FINISHED THE DRAFT!!!!!!!!!!!!!
This commit is contained in:
Connor
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LaTeX/thesis.tex
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LaTeX/thesis.tex
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\section{Overview of Results}
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Quick re-wording of the previous section in a paragraph or two for reader's convenience.
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A mission designer's job is quite a difficult one and it can be very useful to have
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tools to automate some of the more complex analysis. This paper attempted to explore one
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such tool, meant for automating the initial analysis and discovery of useful
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interplanetary, low-thrust trajectories including the difficult task of optimizing the
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flyby parameters. This makes the mission designer's job significantly simpler in that
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they can simply explore a number of different flyby selection options in order to get a
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good understanding of the mission scope and search space for a given spacecraft, launch
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window, and target.
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\section{Applications of Algorithm}
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In performing this examination, two results were selected for further analysis. These
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results are outlined in Table~\ref{results_table} below:
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Talk a bit about why this work is valuable. Missions that could have benefited, missions that
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this enables, etc.
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\begin{table}[h!]
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\begin{small}
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\centering
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\begin{tabular}{ | c c c c c c | }
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\hline
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\bfseries Flyby Selection &
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\bfseries Launch Date &
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\bfseries Mission Length &
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\bfseries Launch $C_3$ &
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\bfseries Arrival $V_\infty$ &
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\bfseries Fuel Usage \\
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& & (years) & $\left( \frac{km}{s} \right)^2$ & ($\frac{km}{s}$) & (kg) \\
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\hline
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EMS & 2024-06-27 & 7.9844 & 60.41025 & 5.816058 & 446.9227 \\
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EMJS & 2023-11-08 & 14.1072 & 40.43862 & 3.477395 & 530.6683 \\
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\hline
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\end{tabular}
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\end{small}
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\caption{Comparison of the two most optimal trajectories}
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\label{results_table}
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\end{table}
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As can be seen in the table, both resulting trajectories have trade-offs in mission
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length, launch energy, fuel usage, and more. However, both results should be considered
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very useful low-thrust trajectories in comparison to other missions that have launched
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on similar interplanetary trajectories, using both impulsive and low-thrust arcs with
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planetary flybys. Each of these missions should be feasible or nearly feasible (feasible
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with some modifications) using existing launch vehicle and certainly even larger
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missions should be reasonable with advances in launch capabilities currently being
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explored.
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\section{Recommendations for Future Work}\label{improvement_section}
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Recommend future work, obviously. There are a \emph{ton} of opportunities for improvement
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including parallelization, cluster computing, etc.
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In the course of producing this algorithm, a large number of improvement possibilities
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were noted. This work was based, in large part, on the work of Jacob Englander in a
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number of papers\cite{englander2014tuning}\cite{englander2017automated}
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\cite{englander2012automated} in which he explored the hybrid optimal control problem of
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multi-objective low-thrust interplanetary trajectories.
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In light of this, there are a number of additional approaches that Englander took in
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preparing his algorithm that were not implemented here in favor of reducing complexity
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and time constraints. For instance, many of the Englander papers explore the concept of
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an outer loop that utilizes a genetic algorithm to compare many different flyby planet
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choice against each other. This would create a truly automated approach to low-thrust
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interplanetary mission planning. However, a requirement of this approach is that the
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monotonic basin hopping algorithm algorithm must converge on optimal solutions very
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quickly. Englander typically runs his for 20 minutes each for evolutionary fitness
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evaluation, which is over an order of magnitude faster than the implementation in this
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paper to achieve satisfactory results.
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Further improvements to performance stem from the field of computer science. An
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evolutionary algorithm such as the one proposed by Englander would benefit from high
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levels of parallelization. Therefore, it would be worth considering a GPU-accelerated or
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even cluster-computing capable implementation of the monotonic basin hopping algorithm.
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These cluster computing concepts scale very well with new cloud infrastructures such as
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that provided by AWS or DigitalOcean.
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Finally, the monotonic basin hopping algorithm as currently written provides no
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guarantees of actual global optimization. Generally optimization is achieved by running
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the algorithm until it fails to produce newer, better trajectories for a sufficiently
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long time. But it would be worth investigating the robustness of the NLP solver as well
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as the robustness of the MBH algorithm basin drilling procedures in order to quantify
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the search granularity needed to completely traverse the search space. From this
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information, a new MBH algorithm could be written that is guaranteed to explore the
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entire space.
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\bibliographystyle{plain}
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\nocite{*}
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\bibliography{thesis}
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\appendix
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% \input appendixA.tex
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\chapter{Description of Analyzed EMS Mission}
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\begin{verbatim}
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Spacecraft: ingested
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dry_mass: 200.0 kg
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specific impulse: 3200.0 kg/s
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max_thrust: 0.00025 kN
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num_thrusters: 1
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duty_cycle: 1.0
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Launch Mass: 3500.0 kg
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Launch Date: 2024-06-27T19:18:02.199
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Launch V∞: [7.318672248992913, -1.529445415719206, -2.1232244559503632] km/s
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Phase 1:
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Planet: Mars
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V∞_in: [7.432780013001029, -6.019743530186103, -1.6225406279089392] km/s
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V∞_out: [8.396365726714938, -4.331889724433616, -2.2036070311537257] km/s
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time of flight: 1.0927270179201803e8 seconds
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arrival date: 2027-12-14T12:49:43.199
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thrust profile:
|
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[0.024235377030207825 0.00888170550219598 0.005275020106447728;
|
||||
0.02399025570663619 0.009687152442138303 0.004849683247103559;
|
||||
0.0237144984626321 0.010458650361418086 0.004447602441224652;
|
||||
0.023365271668340265 0.011247241096547612 0.00410447324935814;
|
||||
0.022940246865578544 0.011992030803744004 0.003821686419038526;
|
||||
-0.0019431547304985285 0.022688407700327172 0.022416659898786426;
|
||||
-0.0025131130230123333 0.023295814088309913 0.02221394673732401;
|
||||
-0.003088246519407214 0.023857826650815685 0.022054838661828224;
|
||||
-0.0037472235028326384 0.024343551156414713 0.021927933373391342;
|
||||
-0.0044375927787249055 0.02478918143527712 0.021844394088438177;
|
||||
-0.026105255729024664 0.038220540187214436 0.036279642377852375;
|
||||
-0.026780618554629817 0.03853252364509573 0.03626804427696657;
|
||||
-0.027455978112321453 0.038792575810529445 0.03625595201277916;
|
||||
-0.028141168092815964 0.03898902440339647 0.03629021876552949;
|
||||
-0.028809778187518193 0.03915971736492042 0.03633253932440753;
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
-0.09349526192155118 0.04200434863352099 0.044382762987534824;
|
||||
-0.09405840998459714 0.04192551288186246 0.04450187342394806;
|
||||
-0.0946401085181183 0.04180206021631332 0.04461269535084477;
|
||||
-0.09517609258972438 0.0416750889768316 0.04474097351038166;
|
||||
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|
||||
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||||
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|
||||
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||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
-0.15829074995512293 0.014483196359902813 0.04182661977219703;
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
-0.21269589565868435 -0.06910164866049198 0.027835587629257585;
|
||||
-0.22095520431071133 -0.1034315240983098 0.02195619219040112;
|
||||
-0.22095363324455022 -0.1039363396014177 0.02208001814134371;
|
||||
-0.2209258519378579 -0.10444228817076168 0.02218803322309374;
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||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
0.18514409741232546 -0.4318093470304242 -0.02842018614555766;
|
||||
0.1865424521966812 -0.4314123035364245 -0.028679538560778695;
|
||||
0.18794100981484788 -0.43087767476266803 -0.028977178116178365;
|
||||
0.18932086049377508 -0.430176573615346 -0.02927532805815704;
|
||||
0.4837483008894513 -0.30082715558431117 -0.05230879791806509;
|
||||
0.4849770899365583 -0.29968442455901756 -0.052680313525351165;
|
||||
0.48605025678632957 -0.29834697789345743 -0.05307023899553684;
|
||||
0.48693403264870355 -0.296777549423668 -0.05347081616460879;
|
||||
0.4875876938768627 -0.29502768045570976 -0.05387046513476967;
|
||||
0.5997886548585618 -0.05017567151672444 -0.04220063350923577;
|
||||
0.5999113857257048 -0.04825130664045737 -0.0425898328606256;
|
||||
0.5997797857664303 -0.046377827441315855 -0.04295737068172849;
|
||||
0.5994264737794556 -0.04459532310393294 -0.04329715637337397;
|
||||
0.5988885340570684 -0.04294830975144203 -0.043619159341178826] %
|
||||
Phase 2:
|
||||
Planet: Saturn
|
||||
V∞_in: [5.118021911011515, 2.7626475209564307, 0.012833534427407025] km/s
|
||||
V∞_out: [0.04582457242616684, 0.2173338665561733, -0.5293480027886823] km/s
|
||||
time of flight: 1.425235096053827e8 seconds
|
||||
arrival date: 2032-06-20T02:41:32.199
|
||||
thrust profile:
|
||||
[0.6329930516298814 0.3754387300559965 -0.041278153465157376;
|
||||
0.6316440411687961 0.3771539432333103 -0.04188668511010197;
|
||||
0.6302151630695931 0.37830148957229065 -0.04241470095684055;
|
||||
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|
||||
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|
||||
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|
||||
0.343350313682236 0.45843215556913436 -0.019974532323669136;
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
0.10346628293604881 0.1326945241515048 -0.04501460858407201;
|
||||
0.10341668769647967 0.13258690813141388 -0.04493381158618556;
|
||||
0.08849399118613269 0.11680369317500992 -0.039280465917766516;
|
||||
0.08844465220057159 0.11670144773928037 -0.039190520117983456;
|
||||
0.0883990105248394 0.11660286252447159 -0.03910152940381651;
|
||||
0.08835588260324095 0.1165080598699651 -0.039008555813330265;
|
||||
0.08831419794222022 0.11641486614981417 -0.03891218778502019;
|
||||
0.07376177902859117 0.10394822833846208 -0.03269665688227769;
|
||||
0.07372107116344209 0.10385982839740802 -0.03259505692154852;
|
||||
0.07368351060048883 0.10377297305809725 -0.03249294989285947;
|
||||
0.07364622913434896 0.10368999081313057 -0.03238728844927299;
|
||||
0.07360970006720247 0.10360783127082533 -0.03227792310783393;
|
||||
0.05680370570981956 0.10115866945703107 -0.02146434058106377;
|
||||
0.05676906375450203 0.10108215492628116 -0.021352075436948753;
|
||||
0.056736188710490354 0.10100483178367703 -0.021237396204120847;
|
||||
0.0567011948020336 0.10092951637553615 -0.021121532106371934;
|
||||
0.05666814786517165 0.10085693189940123 -0.021004878311086102;
|
||||
0.0420923731810672 0.09492980078603513 -0.009680493755208174;
|
||||
0.0420596575933162 0.09486013616427673 -0.009559253194484718;
|
||||
0.04202961101166327 0.09478983646575409 -0.009437219858373647;
|
||||
0.04199789569028146 0.09472227838497276 -0.009314186603688056;
|
||||
0.041969188425221834 0.09465571700171967 -0.009188458157484392;
|
||||
0.01719386670041908 0.09296262595556959 0.0089115031054126;
|
||||
0.0171642684422979 0.09289882405769614 0.009039422189717244;
|
||||
0.017135252657330843 0.09283621883835598 0.009169202649077841;
|
||||
0.01710552610610665 0.0927741969279537 0.00929901662916952;
|
||||
0.01707771370249971 0.09271327760075816 0.00943173754954676;
|
||||
-0.0016483799505183218 0.07938028069231376 0.024714217382829702;
|
||||
-0.0016754504265349072 0.07932176849316722 0.0248486613908432;
|
||||
-0.0017043398581652579 0.07926283876982425 0.02498319887196984;
|
||||
-0.001732622223154404 0.07920473576019973 0.02511898881854544;
|
||||
-0.0017608077747973984 0.07914815845852285 0.025255744358647744;
|
||||
-0.008092509276578796 0.05150236444831255 0.04578840784797782;
|
||||
-0.008120068587494467 0.051446574492129415 0.04592756157575969;
|
||||
-0.008148281565883169 0.05139115211486721 0.046067533608893256;
|
||||
-0.008176404453626634 0.05133685031323035 0.04620825230233717;
|
||||
-0.00820358892659607 0.051282994067783375 0.04634913408495792;
|
||||
0.008342964282222377 0.03510896165031955 0.06135284102436636;
|
||||
0.008314385245044785 0.035057877431210305 0.06149607013527497;
|
||||
0.008286633745210943 0.03500387246553423 0.061638798026826;
|
||||
0.008258897124154313 0.03495281419992153 0.06178278436294488;
|
||||
0.008231407299296863 0.034900022178568836 0.0619271330435043;
|
||||
0.049338794163242446 0.010218649631108702 0.03518291555481896;
|
||||
0.04931153496147123 0.010167641433603034 0.03532738870918014;
|
||||
0.0492836121523927 0.010116746246469603 0.035472649037170186;
|
||||
0.0492556394568435 0.010066283003036306 0.035617726485773375;
|
||||
0.049227886385957084 0.010015154199619465 0.03576338237025743;
|
||||
0.028999848123421643 0.013076326444851995 -0.0020538061417818116;
|
||||
0.02897144523491084 0.013025776906269888 -0.0019074186593764;
|
||||
0.028943969210132623 0.01297546972092727 -0.0017610664493855983;
|
||||
0.028916486144297066 0.012925951671522194 -0.0016148146309075833;
|
||||
0.028888610914008794 0.012876314501514538 -0.0014679290423102944;
|
||||
-0.002388102613327097 0.0009451120845601065 -0.00560054558587805;
|
||||
-0.0024162568174164725 0.0008956034389303988 -0.005453162652982702;
|
||||
-0.002444446078784889 0.0008470308856443604 -0.0053049735651656636;
|
||||
-0.002472450721052887 0.0007975886693055877 -0.00515747636345846;
|
||||
-0.002500372523042182 0.0007481141860366865 -0.005009629534358225;
|
||||
-0.026190217031866518 -0.01783065662929325 -0.005889671840944686;
|
||||
-0.02621824113539601 -0.017879866529648538 -0.005741535261451314;
|
||||
-0.026246514731744483 -0.017928783707094893 -0.005593366094207994;
|
||||
-0.02627442891538959 -0.017977869804518255 -0.005444920908759916;
|
||||
-0.026302480351648998 -0.01802662879261315 -0.005296633832816068] %
|
||||
Mass Used: 446.92274637633045 kg
|
||||
Launch C3: 60.41024885818919 km²/s²
|
||||
||V∞_in||: 5.816058313518406 km/s
|
||||
\end{verbatim}
|
||||
|
||||
\chapter{Description of Analyzed EMJS Mission}
|
||||
|
||||
\begin{verbatim}
|
||||
Spacecraft: ingested
|
||||
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: 2023-11-08T16:28:05.002
|
||||
Launch V∞: [-4.335012055084635, 4.544887484580865, 0.9951321890482566] km/s
|
||||
Phase 1:
|
||||
Planet: Mars
|
||||
V∞_in: [-7.121293324402133, 3.1557449977550442, 0.2574124611969375] km/s
|
||||
V∞_out: [-5.88728969114733, 5.091798086780573, 0.4318349867190985] km/s
|
||||
time of flight: 7.69225867524608e7 seconds
|
||||
arrival date: 2026-04-16T23:51:11.002
|
||||
thrust profile:
|
||||
[-0.03956033280289971 0.014502274153396886 0.013767483820172557;
|
||||
-0.041576479761307766 0.010774744221230172 0.015954618100526122;
|
||||
-0.04353519609600167 0.007026291842675089 0.018015518823847464;
|
||||
-0.04547258505717467 0.0030483408188381605 0.01993777253806961;
|
||||
-0.047309011488274606 -0.0012193548498561485 0.021657327331670945;
|
||||
-0.052415487659225525 -0.06416407139171071 0.01707388662648066;
|
||||
-0.053795860137490825 -0.06910602876361567 0.018377866968160055;
|
||||
-0.05478537648848572 -0.07435827994314907 0.01948872251679001;
|
||||
-0.05534637430302962 -0.07987969781686377 0.020391393740754694;
|
||||
-0.05542234511951779 -0.08557119998417642 0.02112165287536681;
|
||||
-0.04603653494469639 -0.11758339178872364 0.010478731803032337;
|
||||
-0.045131078072944794 -0.12330822437476184 0.010879231121188585;
|
||||
-0.04374974899764054 -0.12899509823771538 0.011155318621208977;
|
||||
-0.04192900589988677 -0.1345812372404263 0.011297583377631603;
|
||||
-0.039688700024628897 -0.1399961637348015 0.011314220390491788;
|
||||
-0.021847974947327285 -0.16435052102367306 0.002129770511850757;
|
||||
-0.0188961179478137 -0.16932814279205108 0.0019686779710134782;
|
||||
-0.015599029971580343 -0.17407912298359424 0.0017313208387575577;
|
||||
-0.012031227415560878 -0.17858564810418573 0.0013985317033249586;
|
||||
-0.008207263100371613 -0.18286189049060542 0.0010060475404519795;
|
||||
0.014387339499824707 -0.19615027292721257 -0.00697183966316377;
|
||||
0.018642044330809005 -0.19987677851880534 -0.007463937791430979;
|
||||
0.023072513804048733 -0.20333133902195877 -0.00801459777552152;
|
||||
0.027678111409082235 -0.2065512162021133 -0.008611471741542965;
|
||||
0.032416273918375434 -0.20950234109176658 -0.009241460528211365;
|
||||
0.05727065647767366 -0.2191433536041639 -0.014881165830189167;
|
||||
0.062210812252887084 -0.22156351523857395 -0.015576788935959698;
|
||||
0.06721613957517825 -0.22373619052124705 -0.016302796271852785;
|
||||
0.07231447457452297 -0.2256683324065783 -0.01705477220837316;
|
||||
0.07744821845226961 -0.22736856704804745 -0.017819357428142422;
|
||||
0.10200350811113468 -0.2278163660730623 -0.021691173614823873;
|
||||
0.10718625444262414 -0.22902365778493775 -0.022499165329662302;
|
||||
0.11238587770647483 -0.23001847034344625 -0.023321075083325548;
|
||||
0.1175907742151868 -0.23079464658829757 -0.024158451967652046;
|
||||
0.12281268073016817 -0.2313256017139053 -0.025009765392792066;
|
||||
0.14734148617688178 -0.23193110054122293 -0.026828068899809883;
|
||||
0.15246062165647492 -0.2320289354192666 -0.027693691138489004;
|
||||
0.15756013484944287 -0.23190919000372037 -0.0285724598987323;
|
||||
0.16262957652479712 -0.23155961671710285 -0.029454306835995363;
|
||||
0.16762616877319578 -0.2310186539384696 -0.030330493888002703;
|
||||
0.19021986463225274 -0.2237256987767045 -0.030832740235886377;
|
||||
0.19505197721608555 -0.22276253734494164 -0.0317116881014192;
|
||||
0.19984023688892388 -0.22157614923229768 -0.03260448718125773;
|
||||
0.204553599155851 -0.22018960071693844 -0.033482125661950926;
|
||||
0.20920235719105212 -0.21858157069918113 -0.0343665518915779;
|
||||
0.2279686631467231 -0.2074422688851766 -0.03356807904648546;
|
||||
0.2323853660755647 -0.2054201599551011 -0.03444494413786678;
|
||||
0.23671311464094724 -0.2032047355747267 -0.03531629778279262;
|
||||
0.24094332815999528 -0.20077041104419038 -0.0361806846806879;
|
||||
0.24508066397640577 -0.1981405377685498 -0.03702438323954723;
|
||||
0.2620323690523707 -0.18676055455915724 -0.035321161962334015;
|
||||
0.2658847553944062 -0.1837111520291871 -0.03616029682180003;
|
||||
0.2696275418295141 -0.18045886191354016 -0.03698682357490637;
|
||||
0.27327302946151294 -0.17699706837176704 -0.03780180073404257;
|
||||
0.27678271265735493 -0.17334151560199165 -0.03859889067141412;
|
||||
0.2909191888741266 -0.15618402096479228 -0.03611127095741274;
|
||||
0.2941076934397531 -0.1520807594030151 -0.036885574493546645;
|
||||
0.2971711407675296 -0.1477847558967073 -0.03765273809608395;
|
||||
0.3000921225525933 -0.14327687220290794 -0.03840483203030062;
|
||||
0.302873185822033 -0.13857943321564622 -0.039116765312786565;
|
||||
0.3116655641933065 -0.11991931768047741 -0.0361834413012538;
|
||||
0.31410598858453276 -0.11476986707549652 -0.03686954460237472;
|
||||
0.3163852071623763 -0.10941364316275648 -0.03753204013869077;
|
||||
0.31848712811881486 -0.10386237940041423 -0.03816423179059982;
|
||||
0.3204262692565581 -0.0981154571983449 -0.03878521398590498;
|
||||
0.3256678044130722 -0.07838444022075244 -0.03511972772107344;
|
||||
0.32721151962628264 -0.07219320123535682 -0.035684990170265496;
|
||||
0.3285634628040565 -0.0658097723763517 -0.03621630172719094;
|
||||
0.3296774910670562 -0.059216512263922466 -0.03672269403520816;
|
||||
0.3306037421484716 -0.052440905826970474 -0.03719693970630558;
|
||||
0.33328388923267627 -0.030327534780048324 -0.033168979778165145;
|
||||
0.33371746054004786 -0.023134888383537524 -0.033576710353787294;
|
||||
0.33389175751698497 -0.01574903993297518 -0.03393973891492299;
|
||||
0.33380633367079 -0.008182342781467823 -0.0342573724908797;
|
||||
0.33342660729643503 -0.0004248833440292039 -0.03453996222672837;
|
||||
0.3390725685662831 0.02756569570957198 -0.030334702196871285;
|
||||
0.3380833432257479 0.03567047160764992 -0.030528989791387733;
|
||||
0.33675065806255133 0.04393525489567044 -0.030663612383741653;
|
||||
0.33506715162123424 0.05238261972835011 -0.030758858718819428;
|
||||
0.3330117665436285 0.0609445328094011 -0.03079110300637972;
|
||||
0.311092400758174 0.09346079037581413 -0.025420523227424406;
|
||||
0.30810889360138993 0.10225487688815191 -0.025340625186851942;
|
||||
0.3046520673782745 0.1111657055432318 -0.02519931087775893;
|
||||
0.3006841235275496 0.12016917200239183 -0.024980281657263303;
|
||||
0.2961738618627909 0.1292489694856472 -0.024701968974558373;
|
||||
0.2735165965939293 0.1619979905410212 -0.01869630655188906;
|
||||
0.2676587760768934 0.1710598613565007 -0.018258442297774177;
|
||||
0.2611268574754945 0.18010472448692472 -0.017743059114779546;
|
||||
0.2538542304726611 0.18910841101106657 -0.01712960149634353;
|
||||
0.24581028537105218 0.19800484453654849 -0.016418319274889952;
|
||||
0.20666869884086048 0.24449798918762772 -0.010479404541833484;
|
||||
0.19661838861414238 0.25278629475126474 -0.009583933716756832;
|
||||
0.185593310022131 0.26078424163575775 -0.008578297521869437;
|
||||
0.1735491928214268 0.2684089062735019 -0.007463828245551458;
|
||||
0.1604241654210947 0.2755419168542371 -0.006243673883006362;
|
||||
0.11764420987192885 0.3026128805297053 -0.0027808955696240526;
|
||||
0.1020256537979734 0.30819300429344426 -0.0013314690854612414;
|
||||
0.08524068300499618 0.31284158307591525 0.0002381332205356246;
|
||||
0.06730138419613374 0.3163648963620088 0.0019230866854307947;
|
||||
0.04826513140941637 0.3185318511746061 0.003707513869349553] %
|
||||
Phase 2:
|
||||
Planet: Jupiter
|
||||
V∞_in: [-2.4700745323840945, 3.5992843576814684, -0.04897910356619292] km/s
|
||||
V∞_out: [2.3726396804033665, 3.660071493225041, -0.18342240674607424] km/s
|
||||
time of flight: 1.0365627669349752e8 seconds
|
||||
arrival date: 2029-07-29T17:15:47.002
|
||||
thrust profile:
|
||||
[-0.05988472231417988 0.5098718574120789 0.003380381450714991;
|
||||
-0.09985679108378966 0.5099970456619252 0.007680524392304216;
|
||||
-0.14083421951474379 0.5051230227055744 0.012059671089214113;
|
||||
-0.1806537704798288 0.49506022146586576 0.01638507392002354;
|
||||
-0.21707969492739523 0.48021220494730227 0.02057113683022605;
|
||||
-0.32471394771469786 0.4295719891811384 0.01872201874781426;
|
||||
-0.347149092726571 0.4026010250742786 0.022369089660714277;
|
||||
-0.3635390170080211 0.37415292304681513 0.025671314432171383;
|
||||
-0.3742393760147842 0.3457764845105525 0.02865266479348716;
|
||||
-0.3800621096770123 0.31860555955757813 0.031325752410159356;
|
||||
-0.39269541135392216 0.2188962027151091 0.03258569777778156;
|
||||
-0.39145308216679325 0.1937691388951771 0.03471143696114105;
|
||||
-0.3880119345885402 0.171349220288765 0.03661393416731571;
|
||||
-0.3830191997329326 0.15157634467357106 0.03831373113348574;
|
||||
-0.3769823877981445 0.13425557848329225 0.039836235108387456;
|
||||
-0.35514383707999975 0.0942343336397406 0.04952161544225744;
|
||||
-0.3477490228181278 0.08104440223464975 0.050723794597789085;
|
||||
-0.3401775362653594 0.06964193109114582 0.0517919222219017;
|
||||
-0.3325828482029597 0.05978311736608686 0.05273028845807096;
|
||||
-0.32506788814378285 0.05127786041217034 0.05356197088206576;
|
||||
-0.30127664757064254 0.03503792324857105 0.0678775597218983;
|
||||
-0.29389828176960936 0.028719164402623547 0.06849638363606865;
|
||||
-0.2867579056968465 0.02327696635356762 0.06903033183753615;
|
||||
-0.279878902965117 0.018597268896111088 0.06948001101246397;
|
||||
-0.2732639685923939 0.014579106100064064 0.06985564581182432;
|
||||
-0.25143317328935577 0.004822032764249745 0.08096437986103547;
|
||||
-0.24522909200643966 0.0018873197727133813 0.08119267602988196;
|
||||
-0.23928898621498146 -0.000608531122887676 0.08136448741577101;
|
||||
-0.23360561093639462 -0.0027289405875453327 0.0814753944747385;
|
||||
-0.22816865402914116 -0.004512956524485317 0.08153804920841505;
|
||||
-0.21234203920450526 -0.011413644583325671 0.0852674329374285;
|
||||
-0.20731416132016534 -0.012646855647744948 0.08522622899852404;
|
||||
-0.2025030171885313 -0.01365436394320526 0.08514312487442337;
|
||||
-0.19789976269436427 -0.014468226957282103 0.08501596072203135;
|
||||
-0.19348767693675864 -0.015105863083131995 0.08484912080149803;
|
||||
-0.18004901233725823 -0.02060449520344064 0.08340217879018821;
|
||||
-0.1759662862657398 -0.020951068437642564 0.08316118843675945;
|
||||
-0.17205156414511996 -0.021182166364363285 0.08288603181978693;
|
||||
-0.1682940386234932 -0.021310823181451173 0.08257708638661887;
|
||||
-0.16468683810346085 -0.021346310895505764 0.08223873732174773;
|
||||
-0.1543320368498933 -0.025660974285847696 0.07442424976309485;
|
||||
-0.15097888054040368 -0.025541687729640335 0.07402819847396758;
|
||||
-0.14775311478422373 -0.02536136401215251 0.0736086638129803;
|
||||
-0.14464992068219282 -0.02512728735566848 0.07316223230628852;
|
||||
-0.1416558613450808 -0.024845085523198057 0.07269211361342709;
|
||||
-0.1415623768665157 -0.028792559619746007 0.06345781418680149;
|
||||
-0.13878387444913906 -0.028431438277586155 0.06294422712493711;
|
||||
-0.13610076696164725 -0.028037829197217028 0.06241031547053575;
|
||||
-0.1335080193450605 -0.027616248159230982 0.061856689730120734;
|
||||
-0.1310011543407292 -0.027173070081896185 0.061282177796602645;
|
||||
-0.11649284418400539 -0.029718660679223928 0.05059493418875514;
|
||||
-0.11412747793329776 -0.029235169928036604 0.04998534694909494;
|
||||
-0.11183185659474973 -0.028739156807069538 0.049357459365379885;
|
||||
-0.10960785386698936 -0.028230136583549347 0.04871458263785479;
|
||||
-0.107449414764391 -0.027712732070757987 0.048054900238084765;
|
||||
-0.1010067742543605 -0.030035913148180264 0.03985652411759926;
|
||||
-0.0989658692805771 -0.029504447321812382 0.03916932532994344;
|
||||
-0.09698208078877331 -0.02896899150495436 0.038466386559246106;
|
||||
-0.09505063546052801 -0.028431606854815376 0.037751657245212324;
|
||||
-0.09317143312733227 -0.027892622486673277 0.03702228867717901;
|
||||
-0.08755719665655483 -0.029654460591863302 0.03165112419363048;
|
||||
-0.08576743409266635 -0.029114549477146912 0.03089813129635783;
|
||||
-0.08402030511855238 -0.028578111035422484 0.030133890557482588;
|
||||
-0.08231359723039965 -0.028044148889432248 0.029358424561623162;
|
||||
-0.08064580281614322 -0.027512635462536118 0.028571943924095334;
|
||||
-0.07562099754108047 -0.029225028527746767 0.026135747885363513;
|
||||
-0.07402205124189658 -0.02870096662135258 0.025329546723042964;
|
||||
-0.07245538189513678 -0.02818103553603966 0.024513810950172413;
|
||||
-0.07091914838573711 -0.027667562066487267 0.0236892820980254;
|
||||
-0.06941194567127179 -0.02715852307168577 0.022855649696120566;
|
||||
-0.06444725216331891 -0.028129807594017883 0.02241381197641579;
|
||||
-0.0629887732988159 -0.02763280189951615 0.021563370700178854;
|
||||
-0.06155686282996444 -0.027142510126807948 0.02070601768968898;
|
||||
-0.060147421316205596 -0.026656699587050477 0.019841340933161766;
|
||||
-0.05875974806303113 -0.026179197427987327 0.01896864012786145;
|
||||
-0.05474981164171225 -0.027817938578884576 0.020689703314815632;
|
||||
-0.05339834306170722 -0.02735214679579984 0.019804305041766553;
|
||||
-0.052064855674675614 -0.026893378665906336 0.0189127175609396;
|
||||
-0.05074918251335782 -0.02644100703367326 0.018015696025811878;
|
||||
-0.04944799401648106 -0.02599578821354754 0.01711307693411162;
|
||||
-0.04436520947052908 -0.02715696450606668 0.02003529214607189;
|
||||
-0.043089584107393296 -0.02672393174200551 0.01912180324645498;
|
||||
-0.04182530873924276 -0.026296220647751358 0.01820385010281347;
|
||||
-0.04057366905297342 -0.025876206610750012 0.01728182977712425;
|
||||
-0.039331241703650065 -0.02545942425212438 0.01635625450605495;
|
||||
-0.02725788215620618 -0.028444223181240496 0.02297009691214131;
|
||||
-0.026027590759992635 -0.02804148220354547 0.022036752187993003;
|
||||
-0.024805147240372426 -0.02764378253724356 0.02110101491862047;
|
||||
-0.023589347866205486 -0.02725091384718256 0.020161683409456097;
|
||||
-0.022379917120656196 -0.026863185354985736 0.019219647145726874;
|
||||
0.0024611476896890623 -0.01530199690864104 0.0012834357703477152;
|
||||
0.0036707313966874316 -0.014923349116622638 0.0003322506378020735;
|
||||
0.0048766102964706085 -0.01454799372327185 -0.0006210748132951684;
|
||||
0.0060798953671353006 -0.014175483649539933 -0.0015758044856345728;
|
||||
0.007280016024428352 -0.013804886358427955 -0.0025320598985469427;
|
||||
0.010063656512470718 -0.011858559656874148 -0.0006649670891605682;
|
||||
0.0112610952310549 -0.01149290667393944 -0.0016238692554735288;
|
||||
0.012457556187847591 -0.011129815323658804 -0.002582669900111043;
|
||||
0.013653698635247962 -0.010768062445170068 -0.0035421759772075873;
|
||||
0.014850558635080485 -0.010407794132715763 -0.004501417594322374] %
|
||||
Phase 3:
|
||||
Planet: Saturn
|
||||
V∞_in: [-1.288181310839508, 3.2263876606130104, -0.15259601195389053] km/s
|
||||
V∞_out: [0.48748673373831564, 0.4905484443382068, 0.477662291276709] km/s
|
||||
time of flight: 2.643066332108945e8 seconds
|
||||
arrival date: 2037-12-13T19:46:20.002
|
||||
thrust profile:
|
||||
[0.05787434800100662 0.06365972987059527 -0.004690937847485817;
|
||||
0.058804962259307765 0.0631535995879651 -0.004740314009454671;
|
||||
0.05983542454257423 0.06268609928169047 -0.004788047127416414;
|
||||
0.060975433718026835 0.062268789932902475 -0.004835524503135446;
|
||||
0.062225980024771796 0.06191324474149255 -0.004880865078012681;
|
||||
0.06285801042135475 0.054884663480775316 -0.004819160140313061;
|
||||
0.06433749312618502 0.054701052047457566 -0.004861768137879246;
|
||||
0.06593351900262197 0.05462711861876099 -0.004903833691377991;
|
||||
0.06764791684805822 0.05468390798107871 -0.004945075327582575;
|
||||
0.06947857183941591 0.05489653022456621 -0.004980756541231241;
|
||||
0.07158131197912566 0.05370903624290616 -0.004989096177551872;
|
||||
0.07363165632802447 0.05431132268456726 -0.005020718083045292;
|
||||
0.07577820988565821 0.05515538438056131 -0.005046798453303127;
|
||||
0.0780073675020361 0.05627588650036708 -0.005067760214972139;
|
||||
0.08029568923374143 0.05771722861801827 -0.005083195330091614;
|
||||
0.08641404640859522 0.06540989432376075 -0.005159860038250109;
|
||||
0.08872876215837687 0.06761198691109115 -0.005157363382001936;
|
||||
0.09098645045139106 0.07027159619046919 -0.005144483070629835;
|
||||
0.09311920513687692 0.07343855878826683 -0.005115355981375685;
|
||||
0.0950435632074984 0.07715907512797704 -0.005070050038753845;
|
||||
0.0908660761179946 0.08874696789878138 -0.004496676548803941;
|
||||
0.09203697993375162 0.09364596073645495 -0.004406109321394195;
|
||||
0.09260828024327085 0.09915333146965871 -0.004286107929658186;
|
||||
0.09240637528208999 0.10523220896976805 -0.004130286277826924;
|
||||
0.09123868316489085 0.11179453929787758 -0.003935854513014516;
|
||||
0.07912465530851204 0.13596343038757475 -0.0028759951878351217;
|
||||
0.07549824173301634 0.14287262484776403 -0.002591877765754475;
|
||||
0.07044590636435358 0.1495962483655315 -0.002262681758105387;
|
||||
0.06394805064460637 0.15579217045212151 -0.0018902947270343009;
|
||||
0.056112548356250944 0.16109946342889161 -0.0014792330372583168;
|
||||
0.01904757213758233 0.17335141612932936 0.0004365544649561594;
|
||||
0.009384103454269783 0.17596362750956665 0.000882767166216666;
|
||||
-0.0006032423594752967 0.17701150517873598 0.0013263367626259854;
|
||||
-0.010480530421161873 0.17651567069549542 0.0017538590199095807;
|
||||
-0.019864131305118157 0.17461251767364694 0.0021520045503883646;
|
||||
-0.05544288687740597 0.16702351088257864 0.0039606324298478435;
|
||||
-0.06295277675747966 0.16300176340850153 0.004276097768694192;
|
||||
-0.06939936202391099 0.15831833114553567 0.004547844760238192;
|
||||
-0.07477991730883271 0.15321727880857572 0.004777783846248338;
|
||||
-0.07914692452014976 0.14790369716999832 0.004966416095723749;
|
||||
-0.09768056439601996 0.1315897001493129 0.0060927517267796195;
|
||||
-0.10025432283625794 0.12627019907626186 0.006210956306072848;
|
||||
-0.10211674495356184 0.12111183400400113 0.006300806993342294;
|
||||
-0.10337178322590118 0.11617115733330916 0.006365439420741851;
|
||||
-0.10411315654262526 0.11148534135157803 0.006408856802719585;
|
||||
-0.11145137599334029 0.09663646118392062 0.006968262186688305;
|
||||
-0.11139513964195542 0.0924950143823055 0.006977002971475946;
|
||||
-0.11104614609848756 0.08863309161697829 0.00697321899610817;
|
||||
-0.11045699644128014 0.08504405119167102 0.0069578095966956605;
|
||||
-0.10967309376541882 0.08171409692812766 0.006932896225461464;
|
||||
-0.11346215033922648 0.07153553263548147 0.007283062872687444;
|
||||
-0.11239133056124612 0.06868639268322956 0.007242651339214947;
|
||||
-0.11122068319797335 0.06605392786207011 0.007196147885643773;
|
||||
-0.10997182069294363 0.06362301141102655 0.007144906756191574;
|
||||
-0.10866203074565452 0.06137874243355965 0.007089031998008915;
|
||||
-0.10882247916215068 0.051286067449190516 0.007021353108173517;
|
||||
-0.1074314564672795 0.049376951298364384 0.006958826502473229;
|
||||
-0.10601734008274794 0.04761439023924965 0.006893783213155025;
|
||||
-0.10458839303537582 0.04598613649007138 0.006826025792342359;
|
||||
-0.10315143090380435 0.044482152407399424 0.006756833630724034;
|
||||
-0.10462193352254216 0.031820244798679787 0.006445645832376893;
|
||||
-0.10318382535379975 0.03054038003667393 0.006373182758224606;
|
||||
-0.10175112664140157 0.029356784730798346 0.006299584979370768;
|
||||
-0.10032722734085553 0.028260174799026126 0.006224819087912654;
|
||||
-0.09891385336534615 0.02724385790286855 0.006149345795101277;
|
||||
-0.093268498989721 0.00812297399147717 0.0052265797092424385;
|
||||
-0.09188304463066377 0.007256655005284251 0.005150213714500697;
|
||||
-0.09051260761340546 0.0064514301571631325 0.0050729858743302735;
|
||||
-0.08915836084794382 0.005702278227716097 0.004995363126314977;
|
||||
-0.08781997142598436 0.005004364824361484 0.004917333622293092;
|
||||
-0.06930476427073393 -0.011470924413190399 0.0037955243203862477;
|
||||
-0.06800277450362639 -0.012076207430019012 0.0037171110540640388;
|
||||
-0.06671770843946283 -0.012642113866850966 0.003638292302041609;
|
||||
-0.06544909624773501 -0.01317286805748239 0.003559164047728649;
|
||||
-0.06419717821147211 -0.013671059649300824 0.003479969719091455;
|
||||
-0.052308544348541604 -0.013794235723210233 0.003839052530209843;
|
||||
-0.05108670201612136 -0.014238447033006175 0.0037593114668918633;
|
||||
-0.04988039768593651 -0.014658240490643328 0.003679278438710183;
|
||||
-0.048688572914389106 -0.015056466003002617 0.003599331650257482;
|
||||
-0.047510999113210946 -0.015434518536486435 0.003519209787879629;
|
||||
-0.023101747816005425 -0.015798620815194387 0.01347655988233254;
|
||||
-0.021948370627499054 -0.016148031734147573 0.013396736522653932;
|
||||
-0.02080732325880399 -0.016482645463410973 0.013316856141104557;
|
||||
-0.019678039496320753 -0.016804022833411883 0.013236971265791304;
|
||||
-0.018560016398954694 -0.01711343885931475 0.013157167864616725;
|
||||
-0.027547965324032513 -0.0157650105890274 0.010572160103389905;
|
||||
-0.026450026136227312 -0.01605247950645985 0.010491180109355212;
|
||||
-0.025361034081685226 -0.01633189614286892 0.010410303278362336;
|
||||
-0.024279917610766172 -0.016604272353015467 0.010329402082475111;
|
||||
-0.02320596089521229 -0.016870405667174137 0.010248635610308603;
|
||||
-0.02493524974482041 -0.008758509250002357 -0.008449923618533303;
|
||||
-0.02387252199314902 -0.0090155341044443 -0.00852950239400513;
|
||||
-0.022814864964132365 -0.00926859385313271 -0.008609325377136852;
|
||||
-0.02176157874947707 -0.00951856095743065 -0.008689050009448928;
|
||||
-0.020712211472897882 -0.009766079471127388 -0.008768924102388106;
|
||||
-0.022316082420292004 -0.015432581100616084 -0.002713090916906717;
|
||||
-0.02127206654031124 -0.01567617264428185 -0.002793411190767065;
|
||||
-0.02022956859236421 -0.0159188548014709 -0.0028738271376681866;
|
||||
-0.01918789336871752 -0.016160901736099867 -0.002954272690873852;
|
||||
-0.018146303148503164 -0.016402883837149045 -0.003034785707982439] %
|
||||
Mass Used: 530.668253715296 kg
|
||||
Launch C3: 40.43861983890888 km²/s²
|
||||
||V∞_in||: 3.4773947099827938 km/s
|
||||
\end{verbatim}
|
||||
% \input archive/best/long_mission
|
||||
|
||||
\end{document}
|
||||
|
||||
Reference in New Issue
Block a user