Earth satellite orbits with resonant lunisolar perturbations - II. Some resonances dependent on the semi-major axis, eccentricity and 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 satisfying commensurability conditions of the following form: ψ 4 = α ώ + γ (ώ p + Ṁ p ) ≈ 0 and ψ 5 = β Ω . + γ (ώ p + Ṁ p ) ≈ 0, where ω is the argument of perigee of the satellite’s orbit, Ω is the longitude of its ascending node, ω p is the argument of perigee of the lunar or solar orbits, and M p is the mean anomaly of the lunar or solar orbits; α, β and γ are integers. Certain simple relations are derived connecting the satellite’s semi-major axis, eccentricity and inclination; they must be satisfied, if the satellite is to exist in the commensurabilities ψ 4 ≈ 0 and ψ 5 ≈ 0. Tables are also given which contain the predominant resonant terms in the lunisolar gravity and direct solar radiation pressure disturbing function expansions for every commensurability of the type ψ 4 ≈ 0 and ψ 5 ≈ 0. Finally some important examples of these resonances are discussed.