Explicit forms of some functions arising in the analysis of resonant satellite orbits

Abstract

The analysis of resonant satellite orbits has been pursued for 18 years, and has led to the most accurate values available for lumped geopotential harmonics of the relevant orders. The basic theory for the resonance effects was developed in the 1960s, but the detailed application of the technique calls for a systematic notation and for the evaluation of two subsidiary functions, namely F̄ , a function of the orbital inclination, and G , a function of the eccentricity. The present paper sets out explicitly the variations in inclination and eccentricity produced by relevant harmonics at the most common resonances (15:1, 14:1, 16:1, 29:2 and 31:2), using the notation that has become standardized in recent years. The paper also gives appropriate expressions for calculating F̄ and G , and lists a Fortran program GQUAD for evaluating G .