Trajectories to Jupiter via Gravity Assists from Venus, Earth, and Mars

Gravity-assist trajectories to Jupiter, launching between 1999 and 2031, are identiŽ 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-optimized results conŽ rm thatVenus–Earth–Earth is themosteffective gravity-assisttrajectory type,with launch opportunities occurring almost every year and launch vis viva for ballistic trajectories as low as 9 km2 /s2. 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 km2 /s2, 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 km2/s2 . 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 signiŽ cantly, at very minor D V cost, when compared with the classical types.