Luni-solar effects of geosynchronous orbits at the critical inclination

Abstract

The luni-solar effects of a geosynchronous artificial satellite orbiting near the critical inclination is investigated. To tackle this four-degrees-of-freedom problem, a preliminary exploration separately analyzing each harmonic formed by a combination of the satellite longitude of the node and the Moon longitude of the node is opportune. This study demonstrates that the dynamics induced by these harmonics does not show resonance phenomena. In a second approach, the number of degrees of freedom is halved by averaging the total Hamiltonian over the two non-resonant angular variables. A semi-numerical method can now be applied as was done when considering solely the inhomogeneity of the geopotential (see Delhaise et Henrard, 1992). Approximate surfaces of section are constructed in the plane of the inclination and argument of perigee. The main effects of the Sun and Moon attractions compared to the terrestrial attraction alone are a strong increase in the amplitude of libration in inclination (from 0.6° to 3.2°) and a decrease of the corresponding libration period (from the order of 200 years to the order of 20 years).