Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc. A98-37361 AIAA-98-4284 TRAJECTORIES TO JUPITER VIA GRAVITY ASSISTS FROM VENUS, EARTH, AND MARS Anastassio . PetropoulosE s * Jame . LonguskisM Eugend Jan . BonfiglioeP * School Aeronauticsof Astronautics,and Purdue University, West Lafayette, Indiana 47907-1282 Abstract Gravity-assist trajectorie Jupitero st , launching between 199 2031d 9an identifiee ,ar d using patched- conic techniques. The classical trajectories, such as the Venus-Earth-Earth gravity assist (VEEGA), and many less conventional paths, suc s Venus-Mars-Venus-Earthha examinede ,ar . Flight timep u f so to about seven years are considered. The AV-optimized results confirm that VEEGAs are the most effective gravity-assist trajector ye Eart th type s f excludei hI . flyba s da y body, Venus-Venus-Venus gravity assists are typically the best option, although at times non-conventional paths are better. These non-conventional paths can occasionally decrease the time of flight significantly, at very minor AV cost, when compared to the classical types. Introduction proven techniqu f graviteo y assist. Voyage user2 d gravity assists from Jupiter, Saturn Uranusd an , o t , Since Galileo Galilei pointe tins dhi y telescopt ea eventually reach Neptune in 12 years; Galileo used Jupite d discoverean r s fouit d r moon 1610n i sr ou , a VEEGA (Venus Earth Earth Gravity Assist) to largest planet has fascinated astronomers and laymen reach Jupiter in just over 6 years. Unfortunately, alike. Four flyby spacecrafd an , t (Pioneer11 d an 0 1 s gravity-assist trajectories usually require long flight Voyagerhav) 2 ed reconnoiterean 1 s d this miniature times, which can drive up mission operations costs. solar system; and now, at the time of this writing, However, wit e developmenhth morf to e autonomous the Galileo spacecraft is orbiting the planet and per- spacecraft and more efficient operations procedures, forming detailed survey s atmosphereit f so , satellites these cost expectee ar s decreaso t d e steadily. Until and magnetosphere. There have been many wonder- other means of space transportation become readily ful discoveries e Galileth s a o d projecan , t completes available (electric propulsion, solar sails, aerogravity its extended mission, the Jovian system beckons for assist r waro , p drive!) gravite ,th y assist option will, further exploration. The mounting evidence of liquid i nflighe spitth f te o time issue, remai mose - nth at t wate rsurfac y beloic e Europf weo th a offer tane th s- tractive alternative. (And eve s othena r propulsive talizing possibilit liff spurrinyo e — g NAS plaAo t na technologies emerge, they will gain considerable aug- Europa orbital missio examino nt e this satellite more mentation when coupled with gravity assist.) closely in the next decade. The principle of gravity assist has been under- With these plansixta r hsfo missio drawe th n n-o stood since the 19th century when Leverrier (see boardg in t seem,i s highly likely that scientific interest Broucke d Tisseranan 1) d (see Battin2) explained in Jupiter will continu increaseo e t same th t e A time. , large perturbations of the orbits of comets by the budget constraint e NASth d A an smandat f "beto e - planet Jupiter. In the late 1950s, Battin3 consid- ter, cheaper, faster" demand that creative solutions ered the use of the gravitational attraction of a planet maintaio t e ar founde e b vigorouna w f i , s program to place a spacecraft on the return leg of its round- of exploratio f Jupiterno . trip interplanetary journey. The former Soviet Union The most potent way of reducing launch costs used lunar gravitational attractio obtaio nt n desirable (whic amone har mose gth e t th expensive e us o t s i ) return trajectories.4 Many investigators in the early 'Doctoral Candidate, Member AIAA. 1960s explored the enormous potential of the grav- 5 'Professor, Associate Fellow AIAA, Member AAS. itational swingby maneuver, including Deerwester, * Graduate Student. Flandro,6 Gillespie et al.J Hollister,8 Minovitch,9 Copyrigh 199) y Anastassio(C t8b . PetropoulosE s , Jame. M s Niehoff,10 Ross,11 Sohn, Sturmd 1 an 2Cutting.d san 13 Longuski and Eugene P. Bonfiglio. Published by the Amer- 14 ican Institute of Aeronautics and Astronautics, Inc. with Stancat t a/.e i demonstrate that VEGA (Venus permission. Earth Gravity Assist) and AV-EGA (Delta-V Earth 116 Copyright© 1998, American Institute f Aeronautico Astronauticsd san , Inc. Gravity Assist) trajectorie outee th o rt s planets (in- is a very powerful tool, it takes several days (on a Sun cluding Jupiter) provide two to three times the net UltraSPARC 1 workstation) to assess one path (e.g. payload capability of direct transfers. A definitive VEEGA) for a three decade launch period. Thus it is stud VEGf yo VEEGd Aan A trajectorie Jupitero t s , impractica merelo lt y grind throug possibll hal e com- Saturn selected an , d comet r launches sfo las e th t n i binations, and so — as is often the case — engineer- decade of the twentieth century is presented by Dieh ljudgemeng in analysid an t requirede sar fine e dth W . and Myers.15 Ten mission designers spent several simple analytic techniques developed by Hollenbeck22 months in the effort. very helpful in predicting the potential performance In order to speed up the search for gravity-assist of combinations of Venus and Earth gravity assists. trajectotries, Williams16 developed automated design Further refinements of these techniques are given by software based on the JPL (Jet Propulsion Labora- Sims; 2detailea 3 d analysi f AV-EGo s A trajectories tory) interactive program STOUR17 (Satellite Tour is presented by Sims et a/.24 We show that extend- Design Program). The new version is capable of find- ing this concep includo t t fouo t rp eu gravit y assists ing all patched-conic, gravity-assist trajectories for a gives deep insight into which path e e likelb ar s o yt given set of launch dates and launch VcoS under a effectiv whicd an e h ineffective cale e probleW th l . m given maximum TOF (time of flight). Patel added18 of selection, pathfinding, and it is the central issue of the capability of including AVs between gravity as- multiple gravity-assist mission design. sists d (witan , h Longuski) demonstrated e pro1th 9 - gram's ability to automatically find all of the VEGA Classical Trajectories VEEGd an A trajectories discovere- DiehMy y db d lan 20 ers, plus a few more. Later, Staugler incorporated Certain highly effective trajectory types have been algorithn a mautomaticallo t y design VOQ-leveraging well know commonld nan y use mission di n planning, trajectories (including AV-EGAs). thus meriting the name "classical." Specifically, in In this paper we use STOUR to identify gravity- this paper the classical trajectories will be taken as assist trajectorie a Venusvi s , Earth d Maran o , t s AV-EGA, VEGA , wher3 ,V " VEEGA d V e an , 2 V , Jupiter during a three decade launch period from denote Venusn s gravity assists after Earth launch. 199 interestee 2031o ar 9 t launc e w lo W . n dhi energy e AV-EGTh a Voo-leveragin s Ai g trajectorn i y trajectories with low total AV and with reasonable which a maneuver (AV) is performed near apoap- TOFs (less than about 7 years). For selected cases sis after Earth launch, such that the spacecraft re- we find the AV-optimal solutions using the JPL soft- encounters Earth wit hhighea finae rth Vclr gravofo - ware MIDAS21 (Mission Analysi d Desigan s n Soft- ity assist. (This describes the exterior AV-EGA for ware). Since we are considering up to four gravity heliocentrically outbound spacecraft. The symmet- assists with innee threth f reo planets0 , ther12 e ear ric case, wher e spacecrafth e s inboundi t s termei , d possible paths (or combinations). Although STOUR interior.) In the case of VEGA, VEEGA, and Vn trajecto- PA?H: 3 2 3 3 5 Vinf(km/s): 3.00 3.25 3.50 3.75 Search 5vcE'. No. 5 : ALTMJ N= -IQQC.lgr . Search Min. Alt.: 200.m 0k rie Jupitero t s e disadvantagth , launchinf eo g intoa lower energy orbi orden i t reaco t r firse hth t Venus s mori e tha ne benefi th offsehiga y f hb o tt VOt a Q a body tha s almosi t s massiv a tEarthe th n s I ea . fact, for typical launch VooS, the VQO at Venus is so high that a single flyby of the planet cannot turn the Voo enough to reach Jupiter. A second flyby of Venus is also insufficientadequatele b n ca t ybu , augmented with a maneuver during or after the flyby. A third Venus flyb alleviatn yca maneuvere e neeth er th dfo . The VEGAs and VEEGAs are more effective from an energy standpoin t onlno t y becaus Earte eth n hca provide slightly more V^ turning, but also because gs s ; g ss sooooooooocooooooaooooaoo afte Venue th r slongeo flybn e yw r nee maintaio dt n Launch Date perihelioa ns Venus' a distanc w lo ss a eorbit . Voo- L/D: 990101. TO 320101. by 5.0 days TFMA X= 2300. 0 Days leveraging can often be effectively incorporated into paths with repeated flybys of the same body. Fig Resonan1 . non-resonantd tan launcw lo , h A salient e featurclassicath f o e l trajectories, energy VEEGAs with arrival VQO < 8 km/s. which accounts for their common use, is the fact that 117 Copyright© 1998, American Institute f Aeronautico Astronauticsd san , Inc.