Periodic gravitational perturbations for conversion between osculating and mean orbit elements

Algorithms for converting between osculating and mean orbit elements are currently limited to computing the contribution due to the second zonal harmonic (J2). This paper presents an improved conversion algorithm that includes the effects of all zonal, sectorial and tesseral harmonics, second order J2, and third-body gravitational perturbations. Mean elements are useful for preliminary orbit and maneuver design; however, for more precise work, such as groundtrack targeting, osculating elements are required. This improved conversion algorithm was developed to meet accuracy requirements for the TOPEX/Poseidon mission; but, additional use can be considered for satellites orbiting planets like Venus that do not have a dominant J2. Results are presented from tests performed using the new algorithm with the planned TOPEX/Poseidon earth orbit as well as the Mars Observer and proposed circular Magellan (Venus) orbits.