 • ## Cassini 1 A visualization of the best solution found

Cassini 1 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 and is called Cassini 2). 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.

## The code

1. MATLAB: use the function cassini1.m and pass to it the MGAproblem variable contained in cassini1.mat
2. C++: call the function “double cassini1(const std::vector & x, std::vector& rp)” provided in the GTOPtoolbox.
3. C++ (PaGMO): use the class pagmo::problem::cassini_1
4. Python 2.7 (PyGMO): use PyGMO.problem.cassini_1().obj_fun(x)

## Problem Description

The box bounds on each of the decision vector variable are given below.

## Units

x(1) t0 -1000 0 MJD2000
x(2) T1 30 400 days
x(3) T2 100 470 days
x(4) T3 30 400 days
x(5) T4 400 2000 days
x(6) T5 1000 6000 days

Constraints on the various fly-by pericenters are also considered to the values:

• rp1 > 6351.8 km
• rp2 > 6351.8 km
• rp3 > 6778.1 km
• rp4 > 671492 km

Solutions are rounded to the fourth digit and only improvements on that level is considered. No constraint violation is allowed.

This problem is considered to be solved. No better solutions are expected.

## Solutions:

The solutions submitted to this problem are listed below in chronological order

## Algorithm

Bernardetta Addis Florence University October 2005 5.0088
x=[-789.936 160.99 449.386 53.1756 1042.15 4577.26]
Monotonic Basin Hopping
Fabio Pinna and Dario Izzo European Space Agency November 2005 4.9340
x=[-790.08992 158.55349 449.38586 54.76621 1024.01505 4552.70303]
Differential Evolution
Manfred Stickel Max-Planck-Institut fuer Astronomie April 2006 4.9307
x=[-789.8117 158.302027105278 449.385873819743 54.7489684339665 1024.36205846918 4552.30796805542]
A Particle Swarm Optimizer