N-body Lunar Free Return Trajectory Analysis – SNOPT

design an n-body, gravity-perturbed lunar free-return transfer trajectory from a circular Earth orbit to a final user-defined Earth orbit

This application is a MATLAB script named nbody_lfr_snopt that can be used to design an n-body, gravity-perturbed lunar free-return transfer trajectory from a circular Earth orbit to a final user-defined Earth orbit perigee altitude and orbital inclination. The trans-lunar injection (TLI) propulsive maneuver is modelled as an impulsive delta-v.

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, lunar 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 user-defined final orbit or entry interface conditions.

This MATLAB script uses the SNOPT nonlinear programming (NLP) method for both optimization tasks. MATLAB versions of SNOPT for several computer platforms can be purchase/requested at Professor Philip Gill’s web site which is located at http://scicomp.ucsd.edu/~peg/. Professor Gill’s web site also includes a PDF version of the SNOPT software user’s guide.

Orbital events are determined using the event prediction feature of the MATLAB ode78 algorithm.

The nbody_lfr_snopt script uses routines from the JPL 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.