Parametric Analysis of Trans-Lunar Trajectories (SNOPT)

Parametric Analysis of Minimum TLI Delta-V Lunar Transfer Trajectories

This submission is a MATLAB script named tli_sweep_snopt that can be used to perform a parametric analysis of two-body and “perturbed” trans-lunar transfer trajectories. The software assumes that the trans-lunar injection (TLI) occurs impulsively from a circular Earth park orbit.

The software initially solves for the minimum TLI delta-v using a two-body Lambert solution for the transfer trajectory from Earth park orbit to the center of the Moon. The perturbed solution uses this two-body answer as an initial guess for solving the two-point boundary-value problem subject to perturbations due to a non-spherical Earth gravity model and optionally, the point-mass gravity of the Sun. Both types of simulation ignore the point-mass gravity of the Moon.

This MATLAB script reads JPL DE430 lunar and solar ephemerides in a machine-independent binary format (kernels) which are available from the SPICE web site and by anonymous ftp from ftp://ssd.jpl.nasa.gov/pub/eph/planets/bsp. These *.bsp ephemeris files are IEEE-Little Endian style of binary kernel. This is the binary form native to PC/Linux, PC/Windows and MAC/Intel machines. Additional information about JPL ephemerides can be found at http://naif.jpl.nasa.gov/naif/.

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

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.