N-body Lunar Free Return Trajectory Analysis – OTB

Design and optimization of lunar free-return trajectories. Target to a final mission orbit or entry interface at Earth.

This is a MATLAB script named nbody_lfr_otb that can be used to design an n-body, lunar free-return transfer trajectory from a circular, low Earth orbit (LEO) to a final user-defined Earth orbit radius and orbital inclination or an entry interface (EI). An entry interface is user-defined by an entry radius, flight path angle and orbital inclination.

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 script uses the fmincon algorithm from the Mathworks® Optimization Toolbox to solve each step. Orbital events are determined using the event prediction feature of the ode45 algorithm.

The nbody_lfr_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.