Long-term orbit prediction for the Venus Radar Mapper Mission using an averaging method

A set of singly averaged equations of motion are presented and applied to long-term orbit prediction of an orbiting spacecraft around a slowly rotating planet, using the Venus Radar Mapper Mission as an example. The equations of motion used are valid for all eccentricities less than one. The disturbing potentials used include nonsphericity of the Venus gravity field and third-body effects due to the sun. Recursive relationships are used in the expansion and evaluation of these potentials and their respective partial derivatives. Special care is taken to optimize computational efficiency. The averaging method is compared with high precision Cowell's method using a desktop microcomputer and shows computational saving of about two orders of magnitude.