Lunar Free-Return Trajectory Analysis - OTB version

Optimization Toolbox version of the MATLAB script which models two-dimensional free-return lunar trajectories.

This submission is a MATLAB script named free_return_otb that can be used to design two-dimensional lunar free-return trajectories. The system dynamics are modeled as a simplified circular-restricted three-body problem (CRTBP). Additional modeling assumptions are;

• the massless third body is subject only to the point-mass gravity of the Earth and Moon
• the Moon is subject only to the point mass gravity of the Earth
• the Moon’s orbit is circular and all motion lies in the Moon’s orbital plane
• departure from the Earth park orbit is in the counterclockwise direction
• trans-lunar injection (TLI) occurs impulsively from a circular Earth park orbit
• the TLI departure maneuver is applied tangential to the Earth park orbit
• the Earth orbit insertion (EOI) impulsive maneuver is applied tangential to the return trajectory
• the lunar flyby is a no maneuver, ballistic trajectory

The algorithm implemented in this MATLAB script is based on the technical report “Optimal Free-Return Trajectories for Moon and Mars Missions”, by A. Miele, T. Wang and S. Mancuso, The Journal of the Astronautical Sciences, Vol. 48, Nos. 2 and 3, April-September 2000, pp. 183-206.

The free_return_otb script uses the fmincon nonlinear programming method of the MathWorks Optimization Toolbox for optimizing the lunar free-return problem implemented in this script.