Trans-Earth Trajectory Correction Maneuver - SNOPT

Optimize a single trans-Earth (Moon-to-Earth) impulsive trajectory correction maneuver (TCM). Target to entry interface (EI) or perigee.

This application is a MATLAB script named transearth_tcm_snopt that can be used to optimize a single trajectory correction maneuver (TCM) at a user-defined time and geocentric state vector (position and velocity vectors) on a trans-Earth (Moon-to-Earth) trajectory. This TCM can be used to correct trajectory dispersions or perhaps re-target a trans-Earth trajectory to different entry interface conditions or a user-defined perigee altitude.

The software assumes the TCM occurs impulsively which results in a discontinuity in the geocentric velocity vector but not the position vector.

In the transearth_tcm_snopt “simple shooting” algorithm, the spacecraft orbital motion includes the Earth’s non-spherical gravity and optionally, the point-mass perturbations of the Sun and 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 transearth_tcm_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 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.

This MATLAB script uses the SNOPT algorithm to solve this optimization problem. MATLAB versions of SNOPT for several computer platforms can be purchased/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.