Trans-Lunar Trajectory Correction Maneuver – SNOPT

Optimize a single trajectory correction maneuver (TCM) on a trans-lunar trajectory

This MATLAB script 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-lunar (Earth-to-Moon) trajectory. This TCM can be used to correct trajectory dispersions or perhaps re-target a lunar free return trajectory to different selenocentric final mission conditions.

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

The type of final selenocentric (Moon-centered) mission constraints can be selected by the user from one of the following script options;

1. selenocentric radius and inclination
2. selenocentric user-defined b dot r and b dot t
3. selenocentric node/apse alignment

The characteristics of the final selenocentric mission constraints can be calculated in one of the following three different coordinate systems;

1. Earth true-of-date
2. Earth mean equator and equinox of J2000
3. mean lunar equator and IAU node of epoch).

In the translunar_tcm_snopt “simple shooting” algorithm, the spacecraft orbital motion includes the Earth’s non-spherical gravity and 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 translunar_tcm_snoptscript uses routines from the MICE software suite to read and evaluate the JPL ephemeris file. Platform-specificMICE 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.