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@@ -1155,9 +1155,9 @@
uniform distribution within those bounds.
A unit launch direction is then also chosen as a 3-length vector of uniform random
numbers, then normalized. This unit vector is then multiplied by a uniform random
number between 0 and the square root of the maximum launch $C_3$ specified by the
user to generate an initial $\vec{v_\infty}$ vector at launch.
numbers and normalized. This vector is then multiplied by a uniform random number
between 0 and the root of the maximum launch $C_3$ specified by the user to generate
an initial $\vec{v}_\infty$ vector at launch.
Next, the times of flight of each phase of the mission is then decided. Since launch
date has already been selected, the maximum time of flight can be calculated by
@@ -1288,17 +1288,17 @@
a tuning parameter to determine the size of the tails and width of the distribution
set to $1.01$, but easily tunable.
The perturbation function, then steps through each parameter of the mission,
generating a new mission guess with the parameters modified by the above Pareto
distribution. After this perturbation, the NLP solver is then called again to find
a valid solution in the vicinity of this new guess. If the solution is better than
the current basin solution, it replaces that value and the drill counter is reset to
The perturbation function then steps through each parameter of the mission,
generating a new guess with the parameters modified by the Pareto distribution.
After this perturbation, the NLP solver is then called again to find a valid
solution in the vicinity of this new guess. If the solution is better than the
current basin solution, it replaces that value and the drill counter is reset to
zero. If it is better than the current total best, it replaces that value as well.
Otherwise, the drill counter increments and the process is repeated. Therefore, the
drill patience allows the mission designer to determine a maximum number of
iterations to perform without any improvements in a row before ending a given drill
loop. This process can be repeated essentially ''search patience`` number of times
in order to fully traverse all basins.
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.
\chapter{Results Analysis} \label{results}
@@ -1436,8 +1436,11 @@
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 thrusters are almost entirely turned
off, allowing for a nearly-natural trajectory to Mars rendezvous.
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.
\begin{figure}[H]
\centering
@@ -1518,11 +1521,11 @@
previous trajectory. However, this time the launch energy is considerably lower, with a
$C_3$ value of only $40.4386$ kilometer per second squared. Rather than employ an almost
entirely natural coasting arc to Mars, however, this trajectory performs some thrusting
at about the apoapsis point of its orbit in order to raise the periapsis enough to
rendezvous at roughly the same incidence angle in Mars' orbit, but one revolution ahead.
In this case, the launch was a bit earlier, occurring in November of 2023, with the Mars
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.
almost entirely in the velocity direction, increasing its orbital energy in order to
achieve the same Mars rendezvous. In this case, the launch was a bit earlier, occurring
in November of 2023, with the Mars 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}[H]
\centering
@@ -1565,9 +1568,11 @@
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
length increases considerably during this leg, arriving at Saturn in December of 2037,
over 8 years after the Jupiter flyby.
to Saturn almost one revolution later. During the most efficient part of the journey,
some thrust in the velocity direction accounts for a little bit of orbit-raising, but
the phase is largely natural. Because of this long coasting period, the mission length
increases considerably during this leg, arriving at Saturn in December of 2037, over 8
years after the Jupiter flyby.
However, there are many advantages to this approach relative to the other trajectory.
While the fuel use is also slightly higher at $530.668$ kilograms, plenty of payload