## Cassini 1

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

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

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

## State

## Variable

## Lower Bounds

## Upper Bounds

## Units