• ## Messenger (reduced version)

A visualization of the best solution found

This trajectory optimisation problem represents a rendezvous mission to Mercury modelled as an MGA-1DSM problem. The selected fly-by sequence is the same used in the first part of the Messenger mission. It is well known that a significant reduction of the required deltaV is possible if a number of resonant fly-bys follow the first Mercury encounter. Those resonant fly-bys are not included in this model creating a much simpler problem.

## The code

1. MATLAB: use the function messenger.m and pass to it the MGAproblem variable contained in messenger.mat
2. C++: call the function “double messenger(const std::vector& x)” provided in the GTOPtoolbox.

## Problem Description

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

## Units

x(1) t0 1000 4000 MJD2000
x(2) Vinf 1 5 km/sec
x(3) u 0 1 n/a
x(4) v 0 1 n/a
x(5) T1 200 400 days
x(6) T2 30 400 days
x(7) T3 30 400 days
x(8) T4 30 400 days
x(9) eta1 0.01 0.99 days
x(10) eta3 0.01 0.99 n/a
x(11) eta3 0.01 0.99 n/a
x(12) eta4 0.01 0.99 n/a
x(13) r_p1 1.1 6 n/a
x(14) r_p2 1.1 6 n/a
x(15) r_p3 1.1 6 n/a
x(16) b_incl1 -pi pi n/a
x(17) b_incl2 -pi pi n/a
x(18) b_incl3 -pi pi n/a

No other constraints are considered for this problem. The objective function is considered to the precision of meters per second.

## Solutions:

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

## Algo

T., Vinko, D., Izzo European Space Agency March, 2008 8.703 km/s
x=[2369.89, 1.67208, 0.380256, 0.499911, 400, 168.06, 224.695, 212.292, 0.237501, 0.0223169, 0.161132, 0.468419, 1.80818, 1.64195, 1.1, 1.29702, 2.80363, 1.57266]
DE
B. Addis, A. Cassioli, M. Locatelli, F. Schoen Global Optimization Laboratory, University of Florence and University of Turin May, 2008 8.631 km/s
x=[1171.64503236 1.40899421278 0.37992647165 0.498004040298 399.999999715 178.372255301 299.223139512 180.510754824 0.234594654679 0.0964769387134 0.829948744508 0.317174785637 1.80629232251 3.04129845698 1.10000000891 1.35077257078 1.09554368115 1.34317576594]
MBH
F. Biscani, M. Rucinski and D.Izzo European Space Agency Feb., 2009 8.630 km/s
x=lost
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