Informatics
Mission Analysis
May 1, 2013

# GTOC 1

This instance of a Multiple Gravity Assist problem draws inspiration from the first edition of the Global Trajectory Optimisation Competition (GTOC1). It is an MGA problem with a rather long fly-by sequence including mainly Earth and Venus. The final target is the asteroid TW229. The objective of the mission is to maximise the change in sami-major axis of the asteroid orbit following an anaelastic impact of the spacecraft with the asteroid J(x) = m_f U v.

# The code

1. MATLAB: use the function gtoc1.m and pass to it the MGAproblem variable contained in gtoc1.mat
2. C++: call the function "double gtoc1(const std::vector & x, std::vector& rp)" provided in the GTOPtoolbox.
3. C++ (PaGMO): use the class pagmo::problem::gtoc_1
4. Python 2.7 (PyGMO): use PyGMO.problem.gtoc_1().obj_fun(x)

# Problem Description

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

# Units

StateVariableLBUBUnits
x(1)t0300010000MJD2000
x(2)T1142000days
x(3)T2142000days
x(4)T3142000days
x(5)T4142000days
x(6)T51009000days
x(7)T63669000days
x(8)T73009000days

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

• rp1 > 6351.8 km
• rp2 > 6778.1 km
• rp3 > 6351.8 km
• rp4 > 6778.1 km
• rp5 > 600000 km
• rp6 > 70000 km

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

# Solutions:

The record holders of this problem are listed below in chronological order:

# Algo

Tamas Vinko and Dario IzzoEuropean Space Agency23 Jan, 2008-1,580,599
x=[6809.476683160, 169.598512787, 1079.375156244, 56.53776494142, 1044.014046276, 3824.160968179 1042.885114734 3393.057868710]
PaGMO
M. Schlueter, M. GerdtsUniversity of BirminghamJan, 2010-1,581,950
x=[6810.40521106, 168.37469758, 1079.47409963, 56.38731208, 1044.09288643, 3820.84181773, 1044.32726019, 3397.21349495]
MIDACO