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pages={1878--1887},
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@article{brophy2002,
author = {Brophy,John R. },
title = {NASA’s Deep Space 1 ion engine (plenary)},
journal = {Review of Scientific Instruments},
volume = {73},
number = {2},
pages = {1071-1078},
year = {2002},
doi = {10.1063/1.1432470},
URL = {https://doi.org/10.1063/1.1432470},
eprint = {https://doi.org/10.1063/1.1432470}
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@article{cybulski1965results,
title={Results from SERT I ion rocket flight test},
author={Cybulski, Ronald J and Shellhammer, Daniel M and Lovell, Robert R and Domino, Edward J and Kotnik, Joseph T and Cybulski, J and Loveli, Robert R},
year={1965},
publisher={Citeseer}
}
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title={Dawn: A mission in development for exploration of main belt asteroids Vesta and Ceres},
author={Rayman, Marc D and Fraschetti, Thomas C and Raymond, Carol A and Russell, Christopher T},
journal={Acta Astronautica},
volume={58},
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publisher={Elsevier}
}
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title={BepiColombo—Comprehensive exploration of Mercury: Mission overview and science goals},
author={Benkhoff, Johannes and Van Casteren, Jan and Hayakawa, Hajime and Fujimoto, Masaki and Laakso, Harri and Novara, Mauro and Ferri, Paolo and Middleton, Helen R and Ziethe, Ruth},
journal={Planetary and Space Science},
volume={58},
number={1-2},
pages={2--20},
year={2010},
publisher={Elsevier}
}
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author={Vallado, David A},
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year={2001},
publisher={Springer Science \& Business Media}
}
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publisher={Cambridge university press}
}
@techreport{jezewski1975primer,
title={Primer vector theory and applications},
author={Jezewski, Donald J},
year={1975}
}
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title={SNOPT: An SQP algorithm for large-scale constrained optimization},
author={Gill, Philip E and Murray, Walter and Saunders, Michael A},
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number={1},
pages={99--131},
year={2005},
publisher={SIAM}
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title={On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming},
author={W{\"a}chter, Andreas and Biegler, Lorenz T},
journal={Mathematical programming},
volume={106},
number={1},
pages={25--57},
year={2006},
publisher={Springer}
}
@book{hohmann1960attainability,
title={The attainability of heavenly bodies},
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number={44},
year={1960},
publisher={National Aeronautics and Space Administration}
}
@inproceedings{Casalino2007IndirectOM,
title={Indirect Optimization Method for Low-Thrust Interplanetary Trajectories},
author={Lorenzo Casalino and Guido Colasurdo and Matteo Rosa Sentinella},
year={2007}
}
@article{sims1999preliminary,
title={Preliminary design of low-thrust interplanetary missions},
author={Sims, Jonathan and Flanagan, S},
year={1999}
}
@book{wie1998space,
title={Space vehicle dynamics and control},
author={Wie, Bong},
year={1998},
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}
@book{bate2020fundamentals,
title={Fundamentals of astrodynamics},
author={Bate, Roger R and Mueller, Donald D and White, Jerry E and Saylor, William W},
year={2020},
publisher={Courier Dover Publications}
}
@article{euler1767motu,
title={De motu rectilineo trium corporum se mutuo attrahentium},
author={Euler, Leonhard},
journal={Novi commentarii academiae scientiarum Petropolitanae},
pages={144--151},
year={1767}
}
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title={B-plane targeting method for orbit maneuver using low thrust},
author={Cho, Dong-Hyun and Lee, Donghun and Bang, Hyochoong and Kim, Hae-Dong},
journal={International Journal of Control, Automation and Systems},
volume={15},
number={4},
pages={1729--1737},
year={2017},
publisher={Springer}
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title={A historical review of the theory of gravity-assists in the pre-spaceflight era},
author={Negri, Rodolfo Batista and Prado, Antonio Fernando Bertachini de Almeida},
journal={Journal of the Brazilian Society of Mechanical Sciences and Engineering},
volume={42},
number={8},
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publisher={Springer}
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@techreport{blanchard1969unified,
title={A unified form of Lambert's theorem},
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}
@article{jordan1964application,
title={The application of lambert's theorem to the solution of interplanetary transfer problems(Lambert theorem applied to solution of interplanetary transfer problems)},
author={JORDAN, JF},
year={1964}
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title={Rocket propulsion elements},
author={Sutton, George P and Biblarz, Oscar},
year={2016},
publisher={John Wiley \& Sons}
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Launch Mass: 3500.0 kg
Launch Date: 2024-12-30T12:47:20.643
Launch V∞: [-0.8585858913059945, 5.43163312454597, -0.21719547468177308] km/s
Phase 1:
Planet: Mars
V∞_in: [-2.5856773315583745, 2.4609561275200487, 0.7295849474445574] km/s
V∞_out: [0.6194643215165332, 3.2309327456082855, 1.5650004450735309] km/s
time of flight: 8.21340000011604e7 seconds
arrival date: 2027-08-08T03:47:20.643
thrust profile: [0.18708793577518806 0.5313802548498593 0.20444668942359182; -0.06350657961080429 0.7363728402067601 0.14591280353760663; -0.5915522558225289 0.7847434950188144 0.026651112465872404; -0.7542562554239148 0.7746896783865607 -0.1237392373650896; -0.7866125946706723 0.6465409532772359 -0.181921929015919; -0.6858815963696551 0.5510566480853467 -0.17868708799185337; -0.7594148821784542 0.7476306773551871 -0.11848928569756635; -0.8151098482182527 0.36136227575490387 -0.07980840799214974; -0.7401577445019838 -0.3095683994157624 0.03448173859798725; -0.6080245532967408 -0.0062406255431043806 0.06699727498541076; -0.43741470194423654 0.4730679368243737 0.0339770148854078; -0.18490322648998495 0.6426379090283426 -0.13028954478184662; 0.47254893347274096 0.7718760888207634 -0.1551009557943166; 0.5190900646391018 0.8753585966827419 -0.08611250544188818; -0.8855993838016015 0.8714238270161355 -0.08045710930215778; -0.8920483208731022 0.293979266137998 -0.1008142011864752; -0.8306385396979714 -0.8016800304530476 -0.043159471100223716; -0.6873350930031549 -0.7928126872627601 -0.02124194344649641; -0.07252547075225568 -0.7402808067151411 -0.037972567496587895; 0.6875211020649464 -0.5605655534502224 -0.13311603635138225] %
Phase 2:
Planet: Mars
V∞_in: [1.1180674616624362, 4.566462924317003, 1.4292875212918483] km/s
V∞_out: [1.2322985249643665, 4.3433091442560645, 1.9398620619570397] km/s
time of flight: 6.237720000073707e7 seconds
arrival date: 2029-07-30T02:47:20.643
thrust profile: [0.5134182009488921 -0.31555188364900766 -0.055374803379038676; 0.5541643860557178 -0.10936971458523223 0.0007152948743699293; 0.5460385559170413 0.1530957100358743 0.05129389787053946; 0.46239205959354684 0.3541230771326737 0.0837352480895128; 0.2788761074398226 0.42401413505230207 0.09850448091487779; 0.0861711281015175 0.3771366798387737 0.08680527911942301; -0.0019793970085822893 0.2716311958716949 0.057899476045225384; -0.02438647027237024 0.1785456275302977 0.03356359507342958; -0.0460851975884734 0.13513224341732036 -0.0075472317756282775; -0.05051028634319777 0.13458427170959206 -0.056361751862420054; -0.059757482177925196 0.1155277298538939 -0.10695473795359935; -0.06308060055392012 0.08656293882186156 -0.14897716336334949; -0.060709990203287566 0.053581479830941116 -0.17880651728419109; -0.05399581102575967 0.019928172160662616 -0.19586000706017498; -0.04455159724330247 -0.012018413567160578 -0.20023332232742197; -0.03435074656279236 -0.04090428121904396 -0.19247441119311592; -0.02473533778237781 -0.06625905911693483 -0.17311082652131804; -0.017001426993727434 -0.08901248109333483 -0.14173368541223236; -0.01492966583523356 -0.11182046547456173 -0.09626664779027602; -0.02419545780950693 -0.1333838006203212 -0.04006325619060162] %
Phase 3:
Planet: Jupiter
V∞_in: [1.0425933248043313, 9.761014809328087, -0.4217373616811835] km/s
V∞_out: [-9.345457932936196, -2.8317056643741645, 1.0859916102035037] km/s
time of flight: 2.6687520000038186e8 seconds
arrival date: 2038-01-12T22:47:20.643
thrust profile: [0.5628431836674769 0.47506205926522466 0.01494314598245946; 0.21922079590638668 0.04171051990989757 0.2601684761848701; 0.6837155305781677 0.5152279955386716 0.0013884449392686086; 0.11204795410174831 0.7194929944329855 -0.05582598783813832; -0.5437076444290293 -0.5507865585159418 0.05488176961971801; 0.3946907920290721 0.3553045067960959 -0.0009333191781478536; 0.6286527350564048 0.15811539062067848 0.0010593852696665147; 0.5244115910894975 0.5054313632357015 0.06734970951936782; 0.16947323257204125 -0.25342029906455155 0.041224265782725; 0.8184810643617919 0.6150207802837899 -0.0007312998992708492; -0.29400957489332924 0.5349618499607386 -0.0022793003860954167; -0.1813961648289101 0.39314833358368484 0.02463460931711496; -0.24079119813027802 0.22304978428092506 -0.0452896662834434; 0.0692938115099807 0.2174985639878364 -0.039548706790466105; -0.055133140610399506 -0.3023901220512069 -0.10050398589752965; 0.4405772740882254 -0.5714961854289461 0.010199886302938704; 0.5508873740881252 0.7290499177697591 -0.009434982976593908; -0.3394222681154409 0.47080066387267466 0.1182603751716305; -0.2838812749863273 -0.14939589284636337 0.05198509208395944; -0.08739787411558196 -0.48848414007930296 -0.019353445078579605] %
Phase 4:
Planet: Saturn
V∞_in: [-0.12467502011680599, -0.21941891947700304, 1.1210048424481494] km/s
V∞_out: [-1.836549550435177, -1.0274249385233098, 0.15074571437514825] km/s
time of flight: 7.985519999979527e7 seconds
arrival date: 2040-07-25T04:47:19.643
thrust profile: [0.9015449791987612 -0.4135045547482888 -0.10493150953252237; 0.8281237041407337 -0.4199865377311189 -0.10871363555015406; 0.5865495210885522 -0.18888729221478687 -0.05376150916405686; 0.5536125796492021 -0.21710904361394967 -0.08288273835216246; 0.5226797275283863 -0.20596461753201076 -0.0816923569899679; 0.492356358914814 -0.1952282536684453 -0.07970598541671017; 0.4625023188662105 -0.18413996987155215 -0.07694322290334572; 0.4328711669558749 -0.17242291902938622 -0.07345517917885007; 0.4032239447511029 -0.16009204113840642 -0.06931306800923256; 0.3733858215361839 -0.14725361285778707 -0.06460897748518732; 0.3432505744179203 -0.13401143205085617 -0.05943463295918488; 0.3127627286749208 -0.12044462830785903 -0.053859778958435967; 0.2819001737662793 -0.10660684717642485 -0.04798048977198586; 0.2505956888019982 -0.09251745970413862 -0.04183914117857803; 0.21859841440967404 -0.07812693858807919 -0.03547943926291368; 0.18535858791227242 -0.06324296041863105 -0.02894834505985858; 0.15015303093566526 -0.047669454737263 -0.02232276989900783; 0.11229167669542692 -0.032210071289352 -0.015683269811579196; 0.07065162071067796 -0.01828153555341133 -0.0091544483837168; 0.02434581489906545 -0.005871680237325595 -0.002964910300780224] %
Mass Used: 2233.4875953911933 kg
Launch C3: 30.286982006636965 km²/s²
||V∞_in||: 1.149060650991836 km/s

30
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@@ -0,0 +1,43 @@
/home/connor/projects/thesis/archive/EMMJS_2022-02-21T05:29:13.100/mission---------------------------
Spacecraft: mySat
dry_mass: 200.0 kg
specific impulse: 3200.0 kg/s
max_thrust: 0.00025 kN
num_thrusters: 1
duty_cycle: 1.0
Launch Mass: 3500.0 kg
Launch Date: 2024-08-13T21:37:18.613
Launch V∞: [-1.6901867322791075, 5.280615079261146, -2.032003347094416] km/s
Phase 1:
Planet: Mars
V∞_in: [-1.7461250307138758, 2.7488621400103193, 1.513513215864433] km/s
V∞_out: [1.2027265638973148, 3.3257187268143342, 0.6259917731579052] km/s
time of flight: 2.4051597753353596e7 seconds
arrival date: 2025-05-19T06:37:15.613
thrust profile: [-0.0017599460808520734 0.021939823461937586 -0.07860824048711292; 0.0038057476482388137 0.01317123732517402 -0.0925516242969978; -0.012111500711155023 0.009175602331176976 -0.10689934082194484; -0.0057786091800751385 0.004785500911625599 -0.11802387642642173; -0.014871641299940966 -0.005768817944699136 -0.12261622402101267; -0.004758948871952711 -0.0018517590809734616 -0.1312674708448622; 0.007589952947205352 -0.009441179217149816 -0.13265233200159024; 0.02957759948608535 0.012559088860055839 -0.1178470071574203; 0.029293581498403685 -0.0027693172907246807 -0.12277829992312493; 0.00043915486764571567 0.012598754358696054 -0.12458999384207707; 0.039545288569820244 0.03314430343814683 -0.10624529827972352; 0.03219377536903767 0.050819916158926205 -0.09961115577485845; 0.03399569316999455 0.04298795510617496 -0.09578630843591786; 0.030077287420831947 0.08313823965268496 -0.06933023697506474; 0.037127301703059834 0.09397497850832547 -0.052654905925240816; 0.022412917519582787 0.10765616559310794 -0.025717008847364307; 0.025327703848176397 0.11276690546887153 0.004843267678066204; 0.007650286567218721 0.11949746525926046 0.021216184066767087; -0.0038980974979574835 0.1248646921852295 0.028322916840977087; -0.019178665908750572 0.12278762564523467 0.04346269663142969] %
Phase 2:
Planet: Mars
V∞_in: [2.043297951821988, 1.6820451775844232, 1.823788193968268] km/s
V∞_out: [0.4882307516881071, -1.2152266867358175, 2.9360573603089075] km/s
time of flight: 1.14134402513377e8 seconds
arrival date: 2028-12-30T06:37:17.613
thrust profile: [0.22291730975859356 0.5098248034605009 0.24720522565212524; -0.4469925923761469 -0.007661162151150529 -0.08117095118772306; -0.5525078400371499 -0.4741527168000471 -0.14631851618865835; 0.18040546081731915 -0.7460124551180657 -0.05214179589449932; 0.6953342845058121 -0.5331751797010302 0.16302204627027528; 0.6185646245916668 0.06025626130956423 0.30205781678787413; 0.44949631635524223 0.03858256309628191 0.34300503738181515; 0.32691770627377126 -0.3565152659582362 0.26806235880669743; 0.3909860773308049 -0.4856009661776308 -0.060179414964323774; 0.3979512624499183 -0.3974411990059185 -0.2619149915820402; 0.4866100975196277 -0.41623220426978347 -0.05594094246998931; 0.43622582167391594 -0.21713526052371673 0.29394158670200404; 0.20594952174764747 -0.4177558340479653 0.3892322018647292; 0.25453944143605217 -0.6261670137409058 0.3258204997833534; 0.5749031989207859 -0.6800207997886729 0.12429472580187996; 0.7530954315757951 -0.3098572647533813 -0.2144972990721993; 0.4851334634524593 0.64491549530751 -0.26752525551583867; -0.5764002596860117 0.3646707634147813 0.14796405075327934; -0.5901573878990791 -0.41314618778501866 0.3805666596159053; -0.42700527824297163 -0.6826390179287234 0.4045024615945392] %
Phase 3:
Planet: Jupiter
V∞_in: [3.7114411433504815, -4.460792211249508, -1.1805018431500913] km/s
V∞_out: [1.7805895932237876, -4.309492902052931, 3.6498067710496795] km/s
time of flight: 1.6335000237429604e8 seconds
arrival date: 2034-03-04T21:37:19.613
thrust profile: [-0.5046672735197064 -0.7996955535271304 0.2112934255095142; 0.5077989036864389 -0.7649454581859021 0.20409797991337683; 0.5808566386587612 -0.6364303545112504 0.18542744111458456; 0.5006095090625132 -0.48372727317177533 0.13748541541649756; 0.36800706000490335 -0.4274801913323154 0.04508051614164652; 0.23616890612114982 -0.4106281022924214 -0.07422701918557366; -0.02614107297996989 -0.4044558701986192 -0.16223559260078177; -0.2964744410521455 -0.34839867086847304 -0.21078013212233546; -0.5176405945957604 -0.3288038834641507 -0.19405120809950877; -0.6330040108688543 -0.42206025464387953 -0.15342166355020417; -0.7099262633889031 -0.6237883136733828 -0.07027765831937338; -0.7822443063582115 -0.7257522470091892 0.046372365248012457; 0.15416780610066894 -0.8145688662272869 0.11743307333391405; 0.6452194124175534 -0.678910631324967 0.054691069558399794; 0.5771299498788154 -0.4641832360664856 0.018420229596808394; 0.4457565039423475 -0.3040316838235003 0.01783058099504133; 0.23801401595031418 -0.13216754190081506 0.010767856013003372; 0.2587404825219754 0.09782617488793967 0.003859597411132576; -0.08344625676841577 0.2827272664297725 -0.026493133998743063; -0.3933999656322405 0.24332107698735156 -0.027081715518899548] %
Phase 4:
Planet: Saturn
V∞_in: [-0.0246480076721461, 0.06541562927953826, 0.07516568061471392] km/s
V∞_out: [-0.5848111974561183, 0.18686923783075082, -0.03206665093199944] km/s
time of flight: 2.1155400016049725e8 seconds
arrival date: 2040-11-16T10:37:19.613
thrust profile: [-0.1627110678115485 0.22700671143458248 0.029986080505317234; -0.16214080594693478 0.23967493565533463 0.08955363564847629; -0.1745196970984745 0.25483610546962543 0.12716395184957408; -0.1952524515982284 0.2505218299754148 0.17036723627980027; -0.21614749560569926 0.24089984374439646 0.19877853523817543; -0.22618695860284732 0.24715274229193332 0.2135402310441893; -0.33485154946340523 0.2613684298843818 0.23512617093629723; -0.3725246027720915 0.15599299255433202 0.25303578361261436; -0.36926821691311146 0.07153107899757735 0.26760363975946333; -0.35478356034012126 0.0018475578322651304 0.26116841888769105; -0.3312470217412482 -0.04985111461820565 0.25331488736816143; -0.30012674484829766 -0.07703821603688417 0.24136867711498777; -0.2634342927812894 -0.096191631413734 0.22794344262127944; -0.22575690873415977 -0.09889406062182618 0.199660205553818; -0.1887069515840364 -0.08881084245979123 0.17583719753517285; -0.14879690447972715 -0.07592681830346394 0.15115513011894557; -0.11724449357420508 -0.058526105092731553 0.11562822849360169; -0.08722592614665677 -0.03788553733718045 0.08344591269592441; -0.05347117156910084 -0.019641127134930575 0.052723601226170855; -0.024200395926615395 -0.005375747843091736 0.013406461289335841] %
Mass Used: 2059.4133968003325 kg
Launch C3: 34.87066440789543 km²/s²
||V∞_in||: 0.10264798282731782 km/s

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14
julia/make_plots.jl
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@@ -3,18 +3,20 @@ using PlotlyJS: savefig
a = ∛(Sun.μ * ( year/2π )^2 )
start = [ oe_to_xyz([ a, 0., 0., 0., 0., 0.5 ], Sun.μ); 10_000. ]
path = Thesis.prop(zeros(100,3), start, bepi, year)[1]
path = Thesis.prop(zeros(100,3), start, bepi, year)
p = Thesis.plot([path],
colors=["#0FF"],
title="Single LaGuerre-Conway-Propagated Orbit")
colors=["#F0F"],
title="Single LaGuerre-Conway-Propagated Orbit",
mode="light")
savefig(p, "LaTeX/fig/laguerre_plot.png")
t = 5year
spiral_sc = Sc("test", 1000., 2000., 0.0005, 50, 0.9)
start = [ oe_to_xyz([ 0.7a, 0.05, 0.1, 0., 0., 0.5 ], Sun.μ); 100_000. ]
spiral_thrust = spiral(0.2, 100_000, start, spiral_sc, t)
spiral_path = Thesis.prop(spiral_thrust, start, spiral_sc, t)[1]
spiral_path = Thesis.prop(spiral_thrust, start, spiral_sc, t)
p = Thesis.plot([spiral_path],
colors=["#0FF"],
title="Spiral Orbit")
colors=["#F0F"],
title="Spiral Orbit",
mode="light")
savefig(p, "LaTeX/fig/spiral_plot.png")

2
julia/src/utilities/conversions.jl
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@@ -132,7 +132,7 @@ function conv_T(Tm::Vector{Float64},
si*sθ si*cθ ci ]
Tx, Ty, Tz = DCM*thrust_rθh
state = prop_one([Tx, Ty, Tz], state, craft, time/n, primary)
state = prop([Tx Ty Tz], state, craft, time/n, primary=primary)[2,:]
push!(Txs, Tx)
push!(Tys, Ty)
push!(Tzs, Tz)

2
julia/src/utilities/plotting.jl
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@@ -286,7 +286,7 @@ function plot(paths::Vector{Matrix{Real}};
traces = [ trace... ]
for i = 2:length(paths)
color = colors === nothing ? random_color() : colors[i]
trace, new_limit = gen_plot(paths[i],label=labels[i],color=color,markers=markers)
trace, new_limit = gen_plot(paths[i],label=labels[i],color=colors[i],markers=markers)
push!(traces, trace...)
limit = max(limit, new_limit)
end

2
julia/src/utilities/propagator.jl
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@@ -20,7 +20,7 @@ function prop(ΔVs::AbstractArray,
time::Real;
primary::Body=Sun)
size(ΔVs)[2] == 3 || throw(ΔVsize_Error(size(ΔVs)))
size(ΔVs)[2] == 3 || throw(ΔVsize_Error(size(ΔVs)[1]))
n = size(ΔVs)[1]
output = Array{Real,2}(undef,n+1,7)
current = copy(state)

19
notes.md
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@@ -52,16 +52,17 @@ Todo:
- investigate different C3 launch capabilites vs. sc mass for comparison
## 2020-02-25
- In the introduction, include some context for the existing literature. Compare to what people have
- [x] In the introduction, include some context for the existing literature. Compare to what people have
done before and explain the goal in comparison to how it's based on someone else's, as well as
the places where I've done things differently than the source work.
- Red/Green colorblindness problem in the plots
- Move table 7.1 to the beginning of Section 6 when the trajectories are introduced.
- Double check that the math is in the definitions of key points, for instance the cost function and
- [ ] Red/Green colorblindness problem in the plots
- [x] Move table 7.1 to the beginning of Section 6 when the trajectories are introduced.
- [x] Double check that the math is in the definitions of key points, for instance the cost function and
the constraints to the NLP solver
- Double check that SPICE is being mentioned
- Include information about coordinate frames being used by SPICE
- Include how mass is being decremented in the SFT propagator section
- Think about how to include plots that show the MBH algorithm jumping through the space and looking
- [x] Double check that SPICE is being mentioned
- [x] Include information about coordinate frames being used by SPICE
- [x] Include how mass is being decremented in the SFT propagator section
- [ ] Think about how to include plots that show the MBH algorithm jumping through the space and looking
at various basins.
- Submit thesis defense form
- [ ] Include some plots of the thrust vectors rather than the raw data in the appendix
- [ ] Submit thesis defense form