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

Abstract

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-optimized results con rm that Venus-Earth-Earth is the most effective 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.

An Ant System algorithm for automated trajectory planning

“…The figure represents two possible solutions to the MGA problem: [1, 1, 2, 1, 1, 1] (continuous line) and [2, 2, 2, 1, 1, 1] (dashed line). These two solutions share the same parameters for the last transfer: [1,1]. This means that they reach the same target planet with the same type of transfer.…”

“…In Fig. 3(b), it is clear that the set of parameters [1,1] for transfer 3 belongs to two different solutions.…”

“…Because of the dependency of each transfer on the initial conditions, it is not possible to state that the last transfer has the same value for both solutions: in fact, the two trajectories can be consistently different, and lead to different final conditions and objective functions. For this reason, it makes no sense, for example, to assign a value to the set of parameters [1,1] of transfer 3 in Fig. 3(a); while it is possible to assign a value to the edge 3-4 in Fig.…”

“…The rationale behind this choice is that, if an algorithm exists that is able to efficiently generate a complete plan for a given t 0 , then an unidimensional search in the time domain can be performed to find the optimal launch date. The angle ϕ 0 on the other hand is often a mission requirement [1]. Furthermore, it is assumed that the departure planet P 0 is given a priori.…”

“…Two-level approaches split the problem into two subproblems which lay at two different levels: one sub-problem is to find a suitable set of sequences of planetary encounters, the other is to find at least one optimal trajectory for each sequence. Two-level approaches define the planetary sequence independently of the trajectory itself [1]. They use a simplified, low fidelity, model at the first level to quickly assess many, if not all, sequences and a more accurate model, at lower level, to optimize the trajectory.…”