Numerical Prediction of Orbital Events - MICE version

MATLAB script and user's manual for predicting important root-finding and extrema orbital events

This submission is an interactive MATLAB script named npoe_mice.m that can be used to propagate spacecraft in Earth orbits and model important orbital events. This script implements a special perturbation solution of orbital motion using a variable step size Runge-Kutta-Fehlberg (RKF78) integration method to numerically integrate Cowell’s form of the system of differential equations. Orbital events are predicted by embedding the RFK78 algorithm within Brent’s derivative-free methods for finding the single roots and extrema of nonlinear equations. The user can control both the integration and root-finding convergence criteria.

This MATLAB script can accurately predict the time and orbital characteristics for any physically realizable user-defined value of the following orbital elements

• argument of latitude
• geodetic altitude
• geodetic latitude
• right ascension
• geocentric declination
• east longitude
• flight path angle
• orbital speed

as well as extrema (minimum and maximum values) for these eight orbital elements.

The npoe_mice software can also predict the circumstances of the following mission events

• spacecraft-to-moon visibility
• spacecraft-to-sun visibility
• Earth shadow - penumbra
• Earth shadow - umbra
• Moon shadow - penumbra
• Moon shadow - umbra
• observer-to-spacecraft visibility

This MATLAB script reads JPL 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 npoe_mice script uses routines from the MICE software suite to read and evaluate the JPL binary ephemeris file. Platform-specific MICE mex files, support functions and the binary ephemeris file (de430_1850-2150.bsp) are available at naif.jpl.nasa.gov/naif/toolkit_MATLAB.html. MICE is a MATLAB implementation of the SPICE library created by JPL.