FINISHED THE DRAFT!!!!!!!!!!!!!

2022-02-20 23:28:20 -07:00
parent 700f7e28cf
commit c94f050eb8
2 changed files with 663 additions and 7 deletions
--- a/LaTeX/thesis.bib
+++ b/LaTeX/thesis.bib
@@ -62,3 +62,24 @@ month = {02},
 pages = {},
 title = {AAS 12-128 CONCEPTUAL DESIGN AND ANALYSIS OF PLANETARY DEFENSE TECHNOLOGY (PDT) DEMONSTRATION MISSIONS}
 }
@article{englander2017automated,
  title={Automated solution of the low-thrust interplanetary trajectory problem},
  author={Englander, Jacob A and Conway, Bruce A},
  journal={Journal of Guidance, Control, and Dynamics},
  volume={40},
  number={1},
  pages={15--27},
  year={2017},
  publisher={American Institute of Aeronautics and Astronautics}
 }
@article{englander2012automated,
  title={Automated mission planning via evolutionary algorithms},
  author={Englander, Jacob A and Conway, Bruce A and Williams, Trevor},
  journal={Journal of Guidance, Control, and Dynamics},
  volume={35},
  number={6},
  pages={1878--1887},
  year={2012}
 }
--- a/LaTeX/thesis.tex
+++ b/LaTeX/thesis.tex
@@ -1197,23 +1197,658 @@
 		\section{Overview of Results}
-			Quick re-wording of the previous section in a paragraph or two for reader's convenience.
+			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.
-		\section{Applications of Algorithm}
+			In performing this examination, two results were selected for further analysis. These
 			results are outlined in Table~\ref{results_table} below:
-			Talk a bit about why this work is valuable. Missions that could have benefited, missions that
+			\begin{table}[h!]
-			this enables, etc.
+			\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 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}
-			Recommend future work, obviously. There are a \emph{ton} of opportunities for improvement
+			In the course of producing this algorithm, a large number of improvement possibilities
-			including parallelization, cluster computing, etc.
+			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.
 	\bibliographystyle{plain}
 	\nocite{*}
 	\bibliography{thesis}
 	\appendix
-	% \input appendixA.tex
+
 		\chapter{Description of Analyzed EMS 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: 2024-06-27T19:18:02.199
 				Launch V∞: [7.318672248992913, -1.529445415719206, -2.1232244559503632] km/s
 				Phase 1:
 					Planet: Mars
 					V∞_in: [7.432780013001029, -6.019743530186103, -1.6225406279089392] km/s
 					V∞_out: [8.396365726714938, -4.331889724433616, -2.2036070311537257] km/s
 					time of flight: 1.0927270179201803e8 seconds
 					arrival date: 2027-12-14T12:49:43.199
 					thrust profile:
 					[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;
 					 -0.060178198449693604 0.045863248834624344 0.0437825750159069;
 					 -0.060832086109981906 0.04595200237956805 0.043845903840319694;
 					 -0.0614637322369173 0.04600218250765508 0.04392587747786364;
 					 -0.06208119542067157 0.046009361980197346 0.0440084727217644;
 					 -0.06270325274839472 0.04598208821563583 0.0441084524424021;
 					 -0.09349526192155118 0.04200434863352099 0.044382762987534824;
 					 -0.09405840998459714 0.04192551288186246 0.04450187342394806;
 					 -0.0946401085181183 0.04180206021631332 0.04461269535084477;
 					 -0.09517609258972438 0.0416750889768316 0.04474097351038166;
 					 -0.09569378105613152 0.041494386743123786 0.044851711195200004;
 					 -0.12403677347765954 0.031062806563607895 0.042227942339192845;
 					 -0.12452087322352202 0.030850448440375176 0.04235699321988777;
 					 -0.12498864069285591 0.030627282643177295 0.0425049647904722;
 					 -0.1254422057489061 0.03037782952573744 0.042636495744786264;
 					 -0.1258602731937137 0.0301269442123315 0.04277532634721488;
 					 -0.15685874809356395 0.015781803191410225 0.04125604163667304;
 					 -0.15724410737409986 0.01548663048123 0.04140397438274824;
 					 -0.15761543915061418 0.015174596469721642 0.041548585916012765;
 					 -0.15796668613822373 0.014825860053564717 0.04170193705279365;
 					 -0.15829074995512293 0.014483196359902813 0.04182661977219703;
 					 -0.18321198149177034 -0.006718420238249819 0.037981449142584056;
 					 -0.18350601725900687 -0.00708380754148209 0.0381377971297988;
 					 -0.18375962522349495 -0.007485844440849063 0.038266130099955505;
 					 -0.18401156514951283 -0.007868425114854648 0.03841853545942695;
 					 -0.18423751994903437 -0.0082750576401688 0.03856460443961429;
 					 -0.2024862754992264 -0.034848711542048265 0.03336400247905138;
 					 -0.2026707344937845 -0.035283049103160546 0.03350436335716191;
 					 -0.20284629279949265 -0.035719294394551654 0.03364110087797018;
 					 -0.2029945887354837 -0.036172019668414865 0.03379806025832671;
 					 -0.20311261765668395 -0.0366322645727282 0.0339245665278438;
 					 -0.21245470288929072 -0.06717661453328558 0.027283225271794283;
 					 -0.21254193080868825 -0.0676387475174252 0.02742259138543629;
 					 -0.2126099084522529 -0.0681289229181636 0.027561473450575184;
 					 -0.21265945852435034 -0.06860590656971097 0.02769054749028669;
 					 -0.21269589565868435 -0.06910164866049198 0.027835587629257585;
 					 -0.22095520431071133 -0.1034315240983098 0.02195619219040112;
 					 -0.22095363324455022 -0.1039363396014177 0.02208001814134371;
 					 -0.2209258519378579 -0.10444228817076168 0.02218803322309374;
 					 -0.22087725118828272 -0.10492891836947225 0.022330163267422397;
 					 -0.22080533929239932 -0.10544299107251072 0.022449713415175286;
 					 -0.19442709993064522 -0.14170202258034095 0.011558151934536999;
 					 -0.19431523610918064 -0.14220741730049713 0.011667367575730591;
 					 -0.19417317244980273 -0.14271188729460021 0.01178096590548684;
 					 -0.1939941491085289 -0.1432112391035578 0.011875683618928344;
 					 -0.19379659796210602 -0.1437113505886065 0.011971596929650875;
 					 -0.20839820924658076 -0.18973385738164752 0.009307451886292192;
 					 -0.20815817838894604 -0.19021671829427775 0.009393548264616419;
 					 -0.20788715281082848 -0.1907053323143535 0.009473574125552149;
 					 -0.20759267564754758 -0.19117297352465665 0.009563518034576692;
 					 -0.20725730932050385 -0.19164267398389476 0.00963504586160516;
 					 -0.1961075700059922 -0.24290142178750415 0.0038507129511980015;
 					 -0.19572169681551538 -0.24334914331638396 0.003899832796131259;
 					 -0.19530334973600788 -0.24379282734187754 0.003967473955005566;
 					 -0.19482592064607568 -0.2442236000134374 0.004013758357476628;
 					 -0.19435132556752394 -0.2446385052975962 0.004041938132303195;
 					 -0.16465195313849423 -0.3004276434505404 -0.0025477773747229144;
 					 -0.16406454228555667 -0.3008173014857693 -0.002534902557883806;
 					 -0.16344445045215752 -0.3011845231864255 -0.0025138987633786056;
 					 -0.1627790118528474 -0.30153330249237564 -0.0025126609092452866;
 					 -0.16205639079546422 -0.3018791849184296 -0.00252773549828917;
 					 -0.11454723260483883 -0.36146563395819015 -0.008724503528927063;
 					 -0.11374530519473426 -0.3617514022893357 -0.008763083025138563;
 					 -0.11286008364160728 -0.3620075243586088 -0.008811341523550892;
 					 -0.11192599887952116 -0.36222778056355126 -0.008862827469500274;
 					 -0.11094519109599958 -0.3624097362213787 -0.008962625818756769;
 					 -0.02391505591401128 -0.41864273911091776 -0.015187178892217643;
 					 -0.02279902972952809 -0.4187484864971973 -0.01532144436549937;
 					 -0.02162632152143365 -0.4187931725195911 -0.015456346700485964;
 					 -0.020391897110791923 -0.4187740995712499 -0.015610805544610595;
 					 -0.019101999843222355 -0.41868878897997275 -0.01579853500286071;
 					 0.18376634235176048 -0.4320763402653023 -0.02817451009484391;
 					 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;
 					 0.6288015612616553 0.3789983607933317 -0.04289870652729237;
 					 0.6274575627177201 0.37938177126004463 -0.04331674239208846;
 					 0.3444831378016049 0.4584427028939501 -0.01962983038346585;
 					 0.343350313682236 0.45843215556913436 -0.019974532323669136;
 					 0.3423488229049882 0.4583226246957569 -0.02026887281309082;
 					 0.3414712037645477 0.45814459638568994 -0.020531801085877724;
 					 0.34069847825976424 0.4579222760137032 -0.020769373866713528;
 					 0.2309654960711884 0.3890497901392047 -0.032657315112688504;
 					 0.23037656940414789 0.3887852800660396 -0.03283600644592424;
 					 0.22986064892155578 0.3885136473355805 -0.03299996243030687;
 					 0.2294073521107295 0.3882409934584674 -0.0331346252769696;
 					 0.22900442123476075 0.3879741809050926 -0.033255534578159524;
 					 0.1776968304910734 0.2857905066551956 -0.052473839368448266;
 					 0.17738168095719187 0.28553616026198864 -0.05255798491622259;
 					 0.17710100604422802 0.2852893588307732 -0.05263007802104745;
 					 0.17684981431112315 0.285050899002354 -0.05269073773925025;
 					 0.17661826565812588 0.2848216419041406 -0.052736460878895185;
 					 0.16302803071535937 0.2288440324934438 -0.05295539189756392;
 					 0.16284148405624235 0.22863476718195005 -0.052979024771766504;
 					 0.16267376993666366 0.22843348716311554 -0.052992796276301664;
 					 0.16252035790823205 0.22823748939942143 -0.0529990756032091;
 					 0.16237974278262335 0.22805068690324026 -0.052998820166630004;
 					 0.13417956270125225 0.18796600274090727 -0.05143256089624221;
 					 0.1340623808993445 0.18779402300149806 -0.05141714589345775;
 					 0.13395315890550555 0.18762968151984613 -0.051392473738747876;
 					 0.1338523104178968 0.18747060727932557 -0.05136297638267751;
 					 0.13375902683375174 0.18731665141801573 -0.05132801422329071;
 					 0.12758214347585456 0.15340398397435048 -0.05168052476232358;
 					 0.12749939620036213 0.15326098428950718 -0.051633621693863346;
 					 0.12742364258649297 0.15312464804515485 -0.051582232628574747;
 					 0.127351796100246 0.15299516000753102 -0.05152580226049547;
 					 0.12728610095610415 0.15286771555716733 -0.05146438099691739;
 					 0.10363864135617362 0.13303810609450925 -0.04523719298505366;
 					 0.10357714058263788 0.13292093309625866 -0.04516603592319711;
 					 0.10352044081060598 0.13280554812600356 -0.04509328051622902;
 					 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}