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AIAA-3650-983 - JOURNAL OF SPACECRAFT AND ROCKETS Vol 37 No...

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J OURNAL OF S PACECRAFT AND R OCKETS Vol. 37, No. 6, November December 2000 Trajectories to Jupiter via Gravity Assists from Venus, Earth, and Mars Anastassios E. Petropoulos, ¤ James M. Longuski, and Eugene P. Bon glio Purdue University, West Lafayette, Indiana 47907-1282 Gravity-assist trajectories to Jupiter, launching between 1999 and 2031, are identi ed using patched-conic techniques. The classical trajectories, such as the Venus Earth Earth gravity assist, and many less conventional paths, such as Venus Mars Venus Earth, are examined. Flight times of up to about seven years are considered. The D V -optimizedresults con rm that Venus Earth Earth is the mosteffective gravity-assisttrajectory type, with launch opportunities occurring almost every year and launch vis viva for ballistic trajectories as low as 9 km 2 /s 2 . If the Earth is excluded as a yby body, Venus Venus Venus gravity assists are typically the best option, with launch vis viva for ballistic trajectories as low as 30 km 2 /s 2 , although in some years nonconventionalpaths are better, such as a ballistic Venus Mars Venus Venus trajectory in 2012, with a launch vis viva of 16 km 2 /s 2 . Nonconventional paths, such as Venus Mars Venus Earth with a 3.7-year ight-time trajectory in 2021, can occasionally decrease the time of ight signi cantly, at very minor D V cost, when compared with the classical types. Introduction T HE principleof gravityassist has a rich and interestinghistory, and numerous researchers have contributed to its theory and application.(See Refs. 1 25 for a small sampling of the literature.) In this paper we identify gravity-assisttrajectoriesvia Venus, Earth, and Mars to Jupiter during a three-decadelaunch period from 1999 to 2031. We are interested in low-launch-energy trajectories with low total D V (i.e., magnitude of the velocity changes effected by thrusters,modeled impulsively) and with reasonable times of ight (less than about seven years). We examine 25 different sequences of gravity-assist bodies with the automated Satellite Tour Design Program 16 ¡ 21 (STOUR), which is capable of nding all patched- conic, gravity-assisttrajectories for a given set of launch dates and launch V 1 (hyperbolic excess speeds). In addition, the automated STOUR can compute trajectories with D V applied in three differ- entmodes:powered yby, 19 brokenplane, 19 and V 1 -leveraging. 21,25 For selected cases we nd the D V -optimal solutions using the Jet Propulsion Laboratory’s Mission Design and Analysis Software 22 (MIDAS). Because we are considering up to four gravity assists with three of the inner planets, there are 120 possible paths (or combinations). Although STOUR is a very powerful tool, it takes several days (on a typical computer workstation) to assess one path for a three-decade launch period. Thus it is impractical to merely grind throughall possiblecombinations,and so, as is often the case, engineering judgment and analysis are required. We nd the sim- ple analytic techniques developed by Hollenbeck 23
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