster.
+			There is another variable that can be varied by the majority of electric thrusters.
+			Either by controlling the input power of the thruster or the duty cycle, the thrust
+			magnitude can also be varied, limited by the maximum thrust available to the thruster.
+			Not all control laws allow for this fine-tuned control of the thruster.
 
-			The algorithm used in this thesis does vary the magnitude of the thrust control. In
+			The approach used in this thesis does vary the magnitude of the thrust control. In
 			certain cases it actually can be useful to have some fine-tuned control over the
 			magnitude of the thrust. Since the optimization in this algorithm is automatic, it is
 			relatively straightforward to consider the control thrust as a 3-dimensional vector in
@@ -857,21 +729,14 @@
 
 			\begin{figure}[H]
 				\centering
-				\includegraphics[width=\textwidth]{fig/low_efficiency}
+				\includegraphics[width=\textwidth]{LaTeX/fig/low_efficiency}
 				\caption{Graphic of an orbit-raising with a low efficiency cutoff}
 				\label{low_efficiency_fig}
 			\end{figure}
 
 			\begin{figure}[H]
 				\centering
-				\includegraphics[width=\textwidth]{fig/high_efficiency}
+				\includegraphics[width=\textwidth]{LaTeX/fig/high_efficiency}
 				\caption{Graphic of an orbit-raising with a high efficiency cutoff}
 				\label{high_efficiency_fig}
 			\end{figure}
-
-			All of this is, of course, also true for impulsive trajectories. However, since the
-			thrust presence for those trajectories are generally taken to be impulse functions, the
-			control laws can afford to be much less complicated for a given mission goal, by simply
-			thrusting only at the moment on the orbit when the transition will be most efficient.
-			For a low-thrust mission, however, the control law must be continuous rather than
-			discrete and therefore the control law inherently gains a lot of complexity.

LaTeX/trajectory_optimization.tex

@@ -6,10 +6,11 @@
 			highly non-linear, unpredictable systems such as this. The field that developed to
 			approach this problem is known as Non-Linear Programming (NLP) Optimization.
 
-			A Non-Linear Programming Problem is defined by an attempt to optimize a function
+			A Non-Linear Programming Problem involves finding a solution that optimizes a function
 			$f(\vec{x})$, subject to constraints $\vec{g}(\vec{x}) \le 0$ and $\vec{h}(\vec{x}) = 0$
 			where $n$ is a positive integer, $x$ is any subset of $R^n$, $g$ and $h$ can be vector
-			valued functions of any size, and at least one of $f$, $g$, and $h$ must be non-linear.
+			valued functions of any size, and at least one of $f$, $\vec{g}$, and $\vec{h}$ must be
+			non-linear.
 
 			There are, however, two categories of approaches to solving an NLP. The first category,
 			indirect methods, involve declaring a set of necessary and/or sufficient conditions for
@@ -20,10 +21,10 @@
 
 			The other category is the direct methods. In a direct optimization problem, the cost
 			function itself provides a value that an iterative numerical optimizer can measure
-			itself against. The optimal solution is then found by varying the inputs $x$ until the
-			cost function is reduced to a minimum value, often determined by its derivative
-			jacobian. A number of tools have been developed to optimize NLPs via this direct method
-			in the general case.
+			itself against. The optimal solution is then found by varying the inputs $\vec{x}$ until
+			the cost function is reduced to a minimum value, often determined by its derivative
+			jacobian. A number of tools have been developed to formulate NLPs for optimization via
+			this direct method in the general case.
 
 			Both of these methods have been applied to the problem of low-thrust interplanetary
 			trajectory optimization \cite{Casalino2007IndirectOM} to find local optima over
@@ -40,7 +41,7 @@
 			Therefore, a direct optimization method was leveraged by transcribing the problem into
 			an NLP and using IPOPT to find the local minima.
 
-			\subsubsection{Non-Linear Solvers}
+			\subsection{Non-Linear Solvers}
 
 				One of the most common packages for the optimization of NLP problems is
 				SNOPT\cite{gill2005snopt}, which is a proprietary package written primarily using a
@@ -48,7 +49,7 @@
 				University. It uses a sparse sequential quadratic programming algorithm as its
 				back-end optimization scheme.
 
-				Another common NLP optimization packages (and the one used in this implementation)
+				Another common NLP optimization package (and the one used in this implementation)
 				is the Interior Point Optimizer or IPOPT\cite{wachter2006implementation}. It  uses
 				an Interior Point Linesearch Filter Method and was developed as an open-source
 				project by the organization COIN-OR under the Eclipse Public License.
@@ -63,7 +64,7 @@
 				libraries that port these are quite modular in the sense that multiple algorithms can be
 				tested without changing much source code.
 
-			\subsubsection{Interior Point Linesearch Method}
+			\subsection{Interior Point Linesearch Method}
 
 				As mentioned above, this project utilized IPOPT which leveraged an Interior Point
 				Linesearch method. A linesearch algorithm is one which attempts to find the optimum
@@ -74,12 +75,7 @@
 				step the initial guess, now labeled $x_{k+1}$ after the addition of the ``step''
 				vector and iterates this process until predefined termination conditions are met.
 
-				In this case, the IPOPT algorithm was used, not as an optimizer, but as a solver. For
-				reasons that will be explained in the algorithm description in Section~\ref{algorithm} it
-				was sufficient merely that the non-linear constraints were met, therefore optimization (in
-				the particular step in which IPOPT was used) was unnecessary.
-
-			\subsubsection{Shooting Schemes for Solving a Two-Point Boundary Value Problem}
+			\subsection{Shooting Schemes for Solving a Two-Point Boundary Value Problem}
 
 				One straightforward approach to trajectory corrections is a single shooting
 				algorithm, which propagates a state, given some control variables forward in time to
@@ -87,39 +83,30 @@
 				iterative process, using the correction scheme, until the target state and the
 				propagated state matches.
 
-				As an example, we can consider the Two-Point Boundary Value Problem (TPBVP) defined
-				by:
-
+				As an example, we can consider the one-dimensional Two-Point Boundary Value Problem
+				(TPBVP) defined by:
 				\begin{equation}
 					y''(t) = f(t, y(t), y'(t)), y(t_0) = y_0, y(t_f) = y_f
 				\end{equation}
-
-				\noindent
 				We can then redefine the problem as an initial-value problem:
-
 				\begin{equation}
-					y''(t) = f(t, y(t), y'(t)), y(t_0) = y_0, y'(t_0) = x
+					y''(t) = f(t, y(t), y'(t)), y(t_0) = y_0, y'(t_0) = \dot{y}_0
 				\end{equation}
-
-				\noindent
 				With $y(t,x)$ as a solution to that problem. Furthermore, if $y(t_f, x) = y_f$, then
 				the solution to the initial-value problem is also the solution to the TPBVP as well.
 				Therefore, we can use a root-finding algorithm, such as the bisection method,
 				Newton's Method, or even Laguerre's method, to find the roots of:
-
 				\begin{equation}
 					F(x) = y(t_f, x) - y_f
 				\end{equation}
-
-				\noindent
 				To find the solution to the IVP at $x_0$, $y(t_f, x_0)$ which also provides a
 				solution to the TPBVP. This technique for solving a Two-Point Boundary Value
 				Problem can be visualized in Figure~\ref{single_shoot_fig}.
 
 				\begin{figure}[H]
 					\centering
-					\includegraphics[width=\textwidth]{fig/single_shoot}
-					\caption{Visualization of a single shooting technique over a trajectory arc}
+					\includegraphics[width=\textwidth]{LaTeX/fig/single_shoot}
+					\caption{Single shooting over a trajectory arc}
 					\label{single_shoot_fig}
 				\end{figure}
 
@@ -138,24 +125,23 @@
 				each of these points we can then define a separate control, which may include the
 				states themselves. The end state of each arc and the beginning state of the next
 				must then be equal for a valid arc (with the exception of velocity discontinuities
-				if allowed for maneuvers at that point), as well as the final state matching the
-				target final state.
+				if allowed for maneuvers or gravity assists at that point), as well as the final
+				state matching the target final state.
 
 				\begin{figure}[H]
 					\centering
-					\includegraphics[width=\textwidth]{fig/multiple_shoot}
+					\includegraphics[width=\textwidth]{LaTeX/fig/multiple_shoot}
 					\caption{Visualization of a multiple shooting technique over a trajectory arc}
 					\label{multiple_shoot_fig}
 				\end{figure}
 
 				In this example, it can be seen that there are now more constraints (places where
-				the states need to match up, creating an $x_{error}$ term) as well as control
+				the states need to match up, creating an $\vec{x}_{error}$ term) as well as control
 				variables (the $\Delta V$ terms in the figure). This technique actually lends itself
 				very well to low-thrust arcs and, in fact, Sims-Flanagan Transcribed low-thrust arcs
 				in particular, because there actually are control thrusts to be optimized at a
 				variety of different points along the orbit. This is, however, not an exhaustive
-				description of ways that multiple shooting can be used to optimize a trajectory,
-				simply the most convenient for low-thrust arcs.
+				description of ways that multiple shooting can be used to optimize a trajectory.
 
 	\section{Monotonic Basin Hopping Algorithms}
 

Makefile

@@ -1,68 +1,42 @@
-OPTIONS = markdown+yaml_metadata_block+smart
-
-NOTES = $(wildcard prelim_notes/*.md)
-NOTES_PDFS = $(patsubst %.md,%.pdf,$(NOTES))
-
-THESIS = LaTeX/thesis.tex
+SRC_DIR = LaTeX/
+THESIS_SRC_NAMES = thesis.tex thesis.bib approach.tex conclusion.tex introduction.tex \
+				   results.tex trajectory_design.tex trajectory_optimization.tex
+THESIS_SRC = $(addprefix $(SRC_DIR)/,$(THESIS_SRC_NAMES))
+THESIS_PRES_SRC_NAMES = presentation.tex presentation.bib
+THESIS_PRES_SRC = $(addprefix $(SRC_DIR)/,$(THESIS_PRES_SRC_NAMES))
+THESIS_PRES = presentation.pdf
 THESIS_PDF = thesis.pdf
+BUILD_DIR = temp/
 
-all: $(THESIS_PDF) $(NOTES_PDFS)
+all: $(THESIS_PDF) $(THESIS_PRES)
 
-$(NOTES_PDFS): $(NOTES)
-	pandoc \
-		--variable mainfont="Roboto" \
-		--variable monofont="Fira Code" \
-		--variable fontsize=11pt \
-		--variable geometry:"top=1in, bottom=1in, left=1in, right=1in" \
-		--variable geometry:letterpaper \
-		-f markdown  $< \
-		-o $@
+$(BUILD_DIR):
+	mkdir -p $(BUILD_DIR)
 
-thesis_pdf/:
-	mkdir $@
+$(BUILD_DIR)/$(THESIS_PDF): $(BUILD_DIR) $(THESIS_SRC)
+	xelatex --output-directory $(BUILD_DIR) $(SRC_DIR)/thesis
+	bibtex $(BUILD_DIR)/thesis
+	xelatex --output-directory $(BUILD_DIR) $(SRC_DIR)/thesis
+	xelatex --output-directory $(BUILD_DIR) $(SRC_DIR)/thesis
 
-$(THESIS_PDF): $(THESIS) LaTeX/thesis.bib
-	mkdir -p temp
-	cp -r LaTeX/fig .
-	cp -r LaTeX/flowcharts .
-	cp -r LaTeX/thesis.tex .
-	cp -r LaTeX/macros.tex .
-	cp -r LaTeX/thesis.bib .
-	cp -r LaTeX/thesis.cls .
-	xelatex thesis
-	bibtex thesis
-	xelatex thesis
-	xelatex thesis
-	rm -rf fig
-	rm -rf flowcharts
-	cp thesis.pdf temp/.
-	rm -rf macros.tex
-	rm -rf thesis.*
-	cp temp/thesis.pdf .
-	rm -rf temp
+$(BUILD_DIR)/$(THESIS_PRES): $(BUILD_DIR) $(THESIS_PRES_SRC)
+	xelatex --output-directory $(BUILD_DIR) $(SRC_DIR)/presentation
+	bibtex $(BUILD_DIR)/presentation
+	xelatex --output-directory $(BUILD_DIR) $(SRC_DIR)/presentation
+	xelatex --output-directory $(BUILD_DIR) $(SRC_DIR)/presentation
+
+$(THESIS_PDF): $(BUILD_DIR)/$(THESIS_PDF)
+	cp $(BUILD_DIR)/thesis.pdf .
+
+$(THESIS_PRES): $(BUILD_DIR)/$(THESIS_PRES)
+	cp $(BUILD_DIR)/presentation.pdf .
 
 .PHONY: clean revise
 
 clean:
 	rm -rf $(THESIS_PDF)
-	rm -rf $(NOTES_PDFS)
-	rm -rf thesis_pdf
+	rm -rf $(THESIS_PRES)
+	rm -rf $(BUILD_DIR)
 
-revise: $(THESIS) LaTeX/thesis.bib
-	mkdir -p temp
-	cp -r LaTeX/fig .
-	cp -r LaTeX/flowcharts .
-	cp -r LaTeX/thesis.tex .
-	cp -r LaTeX/macros.tex .
-	cp -r LaTeX/thesis.bib .
-	cp -r LaTeX/thesis.cls .
-	xelatex thesis
-	bibtex thesis
-	xelatex thesis
-	xelatex thesis
-	rm -rf fig
-	rm -rf flowcharts
-	cp thesis.pdf temp/.
-	rm -rf macros.tex
-	rm -rf thesis.*
-	cp temp/thesis.pdf .
+final: $(THESIS_PDF) $(THESIS_PRES)
+	rm -rf $(BUILD_DIR)

archive/EMS_0.885200034193802

@@ -0,0 +1,29 @@
+archive/EMS_0.885200034193802---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-09-20T14:03:44.662
+Launch V∞: [-0.9544125442488793, 4.650055637860991, 0.8829883975591813] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-2.686848874040082, 5.69557833738042, -0.3426867301634786] km/s
+	V∞_out: [-5.006830246285463, 3.8244101442357286, -0.28590492992060296] km/s
+	time of flight: 1.2959473202133252e8 seconds
+	arrival date: 2028-10-29T12:35:56.662
+	thrust profile: [-0.028074398281491695 0.03725829642101633 0.011493562796176157; -0.04057241823105847 -0.0036979634745522238 0.004188100162030408; -0.018576540265103334 -0.016670623079762328 -0.0036538504180610655; -0.00926818068907572 -0.029823872248843347 -0.00788998730301693; 0.0056536273790355335 -0.039471274595512786 -0.015505661293943124; 0.01795773380852956 -0.024832086810877792 -0.012157101567918709; 0.020276654954958836 -0.008918038755765955 -0.0074245383137495295; 0.026868221096269136 0.007263820280035479 -0.004654400052923847; 0.011894893359756988 0.03223774798632351 0.004633535267024402; -0.047141055295386355 0.040019079580037704 0.013364609633569504; -0.04520469085369964 -0.010120922532993988 0.0020777538652468844; -0.024235864777124916 -0.02628842319518715 -0.005178953753261158; -0.020104196631084845 -0.08663986569488229 -0.025957813503050115; 0.04562945777248198 -0.18858114469692783 -0.07388958835417316; 0.1654642046172344 -0.19639566019786459 -0.09899123711104271; 0.20836768567311814 -0.07684473602532182 -0.06621134288112417; 0.17451643722399424 0.054856569336227734 -0.019947666848185868; 0.09171150949789851 0.24766459803783164 0.03479747010758981; -0.23524183946575974 0.2601294101394598 0.07688820773607916; -0.21879974186036938 -0.008020833470565012 0.021595583194403873] %
+Phase 2:
+	Planet: Saturn
+	V∞_in: [2.746703786000276, 2.98969776442552, -1.0550945579969648] km/s
+	V∞_out: [-2.364529965587132, -1.1050142331661583, -3.0819068226828907] km/s
+	time of flight: 2.2586692153285405e8 seconds
+	arrival date: 2035-12-26T17:24:37.662
+	thrust profile: [-0.17155197556204754 -0.12803647772004534 -0.0010987042854903337; -0.0035589134881411667 -0.06490801713537507 0.0007426295065205218; 0.25580929199297914 -0.3791453683925915 0.015541598652070847; 0.9999998062826643 -0.5828839766311769 0.041611387112901736; 0.9999998812648976 -0.13591929443541234 0.04367451973443414; 0.9999999269970672 0.45531454218125245 0.04521667689652659; 0.9999999228048742 0.9999999183342614 0.04613770201743983; 0.840757310010811 0.9999999579385513 0.026030995407658575; 0.11987829006679744 1.0 -0.0008893319442928411; -0.16626331436648592 0.8682210906007626 -0.017523530916658536; -0.010554991808101162 0.026008419906682182 -0.0010654160560760403; -0.00038326527134042613 0.00042430859777888713 0.00034930741189383597; 8.526053802782655e-5 -0.0008985199777937706 0.000160878965697085; -0.0003967771857136998 0.0010341920913412306 -0.0002243904620731941; -0.001455496554504259 -3.155267804676458e-5 0.00028821667601580344; -0.0002685807673767674 0.000826989980715048 -0.0008420052914367241; -0.0007719825562061786 -0.0008609199968383217 -5.4081725930572875e-5; -0.00011547325119660988 0.00024382875164120964 -0.0003906884145274092; 0.0010448953162641168 -0.0012700408455061536 0.001398368665761554; -0.0009243989271800159 -0.0004827763788561335 -0.00016362116690873035] %
+
+Mass Used: 896.7374359341643 kg
+Launch C3: 23.313589250046537 km²/s²
+||V∞_in||: 4.1947465879304335 km/s

archive/EMS_0.956419624778337

@@ -0,0 +1,29 @@
+archive/EMS_0.956419624778337---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-09-17T04:51:36.159
+Launch V∞: [-1.135592828872187, 4.562737698529162, 1.3727576611586305] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-3.557470090326179, 6.118653602166694, -0.5798401682157046] km/s
+	V∞_out: [-5.645943535485121, 4.274383608710339, -0.5316919206121211] km/s
+	time of flight: 1.3085999999776801e8 seconds
+	arrival date: 2028-11-09T18:51:35.159
+	thrust profile: [-0.09484105234506424 0.13109265638731943 0.010936530688181876; -0.1814554654952118 -0.01317670830456729 -0.013056779511401079; -0.03810385790137717 -0.03831609614699233 -0.0090400245120533; -0.011547804227375344 -0.045340160916842225 -0.010789638825569993; 0.010850150398340981 -0.04880193320022692 -0.012185437423926783; 0.013978839278259155 -0.01840779353950528 -0.004665802971635902; 0.015830676636944672 -0.006108261481050007 -0.001974030494045432; 0.02222629553617521 0.007131223648098273 -0.000366596741242515; 0.05551908016805829 0.2775937664715688 0.01624399186055875; -0.11493741715972325 0.07648127820140446 0.005075332093053433; -0.07281410027212154 -0.023271489715626266 -0.00280576336716608; -0.03991641354611127 -0.052482033366050736 -0.012070494591368944; -0.010823677700697571 -0.06926247781385951 -0.014965378527982062; 0.014553072546870926 -0.0531151232441876 -0.012334544418377249; 0.027433879698947325 -0.03222960647822717 -0.008091377392690582; 0.027896088095082885 -0.010765686776681731 -0.0035677146904594865; 0.1474887355876181 0.04194010217566325 0.0075472784087007245; 0.08740136907489779 0.2476740961050621 0.025348796622511757; -0.3587107107731137 0.3658303122853691 -0.024033216941170596; -0.30793493577932085 -0.02489759271709177 -0.029516702132738652] %
+Phase 2:
+	Planet: Saturn
+	V∞_in: [3.7155109082507987, 4.436831582591491, -1.1732520095761172] km/s
+	V∞_out: [-2.9774108815083147, -1.2560337688716137, -4.9297276650048545] km/s
+	time of flight: 2.0467080000004956e8 seconds
+	arrival date: 2035-05-06T15:51:35.159
+	thrust profile: [-0.05767594934959341 -0.04617371221776187 -0.0018460762847027803; -0.00242135160333423 -0.04166237973886581 0.0014630203665685387; 0.29042498349326934 -0.4463318141243284 0.034252710040742367; 0.9999918983032768 -0.6810996795092573 0.08973482264944235; 0.999994193014499 -0.30520092641941937 0.09457239144251212; 0.9999870255556219 0.2194024540716046 0.09015740448455901; 0.9999831603785917 0.9750561249047252 0.0872456396613651; 0.9999985694625713 0.9999931657134729 0.05615632466445174; 0.687392266640871 0.9999956716419007 0.01734725859208972; 0.029368471497984026 0.99992751557616 -0.014405154294501676; -0.20296396601376304 0.9423006803678043 -0.03524904229410645; -0.12775237609043735 0.3694446313295914 -0.02368746549915993; -0.00034842736779606184 0.0005678692895095884 -0.00031598317940006337; -0.0003712455053865169 -1.6935819288267125e-5 -0.00019252189104459086; -0.0005996017322677676 -0.00028098465395757154 2.2184451692068863e-5; 0.0002022591204715913 -0.00018951661125293372 0.000189711737865895; -0.0007251432775536019 0.0002897166773871866 -3.9173461655229126e-5; -0.000850251276017041 -0.0005646508814492377 0.0013737659604325715; 0.00040972949658941917 -0.0005145490913947212 5.515738964126715e-5; -0.00046082039982410966 -0.0003000114452015229 -0.00026022069154713355] %
+
+Mass Used: 975.8660040548566 kg
+Launch C3: 23.992609974834842 km²/s²
+||V∞_in||: 5.9048298942125665 km/s

archive/EMS_1.4088814420596534

@@ -0,0 +1,29 @@
+archive/EMS_1.4088814420596534---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-10-16T06:12:17.261
+Launch V∞: [-1.7148923713366755, 3.9298192178302784, 2.8299200745152713] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-3.423654294372138, 2.5650341612477567, -0.5338967704352118] km/s
+	V∞_out: [-4.266996673560502, -0.5839080002997025, 0.19402466913132768] km/s
+	time of flight: 1.3088384355378014e8 seconds
+	arrival date: 2028-12-09T02:49:40.261
+	thrust profile: [-0.16843253076284767 0.015174387284071982 -0.2568833411269522; -0.04051411441266916 -0.1706697462481348 -0.09202063132953058; 0.045219798511790026 -0.3096747505733966 -0.15447868293737022; 0.1891430434005993 -0.38802384440125315 0.254163650929716; 0.2878269718158013 -0.2521241423300037 0.1694504332526969; 0.2669620698102962 -0.07974891300102108 0.22353096596670005; 0.25838781033301184 -0.013302459740443208 0.1575979105416097; 0.18877094120583682 -0.1090841631358866 0.0675029255999918; -0.36014421578836414 -0.39909210387062594 -0.10424720248437652; 0.007505343447408759 -0.37070440668154536 -0.020703856519349483; 0.18623264501774142 -0.18772468781032164 -0.012898204728801035; -0.07776052053136313 -0.2150791981555987 0.17906646004157736; 0.0933903030286568 -0.351389278618167 0.2513185206003883; 0.15582528052167877 -0.27898764592860065 0.25820541552552223; 0.1705037874283403 -0.15120215929987232 0.22048201505740622; 0.2478320676125178 -0.0553823274204888 0.008131367787768651; 0.3160196179605864 0.06497580000323308 -0.08737918006790793; 0.18787792768517483 0.24030042469215662 -0.02336463045670074; -0.4500653157082868 -0.43615701512016586 0.031249984200407536; -0.5597015227203471 0.026975117825268798 0.05914640634236509] %
+Phase 2:
+	Planet: Saturn
+	V∞_in: [-0.4447430233297146, -0.5103236773782882, 0.17690937986451852] km/s
+	V∞_out: [0.4026479925582012, 0.16697609141693656, 0.5486720695904586] km/s
+	time of flight: 2.2369063570553738e8 seconds
+	arrival date: 2036-01-11T03:06:55.261
+	thrust profile: [-0.20026176608455784 -0.29694390627659506 -0.03656336874049517; 0.19219210775821996 -0.2745039023151382 -0.008910114775166253; 0.5380981511022175 -0.1752113671787406 0.2750415301381581; 0.8091604929924738 0.059336617760770226 0.16452081995331563; 0.8019293953199363 0.3703939998509808 0.12716583651365265; 0.7628458054564177 0.6219877057473859 0.08804354131656808; 0.6790691189945572 0.7151724861702393 0.07257080916983001; 0.605711392602211 0.7556960844929883 0.05668728294284225; 0.5019330343132242 0.7202977352394476 0.05464681963849307; 0.4355136362347505 0.5812218127189013 0.0598464640192131; 0.2792323417761552 0.6365652142420161 0.06200031759875403; -0.0031648597009793127 0.6439660654725341 0.021229855541562564; -0.22740032522428177 0.585273186623273 -0.0005797994707257422; -0.29907327416889895 0.5556200894768929 0.016308953313994647; -0.3305919828650731 0.6000464102363009 0.008217747003379565; -0.2760568905961062 0.534608626086542 -0.02767524280228222; -0.21717555650995973 0.3271478959702166 -0.000487395179347153; -0.15788889898326117 0.24115731722004857 -0.0013939275969228635; -0.08909459626676448 0.1483902552290073 -0.0013811701172317676; -0.028408442047604864 0.04951927705463767 -0.0006587817095277265] %
+
+Mass Used: 1489.7371174798539 kg
+Launch C3: 26.39278255824143 km²/s²
+||V∞_in||: 0.699659589498638 km/s

archive/EMS_1.7849375588806782

@@ -0,0 +1,29 @@
+archive/EMS_1.7849375588806782---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-12-27T01:12:40.730
+Launch V∞: [1.8466699553948345, 1.3678562790010131, -0.0153057964937058] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-3.1633872892711388, 1.766847714739104, 1.5906318484460866] km/s
+	V∞_out: [-2.6570752417451518, -1.5623087854586397, 2.48153623885944] km/s
+	time of flight: 1.3537387772095194e8 seconds
+	arrival date: 2029-04-11T21:03:57.730
+	thrust profile: [0.9929900810043344 0.9999987852496462 -0.10337727636552446; -0.9999989527606722 0.9999992090099894 -0.3047289804175132; -0.9638713659439484 0.0450322438551014 -0.4055337795064804; -0.22495106561402115 0.7848677069324818 0.3831319023782979; -0.7738893421351393 0.9999990172621287 0.39494769205095726; -0.990946731002965 0.8417897053927665 -0.3815221486365675; -0.9734982361035388 0.7893313668448306 -0.2704704369660258; -0.38723803350107505 0.9976585911266805 0.3624717872401706; -0.6369591805380839 0.9888790443583878 0.2130500370042681; -0.9999988687936101 0.9999990044599046 -0.3329147869188805; -0.5789162319974664 0.1999123448513483 0.028083803862645515; 0.7985291692991425 0.7881953295377477 0.17388971281195142; 0.988850032987504 0.9999996591217118 -0.5009694317683372; -0.9999994842664317 -0.3956604351616602 0.20708177708047873; -0.4450447334188467 -0.9872965011676511 0.25277979453414506; 0.9999992382496556 -0.2261999230664443 0.0610408161667454; 0.9999995915291495 0.9999997964336237 -0.5276666165499095; -0.9999998232725931 0.9999996435539122 -0.2721356921234991; -0.9999996876222519 -0.99999900073252 0.10007758955670606; -0.4315629068159034 -0.9999994920612009 0.07571074821215397] %
+Phase 2:
+	Planet: Saturn
+	V∞_in: [1.327202961748595, -0.2335174765716992, 0.19517799010581816] km/s
+	V∞_out: [-0.10390899330694657, 0.5823202662968701, -1.2235226316464973] km/s
+	time of flight: 1.315170240574828e8 seconds
+	arrival date: 2033-06-12T01:34:21.730
+	thrust profile: [0.9999991434090886 -0.9999989109820826 -0.18840484920575698; 0.999999642574456 -0.7892776436332918 -0.12931408694138657; 0.9999997178412163 0.5267393788441906 -0.06956780561709845; 0.9999997101961674 0.9999994336962261 -0.018610639490947056; 0.9999995326675502 0.9999996674548184 0.04055505772364419; 0.9999985272401802 0.9999997166093685 0.0964843343858098; 0.5108611241098074 0.9999996665528476 0.11541241396889583; 0.11915209802429379 0.9999995788468198 0.1254892030062545; -0.06577608027600101 0.9999995097151354 0.1358163701800956; -0.15786944384121993 0.9999996754541017 0.1375960485939181; -0.19165177643017128 0.9999893885682953 0.12875243461837188; -0.1283595672922781 0.6138567630147376 0.07671724293817712; -0.012317449010467607 0.047087977571726294 0.006452581509892722; -6.34335149466746e-5 0.00091471809306928 8.53716230858717e-5; -0.0002753957972021203 0.0008379366569403406 0.000253847549893273; -0.00012249698733454806 0.000620864691591944 0.0001747719954028129; -0.0007703906582188425 0.00036864647470518063 -0.00026313495806057455; -0.0003679676279671012 0.000462432306598997 -0.0005969365300740931; 0.00010307940670236174 6.503004811360405e-5 0.00016002455788454703; 5.626567684290205e-5 0.00028538089451470705 0.0003865580217838497] %
+
+Mass Used: 2051.6186645766516 kg
+Launch C3: 5.281454991566764 km²/s²
+||V∞_in||: 1.3616506752322357 km/s

archive/EMS_1.7964973464843803

@@ -0,0 +1,29 @@
+archive/EMS_1.7964973464843803---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-12-28T06:03:36.902
+Launch V∞: [1.9113115422257663, 1.0939752985973668, -0.2878460457456588] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-2.396005235896576, 1.5910968460984156, 2.4553745598827215] km/s
+	V∞_out: [-0.738879248789918, -1.3198053438616348, 3.466044691382917] km/s
+	time of flight: 1.3682159997877434e8 seconds
+	arrival date: 2029-04-29T20:03:35.902
+	thrust profile: [0.935248482226924 0.9999431292980571 -0.1290404928548267; -0.9999476163597248 0.9999515515170286 -0.24823663597926307; -0.8795731397232727 0.11883370193334312 -0.6198238490789577; -0.47255877270571917 0.8460911087046892 0.5425122446091334; -0.8842186442310318 0.9999442668703385 0.632114794955067; -0.9467809827443692 0.7397804470130911 -0.5827972578364147; -0.9202889335527289 0.8035048754026284 -0.5573817193425457; -0.7074755326919293 0.9999898297887988 0.5385761857415082; -0.778563476191167 0.9440695192200221 0.5088248662337462; -0.999935848670154 0.9999298047351639 -0.5166619290742501; -0.7958311273920875 0.4445916834284018 -0.20253835385960575; 0.799628199463289 0.787390476804687 0.10921619103766879; 0.6775585821251879 0.9999859279862128 -0.056976618126330265; -0.9999708212123471 -0.6329649627446755 0.30597984975011394; -0.3379623142939624 -0.9999302294951131 0.5845511928965047; 0.9999796032643747 -0.12435864928204078 0.05360464346939001; 0.9999735389912225 0.9999936940242244 -0.6858853667949919; -0.9999932115686956 0.9999647789195363 -0.4065818129789695; -0.9999828349783968 -0.9999811809194908 0.2562488369803276; 0.8477193677430503 -0.9999888051388031 0.44654176461357903] %
+Phase 2:
+	Planet: Saturn
+	V∞_in: [1.687679365659058, -0.3106760396582122, 0.25789343385832764] km/s
+	V∞_out: [-0.13000691471236564, 0.7123751472156044, -1.4816590595134704] km/s
+	time of flight: 1.3038840000839666e8 seconds
+	arrival date: 2033-06-16T23:03:35.902
+	thrust profile: [0.9999943154178064 -0.9999793447580555 0.06826775331348747; 0.9999973057987236 -0.7577830174110806 0.09936609510988814; 0.9999978386167154 0.999996910634015 0.12385129639736782; 0.9999970143501956 0.9999984909994136 0.18181347514052054; 0.9999901589869835 0.9999988995839434 0.2578219962691517; 0.676991268524474 0.9999990090764392 0.2880018307347756; 0.20873881951717477 0.9999990450745354 0.2788781951149253; -0.003991942078742135 0.9999990863624453 0.27800285072408; -0.10377137001550704 0.99999919042469 0.26254279367539807; -0.11890106720112337 0.7958208463902771 0.19525684108652674; -0.05544439551611033 0.27388175650220187 0.07106727942943497; -0.036288195450646675 0.14031424139484425 0.03530510666426885; -0.004277653916611693 0.016826893422196152 0.004178638953119427; 9.200391005419325e-5 0.004147286559672669 -0.00015203464796320339; -0.0001527325932206235 0.0003004840617325797 0.00013127411825929072; -0.000154649294574425 0.0010525030105100078 0.0008862518960764552; -0.0009285177821710427 -0.0009909987221447562 0.002296370239222059; 0.0005316057188195457 0.0015595065628119108 0.00010356134502627535; 0.0034358308362445874 -0.0028793310522562256 -6.702429154429191e-5; -0.00030910308067229515 -0.0011037999999218894 -7.645215422836016e-5] %
+
+Mass Used: 2067.1392010817217 kg
+Launch C3: 4.932749111438047 km²/s²
+||V∞_in||: 1.7353069659620202 km/s

archive/EMS_1.8179951828877143

@@ -0,0 +1,29 @@
+archive/EMS_1.8179951828877143---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-12-26T20:04:12.197
+Launch V∞: [2.2631654921869386, 1.185081360708154, 0.009257038518396843] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-1.819421900582889, 2.4878162265474044, 1.9652452646560326] km/s
+	V∞_out: [-1.3203444171650183, -0.6998249118520182, 3.335963173120055] km/s
+	time of flight: 1.332502281347756e8 seconds
+	arrival date: 2029-03-18T02:01:20.197
+	thrust profile: [0.9998287069413306 0.9999191371392129 0.1213662202450064; -0.9999116954167637 0.9999384805827953 -0.12816381654311323; -0.8828170417862063 0.8028517826222941 -0.49870520497687526; 0.4565104064071078 0.9273836393237869 0.5018109850322613; -0.6327164570700743 0.999925849841719 0.4784105400321262; -0.830428721827531 0.9619162741068041 -0.4768142744373306; -0.8673070786916957 0.8947170888203538 -0.20042275389292005; 0.006746002981440682 0.9998684851484286 0.44190370405202867; -0.43972848998205877 0.9935765596102941 0.1925917898116161; -0.9998921566708584 0.9999191466596513 -0.28295229283611234; -0.5708873223359694 0.3773361758460382 0.3615474185713707; 0.885961186451299 0.9060683313648012 0.2199266449664907; 0.9998597552900677 0.9999744957399328 -0.6986700034250672; -0.9999501734393813 -0.053191236063163554 0.2422651192105141; -0.2946407843080661 -0.9108509783200093 0.30366986723671646; 0.9999502617365811 -0.6719510540879361 0.08569312009428964; 0.999977035033471 0.9999843531322284 -0.8250795371244247; -0.9999843642335481 0.9999752522544111 -0.38417007411620746; -0.9999749850418986 -0.9911828413853273 0.03074032591695355; -0.7555359458601892 -0.9999499953971228 0.1307993165243738] %
+Phase 2:
+	Planet: Saturn
+	V∞_in: [0.9582177076847339, -0.19699918957632162, 0.15581630117660553] km/s
+	V∞_out: [-0.06497216787939741, 0.36319158740168506, -0.9132347096518814] km/s
+	time of flight: 1.2866032712000416e8 seconds
+	arrival date: 2033-04-15T05:00:07.197
+	thrust profile: [0.9999179790353537 -0.9999061112069662 -0.3847027839240411; 0.9999670827320215 -0.9993196899255067 -0.3520428584517027; 0.9999749413896841 0.10728670306699271 -0.20347892697858028; 0.9999770064758384 0.9999429473541616 -0.15892509767413687; 0.9999642130850989 0.9999708004076064 -0.027062892163153125; 0.9999246588230427 0.9999756917747938 0.09553319711816699; 0.575862503562761 0.9999718804815532 0.16723368288218737; 0.1348698059357536 0.9999631099154952 0.18699745173223745; -0.04347818851670972 0.9999540138326606 0.2054654512161514; -0.12936889157582143 0.999966768321729 0.21144524989026273; -0.1589938838387372 0.9999936224369557 0.1997164588314596; -0.12853648815272445 0.6832485852279477 0.14447679147858372; -0.010355042246881451 0.051188278828012496 0.010667915325539963; -0.0014752719235167427 0.00547355770049997 0.0010936545500989869; -0.0031143585237226163 0.0019098863155813648 0.0007045674243290908; -0.0018146510605806672 -0.0020603912304730005 -0.001272418113780502; -0.0015580679285132912 0.0013209738024154483 0.0008370880567315606; -0.005476076545704018 -0.004478067280660263 0.005715586687551187; -0.0006343098431029113 -0.0020565792501144866 -0.003103123685946313; 0.00014069293580912002 -0.0036504980181857414 -0.010638484561936872] %
+
+Mass Used: 2082.9235875481663 kg
+Launch C3: 6.526421569285769 km²/s²
+||V∞_in||: 0.9905900139445544 km/s

archive/EM_3-29/EM_2022-03-29T21:26:22.750/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T21:26:22.750/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-04-22T09:55:35.770
+Launch V∞: [7.3434961975052575, 2.1070520149056207, -1.014351173307538] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-4.0891408313442243e-10, -1.3519558171080589e-9, -2.9347938509608335e-9] km/s
+	V∞_out: [-1.009960237699357e-8, -1.009960237699357e-8, 7.767450588932219e-10] km/s
+	time of flight: 8.599031774086058e7 seconds
+	arrival date: 2027-01-12T16:07:32.770
+	thrust profile: [0.10180817450485931 0.010765994728988202 -0.007544294859875064; 0.16235850598372423 0.10642344368168269 -0.0003675622257710981; 0.1012089195326011 0.215498048785662 0.009263152266136488; -0.005263860097698059 0.23018146612119708 0.014653161556634695; -0.07216616837405394 0.1886632498893549 0.01482047592832661; -0.09398125027080778 0.12777759796739516 0.011338047777898999; -0.08181401680555038 0.06911303246065172 0.005833525852290107; -0.046580710304300145 0.02548722787737307 -0.000870777813142698; 0.0008108654501895264 -0.002069527547353827 -0.010201717802848145; 0.034561814232433444 -0.014025534635558886 -0.008973491598575703; 0.08747966934536043 -0.003895559625340753 -0.007112515261902957; 0.15550075175184433 0.018424169433452726 -0.005669922341139337; 0.20248982822207362 0.14526574995002947 0.0013158139705482853; 0.1119856201004996 0.257928321038749 0.011672620538172137; -0.013956968702964088 0.25905748898149866 0.016710191647944732; -0.08713823665180384 0.20616330494298554 0.01620667875500915; -0.10696574449396443 0.13889689572070454 0.012648766692620108; -0.09152920511480982 0.07897071043001104 0.008095327395193714; -0.05734765938030889 0.03602736492249166 0.004000200225081728; -0.018669314030212245 0.009667853783132363 0.0010959107001852323] %
+
+Mass Used: 102.10077631610102 kg
+Launch C3: 59.395512899082384 km²/s²
+||V∞_in||: 3.256994044580908e-9 km/s

archive/EM_3-29/EM_2022-03-29T21:29:32.797/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T21:29:32.797/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-23T04:29:27.925
+Launch V∞: [3.3948803973755504, -2.4577679470301823, -0.9108626328289409] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-9.533352172826976e-10, -9.477177141496064e-10, -1.6329568148050564e-9] km/s
+	V∞_out: [-4.993330429282141e-10, -4.2879092581858787e-10, -2.3614363530159443e-10] km/s
+	time of flight: 1.7632014328727353e8 seconds
+	arrival date: 2029-12-23T22:18:30.925
+	thrust profile: [0.03456534559612611 0.003378817240313221 -0.005847373254693159; 0.00947257573188261 0.018201878458255185 0.007200303057438418; -0.004323909654354275 0.01249526284025378 0.0148773281730713; -0.01158118824683763 0.0035968703342061353 0.015269664673521784; -0.014059676447250516 -0.008412132946442719 0.008604541649422459; -0.005532635332091579 -0.0222637656012968 -0.0034383221186402285; 0.021986188048601012 -0.02106400050803527 -0.008639248086466517; 0.017681089333976076 0.009993783002874504 0.003021725433334957; 0.0019228014351383971 0.011070063719295309 0.013061259255238647; -0.006139542196052064 0.004677076522798168 0.015910259868307026; -0.008545089251963688 -0.004479324701411431 0.011537788412234507; -0.0016877898391656034 -0.011682836725100527 0.0011701415189322448; -0.0003566125916268421 -0.01179761558953741 -0.008519419526240076; 0.014749885872094748 -0.0029190252507672954 -0.0019352156873499635; 0.00424054036493813 0.005291076160963761 0.010144665911928733; -0.002562774524319081 0.0018319412240714573 0.0157273231044577; -0.004535441668234806 -0.00482430642022855 0.014079386327258895; 0.0021824954095405903 -0.011442073033427643 0.0056673371449387985; 0.00910349572655102 -0.00026356393299342343 -0.0060482701344148565; 0.0010618127127533534 0.0009141380026824337 -0.006122360667166782] %
+
+Mass Used: 24.97711287513448 kg
+Launch C3: 18.395506929817802 km²/s²
+||V∞_in||: 2.1150803439214027e-9 km/s

archive/EM_3-29/EM_2022-03-29T21:30:57.022/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T21:30:57.022/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-10-12T01:36:00.330
+Launch V∞: [-0.34441487078455013, 3.9103321083115397, 2.032019563693426] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-1.323280834421365e-9, -1.305249079827022e-9, -1.756498248174488e-9] km/s
+	V∞_out: [-2.072434338771005e-9, 3.1188692292717017e-10, -9.96060247089551e-10] km/s
+	time of flight: 1.9187428749374934e7 seconds
+	arrival date: 2025-05-22T03:26:28.330
+	thrust profile: [-0.0006647023892816537 0.004035322252316528 0.002450694309122812; -0.0010810936123367345 0.0033648421104130093 0.003041727879478422; -0.0013507121101609906 0.0028319436906776322 0.003294754033895274; -0.0013817337282281677 0.002283246633035519 0.003911472841560675; -0.0014099790469406482 0.0016622747910402052 0.004243346099566735; -0.0012603732201070137 0.0013617718291820912 0.004609732990326976; -0.001109687893062513 0.0010166792245012248 0.005257291391887101; -0.0009765487656423202 0.0007701050283466614 0.0045962916304727545; -0.0008511110507625 0.0005562454707099463 0.004264167411226241; -0.0007373982279473773 0.00044288704744547956 0.0042335052666390175; -0.0005724074417038922 0.0002590516109966243 0.003593127587839534; -0.00048097983471947337 0.00027784548514532824 0.0036573739539471012; -0.0004010082145124844 0.00023837273061184575 0.00295844216959782; -0.00030319886238157107 0.000188351968848797 0.0026590665546669954; -0.00013453010791864773 0.00015049323913512056 0.002533970064140107; -0.00017918516868998714 0.00011876509991415298 0.0020961759015662375; -0.0001309746244392474 9.400293297511669e-5 0.0016359370993405285; -8.735433670043718e-5 6.50059985134959e-5 0.0011999019334906667; -5.205594667799379e-5 3.959950287622984e-5 0.0007255745258836434; -1.69083877031164e-5 1.3250954732018612e-5 0.0002522304876801491] %
+
+Mass Used: 0.5263628244356369 kg
+Launch C3: 19.53842230774253 km²/s²
+||V∞_in||: 2.5573489052095017e-9 km/s

archive/EM_3-29/EM_2022-03-29T21:33:01.420/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T21:33:01.420/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2023-03-11T16:02:09.080
+Launch V∞: [7.290339628882368, -1.8288440801615886, -6.632030600228825] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-0.003664456556782759, -0.0036510052522354575, -0.0017682821659383713] km/s
+	V∞_out: [-0.1893444115511239, 0.18934441155112372, -0.07646642757306271] km/s
+	time of flight: 9.309960005487782e7 seconds
+	arrival date: 2026-02-21T05:02:09.080
+	thrust profile: [-0.1746457094907778 -0.05324520729862655 0.49134886061939687; -0.627027503294072 -0.40066969942751784 0.5818755748236487; -0.4247709197544459 -0.70455535681447 -0.18137441849457178; 0.39985450427415964 -0.6472758630327436 -0.6430237844213548; 0.4656645028614102 -0.26488366431804417 -0.7314105489598725; 0.1191067639913546 0.2223158565414293 -0.7468478853961351; -0.3933541564722199 0.058176480588614785 -0.7289724142316767; -0.5058338906252844 -0.4156231661282735 -0.5643546902998223; -0.5318185912755031 -0.6386622831457283 0.08080900296257724; 0.27321630774062744 -0.7220941798748955 -0.042143171437234374; 0.5425105272566577 -0.48807460643793443 -0.3531814327468772; 0.3522022888052473 0.06262879123129814 -0.6401364976996247; -0.1561236716305922 0.5164836976614604 -0.7196848157274702; -0.6067507933991897 0.5079757344850814 -0.7392991893046754; -0.7130116758304386 0.10035106755129632 -0.6845824948634448; -0.6878836289874771 -0.5954631055945753 -0.6809457412241607; -0.3269757395259158 -0.7281706083760071 -0.725121591528696; 0.5029082823724691 -0.7211592525685994 -0.6308100968795103; 0.5368458661526178 -0.4216537659711369 -0.14188422812553816; 0.16194407043490938 -0.2071575272584137 0.018329982767622783] %
+
+Mass Used: 633.2884274220719 kg
+Launch C3: 100.4775524563663 km²/s²
+||V∞_in||: 0.005466708610011581 km/s

archive/EM_3-29/EM_2022-03-29T21:44:52.679/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T21:44:52.679/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-01-22T12:08:19.865
+Launch V∞: [9.999999510580688, -9.997198712980596, 0.2367016801977378] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-0.000819918545143649, -0.0012451509155042646, -0.001250921976389137] km/s
+	V∞_out: [0.0019338785602035886, -0.0019338785602035886, -0.0006601321083539838] km/s
+	time of flight: 1.7233962915051136e7 seconds
+	arrival date: 2024-08-08T23:21:01.865
+	thrust profile: [-2.3909756762714905e-7 3.7137254328500285e-7 6.84557970113123e-10; -6.490849187612506e-7 -1.6923622503113822e-7 7.597297006308147e-8; -1.3462011970258392e-7 5.4785730096847575e-8 3.065595287593101e-8; 0.15976947743667638 -0.2920794439050224 0.002394761620150665; 0.5616910709675398 -0.7901992734350411 0.010726222487855458; 1.0 -1.0 -0.0032456678933753843; 1.0 -0.6953371235997132 -0.00807847832727659; 1.0 -0.23068593990468247 -0.009476805297354552; 1.0 0.06616898317798338 -0.009396139547492788; 0.8458292750604345 0.20752997653151717 -0.009416373557718996; 0.4899942520164369 0.18998472141046954 -0.007666776709170746; 0.03957676169176063 0.0210088124260986 -0.0012531497610165998; -5.452577185178014e-7 -3.4799035186607614e-7 -1.0511021967736704e-7; -1.3251613739747719e-8 3.0514099445579054e-7 4.002333800730656e-8; 1.6516923938790852e-8 -9.029916507496571e-8 8.144270988392475e-8; 6.025616118742147e-7 -5.477234118696148e-7 1.5445834673209101e-6; 1.2522336398625811e-7 -1.1634639614565971e-6 3.2890058545783734e-7; -1.8707392087284995e-7 1.037143716480063e-7 2.3487962795435016e-7; -1.0032847526436222e-6 -9.961208338104671e-7 1.0945507651240803e-6; 1.5694593639258316e-6 -4.2952948369892885e-7 -3.8494467904625947e-7] %
+
+Mass Used: 50.813640071233294 kg
+Launch C3: 200.0000000038433 km²/s²
+||V∞_in||: 0.0019461431124315834 km/s

archive/EM_3-29/EM_2022-03-29T21:46:54.102/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T21:46:54.102/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-11-11T17:47:11.536
+Launch V∞: [-2.637789291564701, 7.365806125093766, 1.1946168639279173] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-0.044388255339722446, 0.05279424355864281, 0.05040248633053719] km/s
+	V∞_out: [-0.014690038570962082, 6.047928149069252, 0.0402218040709599] km/s
+	time of flight: 9.338400004077721e6 seconds
+	arrival date: 2025-02-27T19:47:11.536
+	thrust profile: [4.550817449124052e-7 7.763476095695704e-6 -8.951834889878114e-5; -1.683989066220231e-5 6.926242475714976e-5 -2.8801022778955843e-6; -3.2857446755970286e-5 0.000111131319945128 5.116462056209784e-6; -1.8729031546388233e-5 5.436146435025702e-5 8.422047807261321e-5; -3.937488649940267e-5 0.00012696227955243206 -8.532134224201484e-5; -1.0059863865866885e-5 2.4658136117281536e-5 -1.684375841787375e-5; 4.906742377377519e-5 -0.00012829316592757872 0.00011336735200215563; 2.089328062485444e-5 -4.091796173674061e-5 4.91054297730873e-5; 3.6303103564460345e-6 -8.192507389662463e-6 0.00018463100624064758; 9.183017844786658e-5 -0.000102961513685098 -2.2996942742832565e-5; -3.570454906404795e-6 7.063475253086773e-7 4.489457323974194e-5; 4.501722144285221e-6 -1.4070298502410475e-5 0.00012324041685903012; -1.7478055220611036e-6 2.873220524346435e-5 -0.0002474631986841141; -2.3178341505326345e-7 6.162662443854e-5 -0.00036775871159988626; 5.113474717292926e-6 0.00011622972164925676 -6.003368153265286e-5; 3.496467618704115e-6 2.008310733865503e-6 -3.261195379666672e-5; 7.630237920042993e-6 1.1841800841292385e-5 -5.3531357169394734e-5; -2.435474741947106e-5 -3.088566762921298e-5 8.568030368819686e-5; 2.05686426229734e-5 2.1197875883934535e-5 -3.1608864977248355e-5; 2.6389349541919505e-5 2.927984365861755e-5 9.508078462673436e-6] %
+
+Mass Used: 0.00865322013714831 kg
+Launch C3: 62.64014167074321 km²/s²
+||V∞_in||: 0.08542809838298922 km/s

archive/EM_3-29/EM_2022-03-29T21:49:25.266/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T21:49:25.266/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-01-22T05:21:14.524
+Launch V∞: [9.999636707630842, -9.999711031426283, 0.11421476860707167] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-0.0005668718069816592, -0.00031760816291536434, -0.000716139266867567] km/s
+	V∞_out: [4.602661802552677e-5, -0.0002767853386654524, -0.0009253970079822862] km/s
+	time of flight: 1.8504181207751602e7 seconds
+	arrival date: 2024-08-23T09:24:15.524
+	thrust profile: [7.857635262435799e-9 -1.3269126706634187e-9 -2.6678444933858832e-8; -1.0637360281620793e-8 -2.286988515481341e-8 -8.80823866575928e-9; 6.0952069265027294e-9 -2.83469800266583e-8 -1.490175153809855e-8; 0.0226345802482894 -0.0425037954420528 0.00013571022638739796; 0.3150512263564853 -0.3307029057599246 6.642556817831003e-5; 0.7436637294478844 -0.4801347645399363 -0.0017893772307274593; 0.8606779112586623 -0.24141142990090325 -0.0037932113948367296; 0.8040060250257044 0.016198399857395514 -0.004471603451557433; 0.6399746211803117 0.16197029278741412 -0.0044542497883041455; 0.3727551022451268 0.16851762370795223 -0.0032249765404340643; 2.1347115495508663e-7 1.2358201767787164e-7 -9.95030121314948e-9; -3.2446413607840104e-9 -4.6723722793820385e-9 -1.7929106379494995e-8; 5.182519495541647e-9 3.4030707061963687e-9 1.3576577417457207e-9; 7.77921539082814e-9 8.910703811213887e-9 -2.795024270457183e-9; -6.239445899255738e-9 -5.3493145318475e-9 -1.0884699785346293e-8; -4.6105410818633964e-8 1.0422534641378147e-8 -3.1989587412074714e-8; -5.043811123979896e-10 -1.5735249773983739e-9 -2.485221976312311e-9; -2.9761057764991258e-9 5.873921191568738e-9 -9.103537944568155e-9; 5.14444314540825e-9 2.6244355859150998e-8 -4.4579652417185817e-8; 1.7864549904100225e-9 -5.672782066774026e-9 -8.346804698233242e-9] %
+
+Mass Used: 30.632832509893888 kg
+Launch C3: 200.00000000999466 km²/s²
+||V∞_in||: 0.0009669922648350091 km/s

archive/EM_3-29/EM_2022-03-29T21:49:36.826/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T21:49:36.826/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-15T10:56:11.057
+Launch V∞: [6.441902798268679, 10.0, -0.8580312930039031] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [1.1346777920325148e-7, -1.6337616718675993e-7, 1.0330204534180961e-7] km/s
+	V∞_out: [-1.0317733873112507e-7, 2.3171717331048837e-6, -1.93986714938645e-8] km/s
+	time of flight: 3.4632733537038654e7 seconds
+	arrival date: 2025-06-20T07:08:24.057
+	thrust profile: [-1.6714820918342543e-8 -1.528466539382287e-8 -2.1954025843586096e-8; -3.349740604524035e-8 1.7981805687302658e-7 -7.022649953046174e-9; 1.8833170950448843e-8 8.548553623260635e-8 -4.108646810746605e-9; 0.015250670354150446 0.8084120898285189 0.022810952919723303; -0.4471453131878308 0.9999999903024106 0.04006905981158459; -0.940578331193299 0.999999993466643 0.0463151648707486; -0.9999999926560775 0.8872505298154237 0.043065678915645736; -0.9999999865564515 0.5078822642356666 0.04002774379588722; -0.962703858267274 0.25286276492713566 0.031382869157176016; -0.7756546264427393 0.08215017131953659 0.018158411737504068; -0.5391748150704597 -0.00685832535402532 0.010123577086814562; -0.28342464446445065 -0.029810747488727737 0.006770186169348639; -1.123224049355356e-8 -1.3141710495594749e-8 -1.7542653699628666e-8; -1.7528478886241226e-7 5.358445351823748e-9 -6.699375227774894e-8; -1.3135303081170559e-7 -1.2185271425829965e-7 -3.228097411495359e-10; 1.1373627184214759e-8 3.001014188079098e-8 -2.51036875849398e-8; 3.6364423359808617e-12 -1.1453961586869118e-7 3.15681037477465e-8; -2.2731576792249495e-8 -7.140875056921905e-9 -4.234566273922648e-9; -8.105071719032486e-8 -1.2311649733884225e-7 5.2532523546505e-9; 3.7930997639741155e-9 2.2050999807275034e-9 -1.6994076482759186e-8] %
+
+Mass Used: 114.99761554896395 kg
+Launch C3: 142.2343293621158 km²/s²
+||V∞_in||: 2.2413839807974726e-7 km/s

archive/EM_3-29/EM_2022-03-29T21:49:40.929/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T21:49:40.929/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-07-14T20:37:13.182
+Launch V∞: [-1.1330208167169828, 8.150093305408548, -0.42599383797196094] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [0.06785386315763219, 0.08160526029107552, 0.10069188976102801] km/s
+	V∞_out: [-0.06019693846168101, 0.1154681190090172, 0.0013638641321443625] km/s
+	time of flight: 3.3249599821579646e7 seconds
+	arrival date: 2025-08-03T16:37:12.182
+	thrust profile: [-3.2390308133578046e-6 -8.205592041810102e-7 -1.7023725789005115e-6; -4.254648394564359e-6 -1.0681074705420982e-5 7.03349069144519e-6; -3.6503599525277004e-5 1.211591857880556e-5 4.998821545861222e-5; 5.8142912412027884e-6 1.815497639490963e-5 4.755326622471413e-6; 2.1131283188873194e-5 -2.658343343429692e-5 -1.3407885571598285e-5; -4.61924068664863e-6 1.233572876146752e-5 5.931451952243551e-6; -1.0093023108865622e-6 -6.117529097643235e-6 -1.4487022912767236e-5; 3.255742051919883e-5 2.414843899996706e-6 -1.6802467693339598e-6; -3.755099218079546e-7 -7.03737787215465e-6 3.678113986874362e-7; 5.000413950443672e-6 -6.750857750004181e-6 -3.69195982831641e-6; -4.843006060165484e-6 -3.981873834068709e-6 -8.39506817046051e-6; 1.9138464837736528e-5 -1.1967250409666853e-5 -5.84236755572486e-5; 1.9835599971523244e-5 -7.450220189850961e-6 -3.2160727631147586e-6; 5.835552646320366e-6 -1.8859087544603728e-5 -9.49615711370029e-6; -2.455723410768635e-5 6.327003737755019e-6 -1.2577725131349784e-5; -5.262439904045446e-6 6.952002003737397e-6 -6.5460093506210335e-6; 1.29796109554274e-5 1.82478532330856e-5 -1.5041887536003234e-5; -9.627406878153045e-6 -5.772049645592626e-6 -1.4348219890042947e-7; -9.78894081123465e-6 3.3042544258109555e-5 1.5879718352840226e-5; -5.425039696689593e-7 -9.226404572856256e-6 9.61839430152342e-6] %
+
+Mass Used: 0.006099916057792143 kg
+Launch C3: 67.88922780796933 km²/s²
+||V∞_in||: 0.14629566608835642 km/s

archive/EM_3-29/EM_2022-03-29T21:51:28.498/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T21:51:28.498/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-09-29T06:36:19.325
+Launch V∞: [-2.587284640962116, 4.633341500696843, 1.7167586419161047] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-0.19753746109783032, 0.25819074680887755, 0.26503536879040035] km/s
+	V∞_out: [-0.315758776271297, -0.8539914904213332, 0.8539914904213984] km/s
+	time of flight: 1.5073200002586758e7 seconds
+	arrival date: 2025-03-22T17:36:19.325
+	thrust profile: [-7.450599065824146e-9 -7.450584303466995e-9 -7.450590836663176e-9; -7.450587576906885e-9 -7.450589090923008e-9 -7.450558189003243e-9; -7.450565194803655e-9 -7.450611457729077e-9 -7.45054991590754e-9; -7.450600513649451e-9 -7.450590716301945e-9 -7.450607153363093e-9; -7.450528020006835e-9 -7.450561990165038e-9 -7.450526461597745e-9; -7.450555250204573e-9 -7.450607011409635e-9 -7.450602548674602e-9; -7.450564628439462e-9 -7.450600629100434e-9 -7.450588565463268e-9; -7.450619650423247e-9 -7.450608473513382e-9 -7.4505692480758075e-9; -7.45064263594121e-9 -7.450567115419777e-9 -7.450562075663264e-9; -7.450580126235538e-9 -7.450587476295809e-9 -7.450568854754488e-9; -7.4505366612824064e-9 -7.450589324902333e-9 -7.450584239263405e-9; -7.450489666957581e-9 -7.450537925286817e-9 -7.450498460628677e-9; -7.450552685353022e-9 -7.450579447503591e-9 -7.450633939663657e-9; -7.450616725224094e-9 -7.45060730810255e-9 -7.450610502067296e-9; -7.450581072447471e-9 -7.4505612150820725e-9 -7.450606871304834e-9; -7.450563685058705e-9 -7.450550577646896e-9 -7.450584512906325e-9; -7.45058338424796e-9 -7.45058208960814e-9 -7.45059162827976e-9; -7.450547249176265e-9 -7.450555252809561e-9 -7.450551428356576e-9; -7.45060469168066e-9 -7.450619817820747e-9 -7.450626574693086e-9; -7.450591348730228e-9 -7.450569077582649e-9 -7.4505992975666e-9] %
+
+Mass Used: 1.549092758068582e-6 kg
+Launch C3: 31.109155510031766 km²/s²
+||V∞_in||: 0.4194368331281437 km/s

archive/EM_3-29/EM_2022-03-29T21:58:30.321/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T21:58:30.321/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-12-10T18:17:03.345
+Launch V∞: [-0.22142913746497983, 8.613702367564114, 0.395646369589788] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-0.003807700964755288, -0.05635954129158412, -0.008059749565666045] km/s
+	V∞_out: [-0.004673762071972183, 0.023969198600263253, 0.0032827185153388007] km/s
+	time of flight: 2.211840042633046e7 seconds
+	arrival date: 2025-08-23T18:17:03.345
+	thrust profile: [-2.7099961488351806e-5 -1.4871074056565297e-5 -2.4409683044127975e-5; 9.646611740529691e-6 -0.0003420396277143331 -1.4868108643254946e-5; 2.133935422770787e-5 -4.4306217453697985e-6 -4.803508959276009e-5; 2.4459845792704493e-5 -3.6995123289765117e-5 -2.9925040076576046e-5; -3.650950167903471e-6 -7.838803352580581e-5 2.4747499455879648e-5; -6.523041671648795e-5 3.5087934323253556e-6 -2.4005599476677803e-5; 2.5824401386028627e-5 -5.305113471826212e-5 4.630647640937965e-5; 3.106981203665597e-5 3.544948660180863e-5 5.523446183421823e-5; 5.22286273436312e-5 0.000123040814806458 -0.00012676926781162037; -7.230267382777404e-5 -0.000260285686999283 0.00028378411056846934; -6.687818964937921e-5 0.00010386642943476749 -1.7433504223833023e-5; 1.628396440937132e-5 9.706470918419143e-6 -2.010464752776144e-5; 1.7691694085809603e-5 1.8769928239818888e-5 8.64374415484856e-5; -1.9940109128613944e-5 -2.4978683584950083e-5 8.154400491960929e-5; 3.746496390446149e-5 -7.996841154215747e-5 8.731190252691787e-5; 8.384626723016047e-5 0.00012055180341030887 -9.12903721447452e-5; 0.00030557244279303915 -1.0874417231438263e-5 0.00027076266521899666; 0.00010797337086871226 2.418131034629288e-6 2.46314050788356e-7; -4.8544246038547224e-5 8.023388406493804e-6 -1.3321622294600293e-6; -2.1337222473883922e-5 0.000161247930621023 -9.715049457277587e-5] %
+
+Mass Used: 0.024185192960430868 kg
+Launch C3: 74.4014353896677 km²/s²
+||V∞_in||: 0.05706010904560232 km/s

archive/EM_3-29/EM_2022-03-29T21:59:56.201/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T21:59:56.201/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-11-02T06:44:24.402
+Launch V∞: [-0.049611423370383025, 4.3887768099156235, 0.2397844149782377] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-0.28117135821620853, 1.194065776563358, -0.1878338484580809] km/s
+	V∞_out: [-0.6401552299219904, 1.0676650444881157, -0.004843562733730455] km/s
+	time of flight: 2.8675341966952853e7 seconds
+	arrival date: 2025-09-30T04:06:45.402
+	thrust profile: [-6.75010685435156e-9 -7.128389367903114e-9 -6.764569952771536e-9; -7.854492591597582e-9 -7.999190980986096e-9 -7.56171297045386e-9; -7.411321266505082e-9 -7.3114050701082215e-9 -7.55580573230112e-9; -7.651530680516069e-9 -7.666997827122132e-9 -8.49436628413585e-9; -8.211778239957757e-9 -7.712874354717269e-9 -7.531646409796486e-9; -1.3041223632506712e-8 -1.1505347567528765e-8 -1.1327175955299429e-8; -7.4382917597938215e-9 -7.470595276285478e-9 -7.436526503122886e-9; -7.4066384907957325e-9 -7.477391356913722e-9 -7.393627041672364e-9; -8.490728461637439e-9 -7.447948593375514e-9 -8.223435454942976e-9; -7.243567265436005e-9 -6.990848569720015e-9 -7.311069521989123e-9; -7.470925069700345e-9 -7.517096742281904e-9 -7.2858921115831336e-9; -5.251447999281985e-9 -5.273780973491265e-9 -6.675361320542912e-9; -7.558627194101523e-9 -7.492146820031137e-9 -7.45645012297696e-9; -7.2878343544302096e-9 -7.2766617254979426e-9 -7.221830929334092e-9; -1.5590145011707196e-9 -1.974892338935215e-9 -1.3189839304906718e-9; -4.649692239474741e-9 -5.02145900568508e-9 -3.3671118225301505e-9; -7.850732664606476e-9 -7.768068826428585e-9 -7.4479836858425065e-9; -7.24166072771011e-9 -7.280881665927263e-9 -7.234374477741455e-9; -5.484578641350827e-9 -5.45192526011684e-9 -5.410771310297238e-9; -7.621367481763838e-9 -7.564226463702764e-9 -7.592122009986836e-9] %
+
+Mass Used: 2.8080553420295473e-6 kg
+Launch C3: 19.321319746248445 km²/s²
+||V∞_in||: 1.2410205341039189 km/s

archive/EM_3-29/EM_2022-03-29T22:02:40.626/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T22:02:40.626/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-12-05T12:41:35.605
+Launch V∞: [0.34208345982054794, 9.685722102267114, 1.0135726196799333] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-1.044189695816697, 5.606992695460721, 0.6669749140025341] km/s
+	V∞_out: [-1.663147851968031, 4.139628155579746, 0.7399548282520139] km/s
+	time of flight: 1.1581200001669213e7 seconds
+	arrival date: 2025-04-18T13:41:35.605
+	thrust profile: [-4.6079105664078877e-5 -0.00012331290696458524 3.857290588633784e-5; 1.080629253868903e-5 -7.862558725402423e-5 -1.577782579822753e-5; 0.00012294508889228685 0.0001157766111977547 -7.561217621375722e-5; 7.982229075851814e-5 -3.220285538923316e-5 -4.4317366310939693e-5; -2.379024823156827e-5 -7.848301760916924e-5 1.0173976438826385e-5; -5.0258317369872474e-5 -9.493318759847104e-5 2.0214040124684093e-5; -5.091418646156128e-5 -0.0001217205174737956 1.2898657418352046e-5; 2.8918514216456975e-6 4.8713183689657356e-5 8.218982364067898e-7; -7.013970277251351e-5 0.00016984599894599242 4.472426555147454e-5; 4.101982487628375e-5 -0.00014567448690259096 -4.20309304000344e-5; -4.70029927248979e-5 -8.284004507475568e-5 1.8925597178656232e-5; 8.670365778542101e-5 7.723828389414057e-5 -4.728960557142774e-5; -1.1273042710496325e-5 1.5796318007177794e-6 1.004719027628209e-5; 1.156788959809497e-5 -9.12107530024284e-5 -4.421958910455016e-5; 5.8489607768559684e-5 -3.186318691478282e-5 -7.568690979128904e-5; -4.101390839132036e-5 -6.912092662580811e-5 1.875683893727222e-5; -9.282793252271017e-5 1.8581365311066747e-5 0.0001607242504965489; 2.5608653889505896e-5 2.5749263651290097e-5 -2.663654795135107e-5; 6.471735913709624e-6 -1.582848279061017e-5 -3.144105357929748e-5; -2.0418356210322056e-5 -5.206011476136069e-5 1.0750219832116774e-6] %
+
+Mass Used: 0.009526397249373986 kg
+Launch C3: 94.95756319119332 km²/s²
+||V∞_in||: 5.742260421097979 km/s

archive/EM_3-29/EM_2022-03-29T22:11:59.808/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T22:11:59.808/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-07-12T14:57:14.038
+Launch V∞: [-2.1356055281697612, 10.0, -9.769298185542464] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-1.4198898735875047, 1.3740951409636546, -1.4192321863480188] km/s
+	V∞_out: [1.4110404995307853, -2.1212048062899553, -0.6728408923695377] km/s
+	time of flight: 1.5440221824979678e7 seconds
+	arrival date: 2025-01-07T07:54:15.038
+	thrust profile: [0.05956977091681903 1.0 -0.10922677780373319; 0.23817833345981507 1.0 0.09826946570814477; 0.40293966085543176 1.0 0.3551237041998419; 0.5317072540959735 1.0 0.7307023601163831; 0.5078043727484851 1.0 0.9982992529843099; 0.33655425425041224 1.0 1.0; 0.1360349738666649 1.0 1.0; -0.026672364591518467 1.0 1.0; -0.19610649486002443 1.0 1.0; -0.29528444695253986 1.0 1.0; -0.35123463549962813 1.0 1.0; -0.3634631832054668 1.0 1.0; -0.34243556937322644 1.0 1.0; -0.2988969593988343 1.0 1.0; -0.23211645533604322 0.8701239790258618 1.0; -0.13699199073043578 0.48199643592034935 0.6802560133378645; -4.9400538315483375e-8 1.4543622135653008e-7 2.2274035599587473e-7; -2.6590282235167093e-8 6.069199505306199e-8 7.406086114073912e-8; 7.262188061710368e-8 -2.6660015831706114e-8 -1.054025466018286e-8; 7.299781920337516e-9 5.276251956583804e-9 -2.5519508317922344e-8] %
+
+Mass Used: 130.30806476829775 kg
+Launch C3: 199.99999800999254 km²/s²
+||V∞_in||: 2.432785380649605 km/s

archive/EM_3-29/EM_2022-03-29T22:26:29.640/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T22:26:29.640/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-10T14:47:37.584
+Launch V∞: [8.454590640928295, 9.260765024912534, -0.9885318724952183] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-0.006319696103929528, -0.0412349395695302, 0.025407019305862494] km/s
+	V∞_out: [0.022415695471427622, -0.032554221329412304, 0.028687979305271248] km/s
+	time of flight: 1.8230010689416587e7 seconds
+	arrival date: 2024-12-07T14:41:07.584
+	thrust profile: [-0.0002622529733463554 0.00010449975350988813 -0.00012030102951252053; 2.2564340820408038e-5 -3.981832926552484e-5 -7.923191359546866e-6; 5.169422416636556e-5 -5.810036687510864e-5 0.00011428268526115506; -0.00014971921355914664 -0.00014100200005065646 0.00016890254129742059; 0.00015620328410727985 -3.366292385390309e-5 -0.00020340087014733029; -3.210609078978168e-5 -6.498562052193143e-5 5.338807325839352e-5; -8.516237377437068e-5 -0.0001612296252470605 4.209812632127493e-6; 6.305171484191589e-5 -0.001682367723787057 3.8599641512170114e-5; 2.2345674659450702e-5 6.798172919803859e-5 -0.0001184406426706027; -1.6251278244512348e-5 -6.533351590187232e-5 -3.92438433311786e-6; -0.00036512149400096404 -4.6068321314717516e-5 -5.609213629078427e-5; -5.621377289755845e-5 2.1241246976381148e-5 -3.414115489177037e-5; -0.00034119461694600184 -6.972852980194507e-5 2.2003699273903694e-5; 0.00018976563510694219 -9.050300294247073e-6 0.00012300348192681063; 5.426150865573059e-5 -0.00010044444909460297 4.785290273646994e-5; -4.4309429079208605e-5 7.02628779669344e-5 -4.7916743218706474e-5; -8.408538773370183e-5 -4.412949196949812e-5 2.4492265814848663e-5; 0.00011172380033234707 6.642438716286984e-5 9.399896039444412e-6; 8.401331768830077e-6 4.877367093015932e-6 -1.2408399381198787e-6; 9.503407085636648e-5 -0.0002551562074474474 -1.3659784774574114e-5] %
+
+Mass Used: 0.03575572314321107 kg
+Launch C3: 158.21906701525444 km²/s²
+||V∞_in||: 0.0488444001924202 km/s

archive/EM_3-29/EM_2022-03-29T22:29:19.608/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T22:29:19.608/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-10-10T01:24:19.159
+Launch V∞: [-1.361280774218496, 4.248905515475195, 1.6131303371846983] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-1.3206429765527528, 0.04508054081073763, -0.10860236471971149] km/s
+	V∞_out: [1.3258015388055073, 0.008890670618699885, -0.015202352520394155] km/s
+	time of flight: 1.6044052824580787e7 seconds
+	arrival date: 2025-04-13T18:05:11.159
+	thrust profile: [-9.649476733530478e-5 -3.874129604104022e-5 0.0001243676257598534; 0.00017944991783773494 -0.0003021068710903314 -0.00023906829442885233; -1.2520197657221369e-5 7.529839362963302e-5 5.22491643077963e-5; 6.0473365960938625e-5 -0.00010443015036179195 0.00013074051319186437; 0.0006044516898117107 -0.00017952114259198458 7.975422345770218e-5; -1.5105320951034641e-5 5.488422632601538e-5 -3.480125630187902e-5; -0.00035693490512667196 -2.9324170471654634e-5 9.386409045588269e-5; 0.0006536233376695634 -0.000323215551438777 -0.000991075858075292; -0.00048048705998534366 -0.0008846136053753608 7.485312552148982e-5; 0.0002457539906734169 2.3610783147200267e-5 0.00031354855012369744; 0.0003084291416236774 0.00030133549870160124 0.00012216085485925468; -3.145870054396133e-5 9.600064248608948e-5 -0.00017139285888021958; 0.0002323428803906647 -0.0003932431132474737 -0.00038269549666544874; -9.648756923300717e-5 7.371414257236465e-5 -0.00010492608262327025; -0.00016513882219009883 5.681301427250039e-5 -0.00023413816734468073; 0.0001688227002363334 3.9296604381294236e-5 -0.0002465079878323193; 4.223349001330004e-5 0.00018462477409466818 0.0004274596352430292; -7.266996009870076e-6 -0.00023420474628868667 3.054421622059266e-5; 4.4599716714522025e-5 -0.00015080232626015259 -0.00017624139057002226; 2.058233894174994e-5 -2.9681895453803056e-5 0.00010285445493880417] %
+
+Mass Used: 0.04864906937473279 kg
+Launch C3: 22.508472910438055 km²/s²
+||V∞_in||: 1.3258674897215847 km/s

archive/EM_3-29/EM_2022-03-29T22:35:03.801/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T22:35:03.801/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-10-15T00:59:25.735
+Launch V∞: [0.08411754828864794, 3.867780292357817, 2.507975455218117] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-0.01111567461793714, -0.2019526290080634, -0.10099494494608693] km/s
+	V∞_out: [0.05863131293194478, -0.1437072200747788, -0.16341819092150492] km/s
+	time of flight: 2.122969403809613e7 seconds
+	arrival date: 2025-06-17T18:07:39.735
+	thrust profile: [-0.0019253353195135495 -0.006208595765491277 -0.0030413706831210283; -0.005094954059343889 -0.006884862652799308 -0.007716049803660748; -0.001169679362784149 -0.003040509785898553 -0.0023827736029818115; -0.0009800602675577555 -0.005005973318342694 -0.0007235675342944551; -0.0035541375195941027 -0.0010759580832810519 -0.0011368932928665326; -0.004023727803229634 -0.0024144419030426778 -0.0020601786180336804; -0.009415901341030907 -0.007648304620004416 0.008910953721132594; 0.00019160911662570728 -0.00041311185476429913 0.002747155966524439; -0.0005053512629044138 -0.000435305465528584 0.0010810134121178056; 0.0018400336528207576 -0.006748721129952468 0.002259933413232509; 0.00022745932395296879 0.010666778341568943 0.0035537786550811704; -0.0004423321131218159 -4.1278833244748e-6 0.0012966352168264361; 0.00584099379819922 0.010506361039734275 0.0023162665551785394; -0.0013489272396317838 -0.0016553055603146898 0.00247736021958195; -0.0003060718810677023 0.0030689000185227426 -0.00026453391075189313; -0.004902002300222478 -0.006091743775746333 -0.0007723370782334376; -0.0010727586684161662 -0.0015117821322166705 -0.0011100152254532457; 0.001981284413785558 0.002082711629710382 0.000757647029883398; 0.0002652136199514425 -0.004511943969868106 0.0007431379304516129; 0.0007883244474613861 -0.00476964812130089 3.034140598992801e-5] %
+
+Mass Used: 0.9889560483511559 kg
+Launch C3: 21.256741035858134 km²/s²
+||V∞_in||: 0.22607167334751047 km/s

archive/EM_3-29/EM_2022-03-29T22:38:25.802/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T22:38:25.802/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-10-07T17:37:26.448
+Launch V∞: [-1.132800064227913, 4.057296625668816, 1.8160423657393692] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-0.09025126720242063, -0.16294649165165395, 0.002018029101130675] km/s
+	V∞_out: [-0.18204756492089805, -0.026081869886201665, -0.0286582298370937] km/s
+	time of flight: 1.7138821243684784e7 seconds
+	arrival date: 2025-04-24T02:24:27.448
+	thrust profile: [-0.001053336200227854 -0.00028654474915887655 -0.0003820424031938627; 0.0008512529608243817 0.0008846317646016004 0.00025282033285603365; 0.00042096876484458586 -0.000407673670480482 -0.000928628092675361; -7.585307650884643e-5 -0.00013518461742213344 0.00156643510514752; 0.0008460627785635593 -0.0007843263217494761 -0.0007202803479853547; 0.002018749793184083 -0.00017983404176264242 -0.0006659097248956292; 0.00040668294946816447 0.0009420606711834561 -0.0007751842339076142; -0.0002948940003770048 1.1828072211327191e-5 -0.00013445879115795128; -0.0004411373325257146 0.002302823369497903 0.0007032460495624283; -0.0004305359949988352 0.0003086368359122586 -0.00012577020060691192; -0.0004796057040344445 0.00048325375373444216 -0.0012858708318398222; 0.0007082846291908338 0.0014131843493881463 0.0012334716036545182; 0.0007516628476279127 0.00019283672154011742 -0.00047698959544296255; 2.8585166048847224e-5 0.0004721397839283915 -0.0004494052618972365; 3.140121868826565e-5 1.8672409758238784e-5 -0.0010892419657405827; -0.0012387600934636242 0.0010224726118372646 0.0005096784526400515; 0.0004830392791164112 -0.00018504611294579005 -0.0007919144470676173; -0.0002823515956750592 0.00015118295801919124 -0.0004211043216927825; 0.000699667738192727 0.0008572250810665738 -0.00044787467026235686; -0.0013106710074165672 1.8187501171149852e-6 -0.0013087579926788614] %
+
+Mass Used: 0.17400800233144764 kg
+Launch C3: 21.04290176833857 km²/s²
+||V∞_in||: 0.18628183704988058 km/s

archive/EM_3-29/EM_2022-03-29T22:49:56.957/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T22:49:56.957/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-09-12T20:18:50.704
+Launch V∞: [-1.2901325972737976, 3.5232401246782135, -4.555427856822656] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [-0.47357409467459016, 0.6120735570744102, 0.2493748383223478] km/s
+	V∞_out: [-0.5474046060397546, 0.593375716049692, -0.4503838007744617] km/s
+	time of flight: 2.33568000005211e7 seconds
+	arrival date: 2025-06-10T04:18:50.704
+	thrust profile: [-3.7741093121961535e-8 -2.6257971335176648e-8 -2.1606384855810645e-8; -2.1363083523959785e-8 -4.234571308044473e-8 -8.269824340036801e-9; -1.7179727443085232e-8 -4.817903392853783e-9 1.1405733095493886e-8; 6.543773827193354e-8 7.63399812774497e-8 3.918240890364693e-8; 1.3414420888442994e-8 1.4060087327107107e-8 -8.242716667432803e-8; -1.8088388278070475e-10 -4.1359611682043475e-10 -9.03470171888568e-9; 4.3064264083954854e-9 3.2442366380236367e-9 -1.598356883588943e-8; 3.261934834405667e-8 6.450483621536437e-8 8.2007353416575e-8; -1.7993125019529573e-8 3.862145335097065e-9 5.231141768695811e-9; 2.5346874206765178e-8 2.0165133642770633e-8 5.961057304477184e-9; -1.8904868856526572e-8 -1.201092354618878e-8 -2.4170378084370648e-8; -1.1110813643371359e-8 -9.930972424447597e-9 -2.2310217231961474e-8; -2.3010965850571813e-8 -4.590923869358927e-9 -5.082758311888812e-8; -1.064446394813755e-8 -1.6835335671720645e-8 -4.524794179174139e-8; 1.6919283931076332e-9 2.0866300176185552e-9 -1.1111279350528446e-8; -4.352351680251087e-9 -5.215082497858078e-9 -1.2228449319478551e-8; 6.0054113300816905e-9 -7.05448971432868e-9 -5.6941027568265595e-9; -1.951082125424566e-8 1.1499547353566501e-8 -5.019589935213733e-8; 1.197134200084507e-8 -2.127430780809517e-9 4.800535709688631e-9; -1.311850186946498e-8 2.508766374053081e-8 3.5397163567430844e-8] %
+
+Mass Used: 7.579702014481882e-6 kg
+Launch C3: 34.82958605340684 km²/s²
+||V∞_in||: 0.8130770396493041 km/s

archive/EM_3-29/EM_2022-03-29T22:58:44.883/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T22:58:44.883/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2023-04-14T07:05:59.170
+Launch V∞: [1.6949045581275466, -1.1749158457323354, 0.4459844940604056] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [0.2807404173223861, -0.5148397948760617, -0.024574238754993954] km/s
+	V∞_out: [0.4816521199334624, -0.31105824990728403, 0.021223537272540942] km/s
+	time of flight: 1.0181159999765144e8 seconds
+	arrival date: 2026-07-05T16:05:58.170
+	thrust profile: [1.4156868146913603e-5 -8.937824771836181e-6 -1.4258721529256393e-6; 6.201501805968712e-6 4.891054084739865e-6 -2.4147768084891413e-5; 8.710377800639082e-6 -2.5247715656786118e-5 -4.228464809233087e-5; -5.49592858423698e-6 -5.956986519709633e-6 -6.0003598197038516e-6; -2.2049093171105036e-6 -2.489010425867444e-6 -3.9225913222362265e-6; 2.1078914306123458e-5 -1.1944173566312533e-5 1.8244198561717057e-5; 1.9561991087389005e-6 -1.1752657963774734e-5 1.683487450213938e-5; -6.055159240369156e-6 -2.206637657527475e-5 1.5277910735365964e-5; -2.1063568637137504e-5 1.0199794653949234e-5 -1.0165697723410959e-5; 0.0006945866286583284 -4.8718537131140276e-5 -0.0010004798714153944; 3.549819219472579e-6 -5.173787731590263e-6 -8.794510883495692e-6; -1.1187037009877784e-5 3.9873466996776687e-7 -1.2842230899218392e-5; 1.819371322436169e-5 -1.985114604615626e-5 7.40305445774715e-6; 4.351771410931808e-6 -1.2633771406394241e-5 4.02517242765969e-5; -0.00021811083392391314 -0.006360908650050679 0.007451776526230452; 0.4683451802604527 -0.7651039839559246 0.09069086407503833; 0.8713044694433868 -0.27831401933737787 -0.20462753606922815; 0.012344351227493076 0.0030669853424402133 -0.014728214668807213; 6.768683876914276e-6 7.65498676530381e-6 -2.3634699931764597e-5; 5.463932969042515e-8 1.6589754704890928e-6 -6.114493334584618e-6] %
+
+Mass Used: 75.80031539540141 kg
+Launch C3: 4.452030874656779 km²/s²
+||V∞_in||: 0.5869234102647126 km/s

archive/EM_3-29/EM_2022-03-29T22:59:31.051/mission

@@ -0,0 +1,22 @@
+/home/connor/projects/thesis/archive/EM_2022-03-29T22:59:31.051/mission---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2023-12-23T04:52:28.411
+Launch V∞: [-2.3721677208600336, -1.1471540814232561, 1.82724714241875] km/s
+Phase 1:
+	Planet: Mars
+	V∞_in: [0.7657978493736273, 0.47268498190867225, 0.5669638080447448] km/s
+	V∞_out: [0.671344291602754, 0.7165876747149759, 0.4086328277033566] km/s
+	time of flight: 6.692110088878082e7 seconds
+	arrival date: 2026-02-04T18:04:08.411
+	thrust profile: [0.0008233730574660627 -0.0006089913686355275 -0.0003656792494954692; 9.277035119329392e-5 0.00018105994933842137 -0.00045064421020144603; -0.0009643656591043792 -0.0005295771327107068 -0.0003527133652685661; -0.0001829291084087302 -0.00028713103539127654 -0.0011612339233188311; 0.0002628094997902115 -0.00038049047451517036 -0.0004438420586700227; 0.00022847673868341134 -8.081668903608331e-5 -0.0004169573293423967; -0.00024469370633056417 -6.337239455279198e-5 0.0008380473882381952; 0.0007752101556583943 0.0006834443935228009 0.00015265143847038387; -5.4459788825500716e-5 -0.0014820986794018846 -0.0012653925633815618; -0.00021218967607504187 -0.00020847681093790597 -0.0002734855651715473; -0.00017082953277056904 -0.00011256508693154773 0.00152134489853549; -0.0007743596333968497 8.88770635961271e-5 0.001957585876424173; -0.0009465135793430943 -0.0008606487267644376 -0.000381605440474747; -0.002413182432020938 -0.0026073704810047824 -0.00027904268175806847; -0.0005254492375900773 -0.002157747734677348 -0.001799801241758866; -0.0005194698886906513 -0.001005331073405558 -0.0013843897937889358; 0.00048689741373146193 -0.001401700406807511 -0.0024375166130219906; 7.266464024313168e-5 -0.00033741672866423523 -0.0004478141428623512; -0.000586239166722991 0.00012793840622519977 -0.0009074360302595961; -0.00018809051058659194 9.565179941071708e-6 0.000633927457634841] %
+
+Mass Used: 0.7381269704351325 kg
+Launch C3: 10.281974301893808 km²/s²
+||V∞_in||: 1.0636378132897837 km/s

archive/ES_0.5550120742732497

@@ -0,0 +1,22 @@
+archive/ES_0.5550120742732497---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T21:35:13.618
+Launch V∞: [8.092028247187812, -5.690394550179761, 0.15870337020149677] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [0.007258340410626599, -0.004915549405160574, -0.0003090327712008995] km/s
+	V∞_out: [0.0063943921161191295, 0.0029021314271309787, -0.005208376883488668] km/s
+	time of flight: 1.8749577773970667e8 seconds
+	arrival date: 2030-04-23T23:44:50.618
+	thrust profile: [0.23623549046119796 0.001523213801416841 -0.0746418855277079; 0.04989778371798442 0.028557974139368027 -0.05866465575542369; 0.035473791749751 0.032507089227488954 -0.0752484296384085; 0.022627986747173957 0.026966919764486865 -0.07156789250913552; 0.04964790396262216 0.0738833298025964 -0.19559483393516622; 0.030631999959579347 0.05365872568512533 -0.15864114884262576; 0.00671793812371244 0.012495789298607023 -0.044004855933096255; 0.006194981641432508 0.01299461151504057 -0.04773667381981179; 0.0013970455272782531 0.0035097621778593085 -0.014148581638031872; 0.0014625087521359605 0.004576093171820035 -0.01812047518926974; 0.0003621287391874434 0.001192919920759847 -0.003924447420406894; 0.0003136102108716024 0.0009510767434047032 -0.003683238027775159; 3.55672194873085e-5 0.0002056947097665128 -0.0009531573613879192; -0.0002219678836028774 0.0002992512020633661 -8.263424581589065e-5; -4.180089723821831e-6 8.500643051220536e-5 2.6176105870720138e-5; 3.966745018590377e-5 5.7559670861396866e-5 -0.0004168195496730593; 0.0002960669240380866 -0.00015608457398720793 9.887024972396908e-6; 2.993253329593611e-5 -0.0001879527007887196 -2.49699959259209e-5; 1.3018003450243295e-5 9.194287517786575e-5 -0.00012566784156294738; -0.0002730423797779337 -0.0001543084966874625 0.0006099289590901544] %
+
+Mass Used: 76.50834802879126 kg
+Launch C3: 97.8866980497143 km²/s²
+||V∞_in||: 0.00877163797273837 km/s

archive/ES_0.5550208270049417

@@ -0,0 +1,22 @@
+archive/ES_0.5550208270049417---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T18:10:53.965
+Launch V∞: [7.99263082663398, -5.710825212380063, 0.28059984202471117] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-5.081837842560198e-10, -8.526455361768017e-10, -1.1565873973246667e-9] km/s
+	V∞_out: [4.964101468366639e-10, -4.5035093005423074e-10, 1.7219192649203768e-10] km/s
+	time of flight: 1.8749577787459874e8 seconds
+	arrival date: 2030-04-23T20:20:30.965
+	thrust profile: [0.32604352432509304 0.00497882797405257 -0.10153659307532245; 0.08445557926807248 0.04770044497023833 -0.09876572943386014; 0.033814070938876443 0.03018025570008468 -0.07300715991004297; 0.04608492411200257 0.0518833149313619 -0.1402660440388014; 0.03884834060219632 0.05278582239338074 -0.14923754573973316; 0.024518500102988346 0.03851013799255814 -0.12433716735236557; 0.00839084566979026 0.015974089948533197 -0.05717977600828847; 0.002497601368124247 0.0054421434781545845 -0.020810974438023645; 0.0012413447145525596 0.003104261838811333 -0.012454121622946294; 0.0002952832571111387 0.0006843670541546354 -0.0028868476886487614; 0.0002931078507387595 0.0009010664583775347 -0.0039940493932757075; 0.0006102507561287979 5.497645561287055e-5 -0.0019532697253708416; -3.7401073132043664e-5 0.00015948185812392776 -0.0007709409707993484; 1.226625166987844e-5 0.00024697253219265044 -0.0010752432398616358; 0.00014082333847703063 -0.0002924799291983615 -0.000786251473718327; 0.0003353336674723642 -0.000283886936406187 -0.00034286151268318505; -0.00015730876019493466 -0.00018136052791405924 -0.0005175862044128118; 0.0003787936943271113 -0.00016400095160184442 -0.0004126141053205723; 0.00016691849941922272 -8.257856256590926e-5 -0.0007529951300763956; 6.211451468212878e-5 -0.0006887860553681131 -0.00026154920097938784] %
+
+Mass Used: 84.17358245583273 kg
+Launch C3: 96.57440840855986 km²/s²
+||V∞_in||: 1.524122559570995e-9 km/s

archive/ES_0.5551378686311677

@@ -0,0 +1,22 @@
+archive/ES_0.5551378686311677---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-15T00:58:50.661
+Launch V∞: [8.11320959943097, -5.645724124239646, 0.16747696452458005] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-2.8516363421996975e-10, 4.096121164742909e-9, -2.0697877390789584e-9] km/s
+	V∞_out: [2.0790724859932675e-9, 4.127970936657118e-9, 1.0865120878585403e-10] km/s
+	time of flight: 1.874916083184456e8 seconds
+	arrival date: 2030-04-24T01:58:58.661
+	thrust profile: [0.2754868791323259 -0.004110502019187116 -0.09891196486261492; 0.04324638696098478 0.02247517183605698 -0.05675135816253204; 0.03892904890147251 0.03216852322138361 -0.09100809525201009; 0.03303057370015382 0.035080690423428366 -0.11279234928351167; 0.02181869863261611 0.025269776676374003 -0.09431813772381838; 0.0169559793237119 0.03232455050637029 -0.13374662433915915; 0.016111389795168594 0.023249907977486148 -0.09458558132535513; 0.007205435769196988 0.014290387230894463 -0.07630245560011156; 0.0015616439293485633 0.002593925533434509 -0.014198480084020042; 0.0006398647395756223 0.0011455341196065034 -0.0066362673778835824; 0.00021448383373943162 0.00048461036268397813 -0.0020121857045428612; -0.0005031708667670048 -0.0003846320758830172 -0.0002312837647398825; 4.666007485336052e-5 0.00010280240718190181 -0.000841627809911724; -8.908260282730824e-5 -5.559857473515914e-5 -0.0008097588799996763; 1.4481010457650478e-6 -0.00016875008215481904 -0.0011842708445230653; 8.682995627457883e-5 8.033742269629829e-5 -4.432971042893808e-5; -0.00029798252705925894 0.00034156180315709714 -0.0006198193274259149; -0.0003061369792923545 -3.25929632625721e-5 -0.0007753052016491007; 2.7198081862265237e-5 -0.00015657437876687814 -0.00016057616392290677; -0.0005144350151837572 0.0002711169996963231 0.0005113294575712331] %
+
+Mass Used: 77.59006675738965 kg
+Launch C3: 97.72641942496672 km²/s²
+||V∞_in||: 4.598211410905106e-9 km/s

archive/ES_0.5552532074026435

@@ -0,0 +1,22 @@
+archive/ES_0.5552532074026435---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T13:38:12.292
+Launch V∞: [8.091283750679898, -5.626635631419599, 0.189242070274835] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-5.760551537680362e-6, -5.050483257379123e-6, 3.7047645776349366e-6] km/s
+	V∞_out: [-1.1464642842370578e-6, -8.482842549920137e-6, 4.006955504298592e-7] km/s
+	time of flight: 1.8749577787195104e8 seconds
+	arrival date: 2030-04-23T15:47:49.292
+	thrust profile: [0.3001191479994197 -0.006491492540972167 -0.10464367891257732; 0.06669371816510525 0.03453350155639435 -0.08275270232210559; 0.03536397022771856 0.028803940826913527 -0.07940536141313202; 0.0479031470852905 0.05031449999723751 -0.15633707136393596; 0.0227660622647329 0.02810528294508086 -0.09968877657664008; 0.018663950493618714 0.02640831159581204 -0.10302780588601725; 0.0128353574734969 0.020056380762119467 -0.08538358674836405; 0.0031883438304667546 0.00558050655485686 -0.025950802036505877; 0.0027307797561800743 0.004971522664544287 -0.024911312123720334; 0.0028886832927905236 0.005725178841952505 -0.02999853498002678; 1.8498507329809847e-5 0.00026193660437474165 -0.0015378352139950996; 0.00017006631355532425 0.00033839543051414307 -0.0008140991473821627; 2.4363084752065985e-5 0.00025524852033090707 -0.0012725427249475124; 0.0001979064541212937 -0.00022515932940935895 -2.233079341374544e-5; -3.4010641263911365e-5 6.898200899598042e-5 0.0003681680601600602; 0.00014706194029745758 6.356885199978188e-5 0.00015283040927299658; 8.779556518282857e-5 -0.0002222581120165586 -0.0006308406782991736; 0.00038537671846016884 0.00019393847803101028 -0.000166612423212043; -0.00053483701939234 8.97317069416954e-5 -0.0002836580926078503; 0.0005714255507435241 -0.00021619220466183268 0.000304464977576498] %
+
+Mass Used: 81.00707799677275 kg
+Launch C3: 97.16371382393909 km²/s²
+||V∞_in||: 8.509795281147307e-6 km/s

archive/ES_0.5553166446815165

@@ -0,0 +1,22 @@
+archive/ES_0.5553166446815165---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T22:04:01.158
+Launch V∞: [8.077142685491271, -5.680604962234028, 0.22204191555666666] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [8.201127399571204e-5, 5.893101311930579e-5, 0.00409450763245035] km/s
+	V∞_out: [-0.0036567863569022425, -0.0012346203807321937, 0.001370498501299504] km/s
+	time of flight: 1.8749577787492463e8 seconds
+	arrival date: 2030-04-24T00:13:38.158
+	thrust profile: [0.23235381129437543 -0.003499034305839029 -0.08150403458003942; 0.101359804889319 0.053657256711614386 -0.12459306140607117; 0.05618052836256829 0.04661460558293996 -0.12432883331653731; 0.038855766875548 0.04125153478496184 -0.12666684845314194; 0.025324118959891024 0.03180040241628622 -0.11099802659340433; 0.018478048063072357 0.026519644261497784 -0.10244311481816155; 0.007574926049108344 0.012062456593750713 -0.051995067543366115; 0.002624539505975554 0.005028891200910454 -0.02411669381157359; 0.0006496950209796248 0.002177155222280389 -0.011592438398649882; 0.0028996826262880884 0.005977834449005585 -0.03111401744332391; 0.00030076578793983527 0.00014708272998598834 -0.001579162518567829; 0.00023884269622201395 0.000308440831864644 -0.0016554872014328096; 0.00016125989310068078 0.0002270644731231439 -0.0002677537550706303; -0.00013653939452338545 -0.00010107875347949283 -0.0006344926280171012; 0.000306835791899565 -2.9310951884917624e-6 -0.0007611802470456345; -0.00018689220058042605 -0.0006643014207581224 -0.00047628754239393363; -6.151749483983737e-5 -0.000734193329061956 -0.00030386985203754914; 2.7399404531041125e-5 -0.0001244879414403385 -6.18471749763314e-5; -3.344731595064874e-5 3.940331310237355e-5 0.00022350296642900322; -0.0008629912071055299 -0.0011018916049755144 -0.00047252733763793707] %
+
+Mass Used: 78.7763644808947 kg
+Launch C3: 97.55880931100707 km²/s²
+||V∞_in||: 0.004095752856992697 km/s

archive/ES_0.555321853072159

@@ -0,0 +1,22 @@
+archive/ES_0.555321853072159---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T07:57:24.826
+Launch V∞: [8.1332663571246, -5.661986515759155, 0.22766044177874376] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [1.123340652251088e-6, -3.7330513819710547e-6, -1.0846981586769346e-5] km/s
+	V∞_out: [-1.0492432785177735e-5, -1.2239051288617402e-6, 4.687451703815964e-6] km/s
+	time of flight: 1.859737203924726e8 seconds
+	arrival date: 2030-04-05T19:19:24.826
+	thrust profile: [0.22943973812293017 -0.004893967763726286 -0.0801253153441409; 0.03144507004413593 0.016005514878668727 -0.039605355975015175; 0.039054529766301194 0.03197291138034155 -0.08689490156094459; 0.0378685260709824 0.04018324616401574 -0.12252200644008435; 0.02803090143364196 0.03535274273841469 -0.12081216327733243; 0.022471665512052253 0.032497625582222536 -0.12157198448109055; 0.01926878492754949 0.03153169051058213 -0.1281842797483311; 0.004043038254003434 0.0066904694410549765 -0.031175306636595977; 0.005131609501874749 0.009234170160377442 -0.04469930754406368; 0.0003470121363472272 0.0008038663204159477 -0.0038167565883837525; 0.00017609752178919131 0.00036474064628598307 -0.001954724463038849; 1.130336567161233e-5 -3.20909344426444e-5 5.0861087076908916e-5; -1.4439041978965607e-5 6.264510601075898e-5 -3.5503708158925043e-5; 0.00012451312434083361 -0.00034084972505136796 -0.0002481717343390714; -2.1043042384554106e-5 -9.974133023427434e-5 0.00022586203596731763; 3.0325725366321253e-5 6.145296121523383e-5 -0.0003832387995866655; -0.0002927026986088235 0.0007786944928326911 0.00012097830464324579; 8.96770273673005e-6 3.9333968087291074e-5 4.9980603904861806e-5; -1.0699601379404263e-5 -2.0172052201893303e-6 0.000372228156627312; -0.0002084346014800331 0.00032609368117262434 -0.0008865061071454217] %
+
+Mass Used: 74.69249898312728 kg
+Launch C3: 98.25994221732427 km²/s²
+||V∞_in||: 1.152625595695103e-5 km/s

archive/ES_0.5553222117675201

@@ -0,0 +1,22 @@
+archive/ES_0.5553222117675201---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T15:05:53.520
+Launch V∞: [7.978669656069434, -5.678185132210282, 0.06288544106185495] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-2.165312749478849e-9, -1.971227457841986e-9, -1.8369808751063008e-9] km/s
+	V∞_out: [-3.660281365501294e-10, 3.2999394084076575e-10, -1.267845070447127e-10] km/s
+	time of flight: 1.8749577786514547e8 seconds
+	arrival date: 2030-04-23T17:15:30.520
+	thrust profile: [0.39564242604082744 -0.006956512613986089 -0.13518366924321792; 0.06712585965363532 0.035648204482678 -0.08142867264258655; 0.04170290709783684 0.035350718096191905 -0.09174748789036437; 0.04352492608733409 0.04770407792297554 -0.14011401076264046; 0.02801348225631629 0.036772428672008674 -0.12141711140061484; 0.026283671902162534 0.04004047420482529 -0.1438274307468821; 0.00847703184692028 0.014366678634369039 -0.05804618230321489; 0.0021762412409529804 0.004185391744174946 -0.017954795552054398; 0.001079457307135401 0.0023049952563308574 -0.010602319561616915; 0.000416421577119403 0.0013468908459330865 -0.0071795189797770175; -0.0003591898924635163 0.0006952444828377452 -0.0024129927467661147; 0.0006183819299710211 -0.0002664932265487625 -0.0019776746683675757; 5.8125164000611285e-5 0.0014147292778764876 -0.001561111670186401; -0.00012928754371600046 0.0002918734607459714 5.5885149871641665e-5; 0.000284543764297461 -0.0011359149866518924 -0.0013977474530503884; 0.0004951169390097958 -0.0003759760138036172 -0.0003820916193990466; 0.0018513876583565177 0.00201643800302882 -0.0002718956342356863; -0.0007442531880618604 -0.0007661924223617269 0.0007792276363972396; 0.00012269135452268562 0.0002372284606531832 0.0005562980079682296; -0.00023389915358777323 -0.00021737906149740262 -0.0007771204183639985] %
+
+Mass Used: 88.43060274107165 kg
+Launch C3: 95.90491045503458 km²/s²
+||V∞_in||: 3.456705907234826e-9 km/s

archive/ES_0.5553496144128125

@@ -0,0 +1,22 @@
+archive/ES_0.5553496144128125---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-15T09:43:55.880
+Launch V∞: [8.10317987564361, -5.696207769870157, 0.1553325957128171] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [0.0071934236702311015, -0.004965730312843872, -0.0003038427526265429] km/s
+	V∞_out: [0.006087772048570902, 0.003123568422287049, -0.0054474103900420765] km/s
+	time of flight: 1.874957778749338e8 seconds
+	arrival date: 2030-04-24T11:53:32.880
+	thrust profile: [0.21852782341239765 -0.004394661947521582 -0.07648165853302688; 0.05449869864346815 0.02812137085624257 -0.06778772029616381; 0.04776021625029402 0.038940209444852 -0.1058035321485391; 0.04348954847800777 0.04581182105111091 -0.1413012320654695; 0.029637491747047877 0.03637476513769563 -0.12460063687764829; 0.018263366525342918 0.025934873925837477 -0.09882208381199613; 0.010393645054657355 0.016616604294121748 -0.06984618131900816; 0.0043639850761715785 0.007630836260250351 -0.035106101396778826; 0.004209775504114455 0.007980983235826225 -0.038849059552370294; 0.000718924087536708 0.0015240733431350023 -0.008551699639035671; 0.0007760856452014337 0.001683530519717075 -0.009501196753692152; 0.00011827705906626506 6.830871604105213e-5 -9.79778720163791e-5; -8.181060694363874e-5 0.00047577208223703674 0.0004365344581833665; 0.00024872050721913515 -8.8839932015217e-5 -0.0008270826346074116; 0.0003545586317562617 -0.00013431066679745396 -0.00023797145127221997; -0.0004402873533663245 -0.00047426965980170306 0.0007773248998385402; 0.000818115058563697 0.0006759914714488732 -0.00016756330756562723; -0.00014461160521534074 -0.000715703708641262 -0.00013038677619263433; 0.0005519329299552718 -0.0006737568257195225 -0.000598372441231225; 0.0006763866155410585 -7.404604347327747e-5 -7.334178511644998e-5] %
+
+Mass Used: 75.4686777407901 kg
+Launch C3: 98.13243526985563 km²/s²
+||V∞_in||: 0.008746207295603122 km/s

archive/ES_0.5553988801556101

@@ -0,0 +1,22 @@
+archive/ES_0.5553988801556101---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T20:27:31.829
+Launch V∞: [8.099371067795309, -5.697342994428108, 0.23961816690038987] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [8.420794762497583e-5, 6.024451843937005e-5, 0.004113130410337279] km/s
+	V∞_out: [-0.003650496205091847, -0.0012380261530165364, 0.0013759417669957801] km/s
+	time of flight: 1.874957778743604e8 seconds
+	arrival date: 2030-04-23T22:37:08.829
+	thrust profile: [0.16756317248501923 -0.0019374981081347836 -0.05553507658755178; 0.12351319739523713 0.0664036700346333 -0.1347883651394778; 0.03980123203677707 0.03566992410321178 -0.0850533180454862; 0.034361614191466876 0.040110551269449644 -0.10705297980293457; 0.03179001997115301 0.046284771186835626 -0.1348862475845847; 0.023807484482126454 0.03937269394744734 -0.12716199488054153; 0.008510351716584706 0.01618435914970713 -0.05802343221350874; 0.004255308128100879 0.009668247630515946 -0.03506206856933895; 0.0012107204699053232 0.002937858550102232 -0.011983965172335811; 0.0017863449653847366 0.003622535975951511 -0.015110293216188748; 0.0002407023305336371 0.0008608860535842083 -0.00389658664661596; -2.1079710467773147e-5 0.0008793513857120929 -0.001967315590027195; -0.00028294766519093974 -0.00034677230489704204 -0.001748699402170058; 4.317707008927486e-5 0.00013589287252711998 -0.00013691337862167894; 0.0001980808409324128 0.0008587519378775326 -0.0025076539679062546; 7.812718254363428e-5 0.0001837438719466311 -0.0006467015644265338; 3.891451479560683e-5 5.552018762208875e-5 -0.0015245825687303762; -0.000110339294204162 0.0003131708817709915 -0.0006406566647075316; -0.0005329265181372854 -0.0006203983788751317 0.0002790052352122322; -6.293376876180599e-5 0.00012561731060751233 -0.0005034354105287017] %
+
+Mass Used: 75.61650993875173 kg
+Launch C3: 98.11694575590745 km²/s²
+||V∞_in||: 0.004114433393905717 km/s

archive/ES_0.5554018322688501

@@ -0,0 +1,22 @@
+archive/ES_0.5554018322688501---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-15T21:09:00.163
+Launch V∞: [8.033420980890492, -5.775163290254046, 0.29451139712426244] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-1.2438520727890286e-6, -1.0851062017930229e-6, 8.218168158950809e-7] km/s
+	V∞_out: [-2.1323339389682597e-7, -1.8295062666380425e-6, 8.40206204986971e-8] km/s
+	time of flight: 1.8749577787468156e8 seconds
+	arrival date: 2030-04-24T23:18:37.163
+	thrust profile: [0.2298938795132756 -0.002382363908888821 -0.07500215742641986; 0.05789187849475886 0.031280672979930334 -0.06995405575677786; 0.043907082176288324 0.03765212776011839 -0.09530427276167132; 0.0511006599696396 0.055510802804240936 -0.1554405077012778; 0.04029329912758011 0.05520684570387007 -0.16865780714135356; 0.013134088356955674 0.019584423155094222 -0.07046550534934869; 0.009439347751905882 0.01592941083088526 -0.06145197693708397; 0.004727927073174679 0.008293510721741467 -0.03720175207021022; 0.0021014155716788238 0.004328291914307116 -0.019935799743980753; 0.0012112852386704117 0.00292969921619415 -0.013082901486547826; 0.00023469430900969806 0.00042648361270350183 -0.002062777628420293; 0.00020187330956979768 0.0003684238860025964 -0.0006286919877773692; -0.00032872241235123545 0.00025130450434917044 -0.0005581186561390136; 8.960475279982197e-5 0.0009770010634579137 -0.001460084323412991; 0.00014360085872644344 -0.00040907257330352956 -0.0004549987596784359; -0.00033797952112663894 5.3210703241990886e-5 -5.717079881615997e-5; 0.00031278347133417337 9.296005909151565e-5 0.0009203157652921157; 0.00016286369672531434 0.00010157592025106992 -0.00042284841744769623; 9.893657168286076e-5 0.00037018789737870185 -0.0006018683982409329; 0.00025852793290105457 -0.00026993613811333384 -0.00035035178740521367] %
+
+Mass Used: 76.44738386497602 kg
+Launch C3: 97.97510064834557 km²/s²
+||V∞_in||: 1.84391060711716e-6 km/s

archive/ES_0.5554393651791023

@@ -0,0 +1,22 @@
+archive/ES_0.5554393651791023---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T02:36:40.662
+Launch V∞: [8.015320347594308, -5.650891123369662, 0.2072178508051127] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [4.841948938567232e-7, 3.0262022612951473e-6, -7.320127622421485e-5] km/s
+	V∞_out: [-2.8670139796813485e-6, 6.709990609312329e-5, -5.090481414750846e-7] km/s
+	time of flight: 1.874957778737431e8 seconds
+	arrival date: 2030-04-23T04:46:17.662
+	thrust profile: [0.3561233393051751 -0.006098174136111534 -0.10217464052682548; 0.075529100415085 0.042981935167420986 -0.085955833298707; 0.05625615221667444 0.05130512609124765 -0.11551167241473989; 0.028197870651471384 0.034050987079248286 -0.08872363919572951; 0.029633021923308987 0.044345294692114644 -0.12486581772974435; 0.01669701348555364 0.028429102130839184 -0.0882282269142744; 0.015070735029327714 0.029937519248560016 -0.09967715481440458; 0.004956474253619485 0.011120126539336708 -0.04064673764428253; 0.0029161054415206195 0.007261967087240697 -0.028496728159587727; 0.0007415412516860645 0.0024616981819384764 -0.00998170261897817; 0.0007314468835220106 0.0019219528185446752 -0.008196849127401115; 7.654371182347835e-5 5.175821500414929e-5 -0.0006458280190958221; 0.0004010858247077206 0.0003286324930280675 -0.0025331981139017036; -6.359708081627111e-5 0.00010070213111805287 -7.147574326211124e-5; 4.941999308085874e-5 -4.143989876220452e-5 9.688743444445332e-5; -6.842487568673179e-6 -0.0001350788482258876 -0.00026026602539886627; 3.6011482074926058e-6 3.396170081582984e-5 0.0003726245143131632; 1.3766361989915927e-5 9.16724968035497e-5 -0.0007902845208497627; -0.00014868028269059738 -0.0003371631928999702 -0.00011851450358111291; -7.681987945286134e-5 9.23427662999305e-5 7.590759767921873e-5] %
+
+Mass Used: 86.72418437311308 kg
+Launch C3: 96.22087000042966 km²/s²
+||V∞_in||: 7.3265402378444e-5 km/s

archive/ES_0.5554813218194097

@@ -0,0 +1,22 @@
+archive/ES_0.5554813218194097---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-13T23:31:28.392
+Launch V∞: [8.0891473400973, -5.692973902821432, 0.17080604884838232] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-2.624253055295607e-10, 2.6031116525534865e-9, -1.963240950595241e-9] km/s
+	V∞_out: [1.5057182218987104e-9, 3.0319245946678542e-9, 7.812492911139819e-11] km/s
+	time of flight: 1.8524360854352963e8 seconds
+	arrival date: 2030-03-28T00:04:56.392
+	thrust profile: [0.22235856867229353 -0.00847503054598866 -0.08028226199077587; 0.07529283563064769 0.03759533143754159 -0.09315704925425514; 0.048321534442807665 0.0383265421453116 -0.10749810607402345; 0.03802125053160061 0.038623386474410916 -0.1235390067423918; 0.035035407326052946 0.042471937457964466 -0.15068597133732428; 0.0221428992625299 0.030381962912583303 -0.11963989862423495; 0.012030072795253723 0.01812043871300703 -0.0786051663508672; 0.0035871556203987648 0.005845780417505831 -0.02754848675183922; 0.0017038630505681143 0.002812994055315353 -0.015134097962005714; 0.0004559181219149022 0.0007414201032812668 -0.004822885634474083; 0.00019366963896819508 0.0003134059853220376 -0.0007272799277156995; 0.000245281514840613 0.0005535934511823185 -0.002713600883880549; 0.0001552398158292699 0.0001613321569179683 -0.00028192567763878843; -6.622549407408435e-5 -5.6893192231886834e-5 0.0004896166245428691; 0.00023118820212565642 0.00015471716146732504 0.0006653987429265666; 0.00011596005606976002 -0.00011503710953939407 -0.0002432255567259898; 6.198729085098857e-6 -0.00014805820961753878 0.000805655991443695; 0.00036292064525340374 -0.00019917999642682892 -0.00015432941473323157; 0.00032732974457299555 0.0004531813500036276 -0.0005485052880291339; 0.000614074688792294 -0.0008165598404809293 0.000334425216688537] %
+
+Mass Used: 77.13319313903958 kg
+Launch C3: 97.8734312543323 km²/s²
+||V∞_in||: 3.270989505751453e-9 km/s

archive/ES_0.5555149418109946

@@ -0,0 +1,22 @@
+archive/ES_0.5555149418109946---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T16:16:45.227
+Launch V∞: [7.886453692881989, -5.766146669242591, 0.17731826006147883] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-4.836910169257413e-10, -9.375329875181162e-10, -1.1582799285250461e-9] km/s
+	V∞_out: [9.504450631657843e-10, -9.110896323774704e-10, 3.2446331384196525e-10] km/s
+	time of flight: 1.8578408420707503e8 seconds
+	arrival date: 2030-04-03T22:58:09.227
+	thrust profile: [0.42007645142641625 -0.02131548891750738 -0.14069301019438915; 0.08953349621835163 0.04150785072471936 -0.11169464971176427; 0.06786122343006948 0.04954984121876103 -0.15101372550178468; 0.03674577054207439 0.033749736956093415 -0.12061690355354283; 0.022125015413372588 0.023934154012362156 -0.09634798551306989; 0.024730692216342626 0.029776021239070798 -0.1317667777392725; 0.0074123780950023236 0.009856747845124348 -0.048619156418719646; 0.002694714312697033 0.003884994057635316 -0.02125927372055324; 0.0017148813402562892 0.002663889746125444 -0.01530517929419418; 0.0005610342798146018 0.0008897162395053332 -0.005413768922161111; -6.208974296115196e-5 1.0228331061479925e-5 -0.0003640360929690432; 0.00010073726097622381 -3.56832836566312e-5 1.644789268456803e-5; -9.148431767651544e-6 9.923576995625314e-5 -0.0004964428076852081; -2.7239255440105487e-6 1.555041927077985e-5 -4.85747570741195e-5; 2.030947003099046e-6 2.4184634377666606e-5 -8.020747864168754e-5; 7.26642570323925e-5 0.00018837509337221064 -0.00039135500520177214; -0.00015038100314065543 0.00043575027422096396 -0.0005037035493860557; 0.0004557424872628663 -0.0003999451460967983 -6.622367583560193e-5; 1.2464616354565701e-5 0.0005183325062460401 2.1627829344008482e-5; 0.0003892447055876588 0.00022211057796742216 -0.0006804821734761649] %
+
+Mass Used: 91.1571927913401 kg
+Launch C3: 95.47604102654061 km²/s²
+||V∞_in||: 1.5666963634869674e-9 km/s

archive/ES_0.5555886306746982

@@ -0,0 +1,22 @@
+archive/ES_0.5555886306746982---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T21:45:44.751
+Launch V∞: [8.097157966208412, -5.7235444752915985, 0.1306763857131603] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [1.354583227548992e-6, -2.033861909972328e-6, -1.9902747505106622e-7] km/s
+	V∞_out: [1.711149734140751e-7, -8.486974320046878e-7, -2.2954795020027925e-6] km/s
+	time of flight: 1.874957778749071e8 seconds
+	arrival date: 2030-04-23T23:55:21.751
+	thrust profile: [0.13697728884613816 -0.0012462171285798694 -0.04231430720767637; 0.09061310387649295 0.04941404808359705 -0.09301349514541098; 0.07206425953696069 0.06270967380872773 -0.1316019524779482; 0.05142325879063578 0.05789117521336941 -0.13907928980775816; 0.034724693966127596 0.04696247910122261 -0.1271640404615248; 0.021664043227228043 0.03406718740673748 -0.10162959083047443; 0.011526309808033661 0.02088953844172639 -0.06650568585777802; 0.0036540813082757075 0.007795868388542844 -0.026782258005114218; 0.002748998147299548 0.006167505533935089 -0.022833530110010134; 0.00045966652234908853 0.0020603589920435974 -0.004837216705160525; 8.331411168620227e-5 0.0012795607654485688 -0.0009501956463345632; 0.0009148806188941994 -0.0004167900274393787 -0.002174374051332414; -0.0013790567604535032 -0.0002999678699475404 -0.002259765855076702; 0.0002308293331623607 0.0003590641436721085 -0.0014202991854615767; -0.0006471076503101953 0.001336938439675547 -6.724792531199639e-5; 0.0017802574380088548 -0.00032790554594502115 -0.0007366313548920879; -0.0003033508980936425 -0.0026991605543110735 -0.0018136105163869749; -0.00024710811844636996 3.984844856063307e-5 0.0012667890406400152; -2.865006595770774e-5 -1.810085979889913e-5 -0.00011678869749445135; -0.00013489262485826345 0.0005807050881182493 -0.0005724390058631687] %
+
+Mass Used: 74.53670773956901 kg
+Launch C3: 98.34000480815638 km²/s²
+||V∞_in||: 2.4517548664208936e-6 km/s

archive/ES_0.5555895920983202

@@ -0,0 +1,22 @@
+archive/ES_0.5555895920983202---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-13T15:32:29.766
+Launch V∞: [7.954026518859595, -5.651936525144275, 0.34283036341455375] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-1.4772590225260715e-5, -1.2392091138211298e-5, 9.497081706989166e-6] km/s
+	V∞_out: [-2.7897781490311477e-6, -2.129279966966492e-5, 9.546532130825573e-7] km/s
+	time of flight: 1.8749577787603047e8 seconds
+	arrival date: 2030-04-22T17:42:06.766
+	thrust profile: [0.4221003625778134 0.0024543240573022336 -0.12460143742651807; 0.08841015987257779 0.05250420784808357 -0.0967517469099731; 0.05316870742999599 0.05056322435215213 -0.1062279546235885; 0.03886614863645844 0.04944665659247456 -0.11689275674361002; 0.02500576523814115 0.04066644559618659 -0.1069162014326775; 0.0195872956233084 0.03673437221585266 -0.10476406166276402; 0.010394089317653295 0.021034861908135444 -0.06272875518522406; 0.008328051608330151 0.01222352328662478 -0.043392320306426084; 0.002576596033412328 0.006661521160027185 -0.025507476262502757; 0.0009641193100614219 0.0026478188882584535 -0.01113969788388293; 0.00015409864763691586 0.0005497379206734901 -0.002113724698805902; 0.00016568269854158854 0.0006468183611313067 -0.0028208235559074465; 0.00019734230581279572 0.00011256427006853706 -0.00044691796679938736; -1.611920081808971e-5 0.0001536912782015656 -0.0006493926058376988; 1.2652188508059165e-5 0.00016496459316419325 -0.0006311914772119577; 0.00013136446789655573 -6.599013967282938e-5 -0.0010739640436663615; -4.070635175490843e-5 2.8819239964566348e-5 0.0002686223663615027; 0.0001988522613017184 5.7429486625579095e-5 -0.0008735736425061699; 0.00021337346157853458 -0.0001873608069724977 -0.00030585885166558896; 0.00018152047352259707 -0.0002772759720853931 -2.5427888388273304e-5] %
+
+Mass Used: 92.10519158518673 kg
+Launch C3: 95.32845700506059 km²/s²
+||V∞_in||: 2.1493903919261194e-5 km/s

archive/ES_0.5555981137552012

@@ -0,0 +1,22 @@
+archive/ES_0.5555981137552012---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T15:07:07.613
+Launch V∞: [8.082773809515784, -5.709511979563037, -0.08221754559998876] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-4.271618879525547e-10, -9.467188797709204e-10, 2.7925623958736294e-9] km/s
+	V∞_out: [2.0710433474319867e-10, -6.893777317405418e-10, 1.1086040371862895e-10] km/s
+	time of flight: 1.8749577786971304e8 seconds
+	arrival date: 2030-04-23T17:16:44.613
+	thrust profile: [0.19262882219372876 0.0017682977351410924 -0.06078570749456977; 0.07510854426601425 0.04483363097579235 -0.08152090897510195; 0.05247612556652213 0.05173429616485974 -0.10334129305288119; 0.03699212147964636 0.04836776779914272 -0.11420009851892877; 0.015257947545094692 0.023616672516294634 -0.06151535097167395; 0.05017375150264386 0.08830370298816641 -0.2186226342882601; 0.008321797426523236 0.020875746774835446 -0.0620611019471654; 0.0016554003603538512 0.004422884420023118 -0.014999979304444628; 0.0029079581542708643 0.008455953550443632 -0.03441057189742003; 0.0014578145592288889 0.005998444591665279 -0.021590817094686094; 0.00010189419917084582 0.00036538089525199125 -0.0013457387446312698; 3.4267406230693495e-5 0.00012128214999226729 -0.0004984499190272592; -3.630324776009653e-5 0.00013568298390632396 -0.0001933222589807255; -0.00011464061902182116 1.729493075479877e-5 -0.00022822609938822459; 3.130844266011417e-5 -6.033277523730223e-6 -0.00028834664280309296; -2.4080693230419574e-6 2.2064196459154254e-5 -0.00010496253498183353; 5.629619319618323e-5 -0.00017764941434590838 -8.429129071450761e-5; 4.5321256872056e-5 7.763583113794498e-5 3.631885057500916e-5; 0.0001761123035687706 0.00017277995294965204 6.818358448922729e-5; -0.0003107464502650623 6.280586170101499e-5 -5.122958464710797e-5] %
+
+Mass Used: 76.90143723306119 kg
+Launch C3: 97.9365192253726 km²/s²
+||V∞_in||: 2.979454421648595e-9 km/s

archive/ES_0.5557824943431257

@@ -0,0 +1,22 @@
+archive/ES_0.5557824943431257---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T19:54:42.769
+Launch V∞: [7.947030030148891, -5.725766684710527, 0.24202104722470721] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-2.759344025344734e-6, -2.4204246885162136e-6, 1.776701782704104e-6] km/s
+	V∞_out: [-3.9976382777979477e-7, -4.0526356815121425e-6, 1.6070450518301959e-7] km/s
+	time of flight: 1.8749577787488315e8 seconds
+	arrival date: 2030-04-23T22:04:19.769
+	thrust profile: [0.3960965326719643 0.004259382470233035 -0.12416769816722709; 0.04264462785093866 0.024163839407926626 -0.05007198382581099; 0.04641569782912802 0.042447237818555895 -0.0976623070227238; 0.06000137009233807 0.07281320449422427 -0.1833637869953763; 0.027339463431665722 0.03988389687606256 -0.11532986210137897; 0.016392180324669884 0.02764688048304604 -0.088278672916249; 0.007684696982986988 0.014735717216941745 -0.051844821781153766; 0.005695678176768902 0.011978794011892344 -0.0450846309818904; 0.0015313692750855378 0.004017116318282095 -0.016246969671378612; 0.0013959084340388242 0.003510673757082177 -0.015182286932493894; 0.00018520527178236566 0.000528320331060851 -0.003527162039857431; 0.0005931763915346057 0.0019233939908585712 -0.008836752661479331; -0.00020609688838255314 -0.00029171179683564006 -0.00016409366406674344; -0.00035832118245100606 0.0009050915210500756 5.1892988268757245e-5; 0.0013802105825223643 -0.0002956780681465251 -0.00018081590039303056; 1.2820170612769873e-5 0.00021476799737743432 -0.0005181737657272314; -7.816440173557716e-5 0.00022768666887319221 0.001407493734060039; 0.002351769163508304 0.00013991003499428924 -0.0009362672492040228; -0.0002162265530962279 0.0020183627256214593 -0.0021072091822542283; 0.00052609584762935 9.227976670804017e-6 0.0008696703291690283] %
+
+Mass Used: 88.42303314539413 kg
+Launch C3: 95.998264615129 km²/s²
+||V∞_in||: 4.077879883916204e-6 km/s

archive/ES_0.5557834365111958

@@ -0,0 +1,22 @@
+archive/ES_0.5557834365111958---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T10:36:44.855
+Launch V∞: [7.998211811049221, -5.6889764199794595, 0.16579943332476535] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [8.607330122588107e-6, 7.585618519006446e-6, -5.516980767695332e-6] km/s
+	V∞_out: [1.7044773987531268e-6, 1.2573006635761295e-5, -5.978193920049432e-7] km/s
+	time of flight: 1.8749577787394667e8 seconds
+	arrival date: 2030-04-23T12:46:21.855
+	thrust profile: [0.33574349798395897 0.00022780531375672173 -0.10962357523730464; 0.08229530639165769 0.04774551014678654 -0.09587120157684394; 0.056042617861322704 0.05242218020328153 -0.11832645419653522; 0.040295755662508925 0.04970869349161298 -0.12699339828045553; 0.02595014094582373 0.03928316854813051 -0.11236569345355266; 0.013559779913649305 0.023658284920628166 -0.0767136924923864; 0.008592255150081909 0.016720570100730938 -0.059820306918130596; 0.004322661529306686 0.009315012365338918 -0.03486570051548452; 0.003482728722009579 0.008317889096073222 -0.03367490985583191; 0.0015227573128690293 0.005144050668324006 -0.022075030429857635; 0.00010926529240131475 0.0005843875807441641 -0.004574145172846127; 0.00027819379105144227 0.003182601609830852 -0.014891439446973666; -9.85304886924253e-5 -1.3426602311527778e-5 -0.0003835232730023135; 5.602341118698953e-5 0.0001880036072309773 -0.0006281716766106916; 0.00018122159141822488 0.00030927740320518685 0.0001018819378548282; 9.629454558657402e-5 0.00016123996751249526 -0.00017437142981505945; -0.00012885310087460235 0.00012253124744784178 -0.0001268114277722781; 0.0006014936861673025 0.0006988495319844413 -0.000446181986860041; -0.0003317729364954457 0.0008610760201880722 0.00045461438515241104; 0.0002603128653303449 0.0006148525916535956 -0.0001437275203020101] %
+
+Mass Used: 86.29455898384276 kg
+Launch C3: 96.3633343335804 km²/s²
+||V∞_in||: 1.2730468056840107e-5 km/s

archive/ES_0.5558224886874478

@@ -0,0 +1,22 @@
+archive/ES_0.5558224886874478---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T23:54:28.525
+Launch V∞: [8.145087344616607, -5.6662314525547375, 0.16493094089055843] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [5.9367104147365403e-5, 4.8730360644439784e-5, 0.003145934483615344] km/s
+	V∞_out: [-0.002776269848909524, -0.0009653862811910221, 0.0011239259333138203] km/s
+	time of flight: 1.8749577787493294e8 seconds
+	arrival date: 2030-04-24T02:04:05.525
+	thrust profile: [0.1821993945438948 -0.0013631485982507586 -0.062188082882081594; 0.06155488770018268 0.03373818926367287 -0.07381192082647672; 0.055309765667404066 0.04719652683531835 -0.11759484451663701; 0.026038131174086047 0.029379113849091566 -0.08364320573355498; 0.022595436497182136 0.029956681404161033 -0.09658388251120247; 0.02470275525312149 0.0430988355309665 -0.14207007999096813; 0.010827262712412224 0.018390342920860427 -0.07097463884429948; 0.00875532657762532 0.01796682364984792 -0.0717923864930178; 0.0024836625650917917 0.004959870337903752 -0.022261877516037677; 0.0021411689330728535 0.004837123252528673 -0.022278748740835415; 0.0001663714690442312 0.00026262274430156245 -0.0015855030381359092; 4.403396740945333e-5 0.0002216138020192659 -0.001114785770396187; 0.00014639728872106348 0.00038526343831065714 -0.0024171809464598295; 0.0004986791055819131 -6.42503190641782e-5 -0.0005868243646974211; -5.389137094538407e-5 0.0010913791581246219 -0.0018423804824721113; 0.00013191521534491798 0.0004661208244784152 -0.0015385708622525952; -0.00047700244518037284 0.00025406105242428267 -0.0008935614130410638; 9.71062850629971e-5 -0.0005652859915543438 -0.0001187656591950957; -0.0016289619577609972 0.0004241308900837115 -0.00292004875705; -0.0012074844002367266 0.0005798686307722407 0.002719243510055672] %
+
+Mass Used: 74.01723464842189 kg
+Launch C3: 98.47582894061723 km²/s²
+||V∞_in||: 0.0031468719192721396 km/s

archive/ES_0.5558472505548713

@@ -0,0 +1,22 @@
+archive/ES_0.5558472505548713---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T18:16:40.858
+Launch V∞: [8.020180222127914, -5.691590916263975, 0.20675721586302248] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-3.382218630453822e-5, -3.120871769234988e-5, 3.069687137628679e-5] km/s
+	V∞_out: [-7.839920172447044e-6, -5.6989678678280376e-5, 2.735496097299929e-6] km/s
+	time of flight: 1.8749577785753152e8 seconds
+	arrival date: 2030-04-23T20:26:17.858
+	thrust profile: [0.34397332976981154 0.0019211086043523901 -0.1103007434085456; 0.03571069754629575 0.020356200595922438 -0.04085081866609469; 0.03200885481060013 0.029341661430218265 -0.06612625343035164; 0.03950983503425282 0.04789285610425227 -0.12053667359073973; 0.04016880692530358 0.05952065499594405 -0.1639035370673269; 0.021250394462809602 0.0368045310211113 -0.1122121732957696; 0.016518228898727245 0.03280018690991797 -0.10764831048231813; 0.004215834930408646 0.009162092268123402 -0.03277710819320587; 0.0008073122802082747 0.0023318159176960044 -0.007903723016192054; 0.001409980353398891 0.002700844883547664 -0.00874442461005192; 9.533975278373994e-5 -0.0011954719260895883 -0.0020415622386658547; -0.0008676221505528904 -0.0006095180246605739 -0.0015822111759879734; -0.00015129546579974043 -0.0005662361412312537 -0.0016584937869259728; 0.0015362115192581556 -0.00020190711922243073 -0.0006597526367618477; 0.0012586546184986695 0.00134936604139315 -0.002215507211306132; -5.4933173473768835e-5 0.0006124746382959935 -0.002220402869587243; 0.000248654535235742 -0.0004993183743947807 -0.004208702729329133; -0.002003849507640907 -0.0020632617955001096 -0.0039084560839903705; -0.001956170593537257 -0.0005413529933416728 -0.0030028792644693483; -0.0017721652231622361 -0.0001376039351070372 -0.00040273531230205605] %
+
+Mass Used: 84.05368773172268 kg
+Launch C3: 96.76024649982179 km²/s²
+||V∞_in||: 5.531927565245211e-5 km/s

archive/ES_0.5558533611237318

@@ -0,0 +1,22 @@
+archive/ES_0.5558533611237318---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T17:03:16.528
+Launch V∞: [8.06850332079006, -5.665661254292966, 0.16779196569355997] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-1.1412983953857728e-5, 0.00026462375915336475, 4.662268940587834e-6] km/s
+	V∞_out: [0.00025609049237426706, -3.840562420470978e-5, 5.5895068284245824e-5] km/s
+	time of flight: 1.8749577787493658e8 seconds
+	arrival date: 2030-04-23T19:12:53.528
+	thrust profile: [0.2879444151060303 -0.0032769099727066897 -0.09518863084849954; 0.056111400619534034 0.030923793956691526 -0.06594970344083223; 0.04269376209902795 0.036674028395639435 -0.08984553707155178; 0.050502627129324816 0.05696895048537511 -0.15680529977596813; 0.027928103604976745 0.03767267671133755 -0.11509610760991872; 0.017376446035021677 0.02631384642025439 -0.08953117211467436; 0.01248684645883106 0.023326248304538836 -0.08370693572956045; 0.003280702289041826 0.006223618897104122 -0.0295749332692172; 0.0019037768824084992 0.0040702658780207256 -0.018410000949822602; 0.000922524644747056 0.0020770697469395865 -0.010977767708480605; 0.0010429375350594734 0.002914841776064981 -0.015177405498180483; 0.0003537499932884955 0.0009101101778355857 -0.0041892756669427746; 0.000967335997969096 0.002460335295015552 -0.013385888495663535; 0.00028186841488487754 0.0008509651947054618 -0.0046533703124217556; 0.0007182624812921339 0.0008198796909274933 -0.0014994399709984977; 0.00028118878779284976 5.9385975795101474e-5 -0.0007068045823105662; 0.0007259756114810482 0.0007491114555815853 -0.0007497066843321215; -0.0001598865576742702 -0.000516621021246607 -0.0007915945292954795; 0.0007526444827450972 0.00026007121398408475 -0.0004884519648876557; 0.00199177897272931 -1.9999228634536795e-5 -0.0010394116855884233] %
+
+Mass Used: 81.32865297082344 kg
+Launch C3: 97.22861742974807 km²/s²
+||V∞_in||: 0.0002649107903858644 km/s

archive/ES_0.5558662372895594

@@ -0,0 +1,22 @@
+archive/ES_0.5558662372895594---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-15T05:44:11.020
+Launch V∞: [8.139803167680254, -5.647315242872821, 0.15738329700479445] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-0.016631203558507637, 0.10220769452895039, 0.1066376381916789] km/s
+	V∞_out: [-0.02558744762007931, 0.02319501815077483, -0.14455664775647756] km/s
+	time of flight: 1.8749577787516823e8 seconds
+	arrival date: 2030-04-24T07:53:48.020
+	thrust profile: [0.2412491490531724 -0.0075435708360372545 -0.08696910011384751; 0.025358972834204803 0.012681760164543929 -0.033362581146555055; 0.0491675035584243 0.037898367149471826 -0.11011123911971735; 0.034761469088207 0.03393001069771068 -0.11395322206213486; 0.02877504164106272 0.032905220949458365 -0.12448552493786565; 0.02597432034420042 0.033565966041392385 -0.1399317638039783; 0.015316436989942435 0.02157759060619915 -0.09926973307474879; 0.005115558445724777 0.007963819520976382 -0.041488742403563886; 0.0011703918745264534 0.0019490370220689147 -0.010656599371909783; 0.001065638256009031 0.0009347430282915833 -0.008334405585172372; 0.0004373664945973918 0.0007342543411028775 -0.0035260864822668474; 0.00044598933615717007 0.001055043566326496 -0.001739393971164116; 0.00010611527132477588 0.0003757715991527618 0.000535072055176574; -9.790043793468507e-5 1.7093336149475233e-5 0.0004061769557542628; 0.00143390439412798 0.0005842142186828458 0.0016107682429857407; -0.000501502132164686 -0.0006540398062925176 0.0016923685271037713; -0.0026708940402657643 -0.0007461704232461983 0.0017946241364393137; -0.0008577638507745552 -0.001801082441750256 0.001369975426384974; 0.0007874515174102044 -0.001659216035796467 0.001191550306468037; 0.00271791041746247 -0.002136020899016181 -0.00036446217710833415] %
+
+Mass Used: 75.83282521951833 kg
+Launch C3: 98.17333456313732 km²/s²
+||V∞_in||: 0.14864250950460695 km/s

archive/ES_0.5558687243860738

@@ -0,0 +1,22 @@
+archive/ES_0.5558687243860738---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T04:44:44.406
+Launch V∞: [7.926674977701113, -5.704295701074707, 0.18612421009155877] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-4.267040665413368e-10, 1.479066662287573e-9, -1.6399911979666534e-9] km/s
+	V∞_out: [1.0817865429485196e-9, 2.1201569902862085e-9, 5.45134206289995e-11] km/s
+	time of flight: 1.8696668599230942e8 seconds
+	arrival date: 2030-04-17T03:56:09.406
+	thrust profile: [0.41070806098542656 -0.008787243861247296 -0.12842175329010364; 0.1050983721593386 0.05482007971439309 -0.1151227079934063; 0.047489037678421796 0.04004617616998803 -0.09435952858893684; 0.024118304218830853 0.027298630096615345 -0.07331617603572899; 0.03332830151352836 0.04318034811654563 -0.12845753288179196; 0.0224471018473126 0.03536855993795905 -0.11206153554862952; 0.013863252896323904 0.028595534434234866 -0.09142079495876052; 0.0063894129470417746 0.012958688182379718 -0.04836183136475473; 0.0015196675707367946 0.002115234339886667 -0.00889135073026112; 0.000882564864626453 0.0022296862624698443 -0.009532497920043634; 0.00020505950604224126 0.000791393167795662 -0.0038024885840200005; -2.9277205689760225e-5 -7.923410806971189e-5 -0.0022771331454883104; -0.0006133391353344056 0.0005498496943153982 -0.00252758957448163; 0.00015738844184753708 0.0011873677091615027 -0.00361278984725187; 7.574085962876566e-6 0.0005895940058300447 -0.00204990573982413; -0.0005471488810656964 0.0003339056838708725 0.0006812693995493719; 0.0004495756325669218 0.0008664988009671715 -0.00024822004333460213; 0.0008356148738293636 -0.0012464050318468027 -0.001502825834394564; 4.594851882598074e-5 4.346039730665198e-5 -0.00017049846874473491; -7.192850005651835e-5 -0.0003729149276862026 -0.00020869961771174307] %
+
+Mass Used: 91.9796325479515 kg
+Launch C3: 95.40580786899451 km²/s²
+||V∞_in||: 2.2492855935388716e-9 km/s

archive/ES_0.5558779781677604

@@ -0,0 +1,22 @@
+archive/ES_0.5558779781677604---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-15T08:10:09.677
+Launch V∞: [7.894381291534464, -5.785139007377959, -0.08494684631296423] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-1.9034379560346155e-9, 2.302025376630676e-9, 9.233393374906011e-10] km/s
+	V∞_out: [2.508998396217692e-9, -2.308370756981814e-9, -1.8870685581830936e-9] km/s
+	time of flight: 1.8749577787470794e8 seconds
+	arrival date: 2030-04-24T10:19:46.677
+	thrust profile: [0.3795819420374527 -0.003768633453468938 -0.1239326663584129; 0.09794470904025773 0.05578611794694805 -0.11743536837114588; 0.06504884963741392 0.05744204155321652 -0.1393410922487926; 0.027549147915339748 0.03144574045624916 -0.09023581588392661; 0.02843485432910916 0.03967245820343552 -0.12453309035323756; 0.01434010947560126 0.02322679269369038 -0.08178498720083793; 0.01057921776971638 0.019018700672330743 -0.07394958555043603; 0.004791032285740364 0.00972817550556817 -0.041161520238384854; 0.001423368274942205 0.004597516902262278 -0.018419472303710577; 0.0010348087333635588 0.0026947177146075772 -0.011409050605615628; 5.150679715794969e-5 0.00016032361211856425 -0.0006044108486849174; 0.00020403454557339372 0.0005272748954227537 -0.0026084863602975046; 3.084653317123268e-5 -5.281500999293916e-5 -0.00019017181288307898; -0.00011666855441256528 -7.987156532713148e-5 -0.0003686507106282742; 0.00023745646356933872 0.00018793775512487935 -0.00023735984487069752; 1.2671917395674077e-5 -7.244969914968518e-6 -0.00018704249470194272; -9.849995183951334e-5 -3.900843859143215e-5 1.7210650528979242e-5; 9.357834425714433e-5 0.00023348563805860174 8.355049469364135e-5; -0.00023633066851157567 9.058746275186138e-5 0.00020906591152564878; 0.00014150045409054975 0.00026982721645029464 -0.00012436396049234023] %
+
+Mass Used: 89.71252707688927 kg
+Launch C3: 95.79630527751392 km²/s²
+||V∞_in||: 3.1264920309001944e-9 km/s

archive/ES_0.5559128041821125

@@ -0,0 +1,22 @@
+archive/ES_0.5559128041821125---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-15T08:14:42.991
+Launch V∞: [7.866779426893698, -5.752572268964739, 0.1606977487911105] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [1.5378864130849763e-7, 9.510877930514063e-7, -2.2789178909471312e-5] km/s
+	V∞_out: [-9.56708492923167e-7, 2.2781984183249892e-5, -2.7450486135648703e-7] km/s
+	time of flight: 1.8749577787769815e8 seconds
+	arrival date: 2030-04-24T10:24:19.991
+	thrust profile: [0.49396114761661103 -0.0078125974697869 -0.16236485369121081; 0.05758971629702417 0.02946467299117961 -0.07080284190262136; 0.039999863532085074 0.03237501568425605 -0.08844071540389459; 0.03883900656247109 0.040086274856215603 -0.1252504154874446; 0.03480336417898244 0.04306180378055577 -0.14962433154364452; 0.016438242231518248 0.023045497470434155 -0.08963878147683864; 0.013567856729339283 0.021258593539582437 -0.08984742550691868; 0.003427296949281673 0.005669910290559113 -0.026280883826344588; 0.0011385696824643288 0.002106972691260799 -0.010234048341935321; 0.0007988372538301461 -0.0003610677249334009 -0.002008719135664823; 0.0008669085246602328 0.0009496156917026651 -0.0034578577157030783; -0.00011560835650556488 0.00021091875123499992 -0.0008096808214678602; 0.0010719971133464862 0.0010273816009384125 -0.0020109467302602477; 0.0013017474524907244 0.0015761826496794532 -0.0024755448736099514; 0.000529278404990742 -0.00013970788348503815 -0.003159726912437057; 0.000464366846193499 0.0009515824620475557 -0.0025551226987178947; 0.0007408115557011497 -0.0003502607794663498 0.0012445939403221298; -0.0010785848917700405 0.0010126033272391233 -0.0003719420652615623; 2.3394232892742024e-5 0.0003407428464003145 -0.0010848168493393505; -0.00011114850434629472 0.0008863352816601983 -0.0013988737116514469] %
+
+Mass Used: 94.37417971855939 kg
+Launch C3: 95.0041300275266 km²/s²
+||V∞_in||: 2.2809535161948808e-5 km/s

archive/ES_0.5559161153091994

@@ -0,0 +1,22 @@
+archive/ES_0.5559161153091994---------------------------
+
+Spacecraft: mySat
+	dry_mass: 200.0 kg
+	specific impulse: 3200.0 kg/s
+	max_thrust: 0.00025 kN
+	num_thrusters: 1
+	duty_cycle: 1.0
+Launch Mass: 3500.0 kg
+Launch Date: 2024-05-14T22:59:25.220
+Launch V∞: [7.902723530690704, -5.792477101021152, 0.1737027323535227] km/s
+Phase 1:
+	Planet: Saturn
+	V∞_in: [-8.034636198766216e-6, 0.0001907281087354548, 3.167142492142628e-6] km/s
+	V∞_out: [0.00018481747137806098, -2.7201160346527105e-5, 3.908934538923173e-5] km/s
+	time of flight: 1.8749577787493783e8 seconds
+	arrival date: 2030-04-24T01:09:02.220
+	thrust profile: [0.3620603035699699 0.012159716002029659 -0.10953393936396177; 0.07170183015250459 0.044084045654540896 -0.07812291295302695; 0.04923935872859461 0.049179750328895176 -0.09719646613221114; 0.048535758756893754 0.06485744175314566 -0.14225317021866515; 0.033218282523832465 0.055075959769179 -0.13361715337862104; 0.014293842185512976 0.028195630940955806 -0.07652366322881445; 0.009381512368472284 0.021467421967629862 -0.06295310538846842; 0.006958176455256972 0.01840877546629484 -0.05757115538475504; 0.0007250001900832797 0.0020864928070601853 -0.007224342686006196; 0.002277093475859385 0.006662324032877546 -0.021197251161165477; 0.0006013625066908898 0.0023591314556498486 -0.008634526017830496; 0.0004563211966331974 0.00046385842723694275 -0.0016054051345550159; 4.327730777362032e-5 0.00037731618149751975 -0.0014634664029315931; 8.267248029622195e-5 9.417518517602528e-5 -0.0015402683930081295; 2.2894819858776736e-5 0.0004011241181129774 -0.0011518083629152116; -3.772530601714994e-5 -3.006590994584059e-5 -0.00046134586183175824; -0.00052409624316835 0.00015814867361838453 -0.0002361334461810562; 3.451441574399709e-5 3.5704795107332522e-6 -0.0003387605449442791; -0.0010367677148064383 0.0006457575305781564 -0.0003675513769867823; 0.0002867443419824131 -1.2678068253483936e-6 0.00010788365830646774] %
+
+Mass Used: 88.35878481631744 kg
+Launch C3: 96.03600280761403 km²/s²
+||V∞_in||: 0.0001909235387065082 km/s