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Keeping on keeping on

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LaTeX/thesis.tex
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@@ -919,7 +919,7 @@
phase complete one ``Mission Guess'' which is fed to the non-linear solver to generate
one valid trajectory within the vicinity of the original Mission Guess.
\begin{figure}
\begin{figure}[H]
\centering
\includegraphics[width=\textwidth]{flowcharts/nlp}
\caption{A flowchart of the Non-Linear Problem Solving Formulation}
@@ -980,7 +980,7 @@
period, the state should remain exactly the same as it began. In
Figure~\ref{laguerre_plot} an example of such an orbit is provided.
\begin{figure}
\begin{figure}[H]
\centering
\includegraphics[width=\textwidth]{fig/laguerre_plot}
\caption{Example of a natural trajectory propagated via the Laguerre-Conway
@@ -1007,7 +1007,7 @@
designer to trade-off speed of propagation and the fidelity of the results quite
effectively.
\begin{figure}
\begin{figure}[H]
\centering
\includegraphics[width=\textwidth]{fig/spiral_plot}
\caption{An example trajectory showing that classic continuous-thrust orbit
@@ -1122,7 +1122,7 @@
Section~\ref{mbh_subsection}, but Figure~\ref{mbh_flow} outlines the process steps of
the algorithm.
\begin{figure}
\begin{figure}[H]
\centering
\includegraphics[width=\textwidth]{flowcharts/mbh}
\caption{A flowchart visualizing the steps in the monotonic basin hopping
@@ -1208,7 +1208,7 @@
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
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.
@@ -1307,6 +1307,31 @@
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:
\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
@@ -1357,31 +1382,6 @@
efficacy of the lower fidelity method. Orbits can be found quickly in the lower fidelity
model and easily refined later by re-running the NLP solver at a higher $n$ value.
Finally, the relevant values for the two selected missions are listed below for
reference:
\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}
\subsection{Cost Function}
Each mission optimization also allows for the definition of a cost function. This
@@ -1439,18 +1439,18 @@
per second squared. However, for this phase, the thrusters are almost entirely turned
off, allowing for a nearly-natural trajectory to Mars rendezvous.
\begin{figure}
\begin{figure}[H]
\centering
\includegraphics[width=\textwidth]{fig/EMS_plot}
\includegraphics[width=0.9\textwidth]{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}
\label{ems}
\end{figure}
\begin{figure}
\begin{figure}[H]
\centering
\includegraphics[width=\textwidth]{fig/EMS_plot_noplanets}
\includegraphics[width=0.9\textwidth]{fig/EMS_plot_noplanets}
\caption{Another depiction of the EMS trajectory, without the planetary ephemeris
arcs}
\label{ems_nop}
@@ -1467,6 +1467,21 @@
$3500$ 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}
\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}
\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
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
@@ -1509,18 +1524,18 @@
flyby occurring in mid-April of 2026. This will prove to be helpful in comparison with
the other result, as this mission profile is much longer.
\begin{figure}
\begin{figure}[H]
\centering
\includegraphics[width=\textwidth]{fig/EMJS_plot}
\includegraphics[width=0.9\textwidth]{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}
\label{emjs}
\end{figure}
\begin{figure}
\begin{figure}[H]
\centering
\includegraphics[width=\textwidth]{fig/EMJS_plot_noplanets}
\includegraphics[width=0.9\textwidth]{fig/EMJS_plot_noplanets}
\caption{Another depiction of the EMJS trajectory, without the planetary ephemeris
arcs}
\label{emjs_nop}
@@ -1533,6 +1548,21 @@
beginning of the phase, very similarly to the previous result. In this trajectory, the
Jupiter flyby occurs late July of 2029.
\begin{figure}[H]
\centering
\includegraphics[width=0.9\textwidth]{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}
\caption{The inertial x, y, and z components of the unit thrust vector over time for
the EMJS trajectory}
\label{emjs_components}
\end{figure}
Finally, this mission also has a third phase. The Jupiter flyby provides quite a strong
$\Delta V$ for the spacecraft, allowing the following phase to largely be a coasting arc
to Saturn almost one revolution later. Because of this long coasting period, the mission
@@ -1556,7 +1586,7 @@
of which are possible for the other result, meaning that either different launch
vehicles must be found or mission specifications must change.
\begin{figure}
\begin{figure}[H]
\centering
\includegraphics[width=\textwidth]{fig/c3}
\caption{Plot of Delta IV and Atlas V launch vehicle capabilities as they relate to