Problem "Cassini1" (MGA)

This code evaluates the deltaV required to reach Saturn using an Earth, Venus, Venus, Earth, Jupiter, Saturn fly-by sequence; no deep space manouvres are allowed.

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Short description

This is an MGA problem that is related to the Cassini spacecraft trajectory design problem (a more complex representation of this problem is found in the MGADSM section). The objective of this mission is to reach Saturn and to be captured by its gravity into an orbit having pericenter radius r_p=108950 km, and eccentricity e=0.98. The planetary fly-by sequence considered is Earth, Venus, Venus, Earth, Jupiter, Saturn (as the one used by Cassini spacecraft). As objective function we use the total deltaV accumulated during the mission, including the launch deltaV and the various deltaV one needs to give at the planets and upon arrival to perform the final orbit injection. For the six dimensional state vector we use the bounds given in the following table.

As constraints we limit the various fly-by pericenter to the values:

Solutions

The two best feasible solutions were found by Bernardetta Addis (October 2005) of Florence University who used a Monotonic Basin Hopping method:

5.0088

x=[-789.936 160.99 449.386 53.1756 1042.15 4577.26]

Manfred Stickel (April 2006) from the "Max-Planck-Institut fuer Astronomie" found a better value using a modified version of Particle Swarm Optimisation:

4.9307

x=[-789.8117 158.302027105278 449.385873819743 54.7489684339665 1024.36205846918 4552.30796805542]