Earth satellite orbits with resonant lunisolar perturbations I. Resonances dependent only on inclination

Abstract

Earth satellite orbits resonant with respect to lunisolar gravity and direct solar radiation pressure perturbations are discussed with particular reference to those resonances the occurrence of which is dependent only on the satellite’s orbital inclination. All types of lunisolar resonance orbits are first classified in terms of the general commensurability condition, which is then expressed as a function of the non-angular elements of the satellite’s orbit and certain parameters of the perturbing forces. Rules and constraints for ascertaining the predominant resonance terms in the disturbing function expansion for a given commensurability are also derived. Finally, the resonances dependent only on inclination are discussed. Criteria for determining their existence are found and the predominant resonant terms for every commensurability of this type are given. A num­ber of important examples of resonance orbits in this category are also discussed.