Lunar Gravity Assist to a Geosynchronous Transfer Orbit

Design an n-body trajectory from low Earth orbit (LEO) to a geosynchronous transfer orbit (GTO) using a gravity assist of the Moon.

This is a MATLAB script named lga2gto_otb that can be used to design an n-body transfer trajectory from a circular, low Earth orbit (LEO) to a geosynchronous transfer orbit by way of a lunar gravity assist (LGA). The n-body equations of motion implemented in this script include non-spherical Earth gravity and the point-mass gravity of the sun and moon.

The major computational steps of this divide and conquer script are as follows;

Step 1 - Solve the two-body, zero sphere-of-influence (ZSOI) Lambert problem while minimizing the trans-lunar injection (TLI) delta-v magnitude

Step 2 - Using the two-body solution from Step 1 as an initial guess, target to user-defined B-plane coordinates at the moon again minimizing the TLI delta-v magnitude

Step 3 - Using the n-body solution found in Step 2 as an initial guess, target to a perigee of an inbound transfer trajectory equal to geosynchronous radius (42164.336 kilometers) and zero orbital inclination.

This script uses the fmincon algorithm from the Mathworks® Optimization Toolbox to solve each step.

The lga2gto_otb script uses routines from the MICE software suite to read and evaluate the JPL ephemeris file. Platform-specific MICE mex files, support functions and the binary ephemeris file (de430.bsp) are available at naif.jpl.nasa.gov/naif/toolkit_MATLAB.html. MICE is a MATLAB implementation of the SPICE library created by JPL.