Long-Term Third-Body Effects via Double Averaging

Abstract

Westudy thelong-term effects of a third body on a satelliteof negligiblemass. Wehavein mind to study thelunisolar effects on an Earth satellite but many other applications can be imagined. We begin with the representation of the disturbing function in an ine nite series in Legendre polynomials but we truncate it at the second-degree terms. Our approach consists of a double analytic averaging: with the period of the satellite and with the period of the third body. We concentrate on using the two important integrals (energy and angular momentum ) to discuss and classify properties of the perturbed orbits of the satellite. For inclinations below 39 deg, the perigee of the orbits always circulates. There are circular and elliptic orbits but the eccentricity does not vary much. For the inclinations above 39 deg, the circular orbits are unstable and the eccentricities can increase rapidly but we have the appearance of new stableorbits: two ellipticfrozen orbits with constant eccentricity and e xed perigee location, at either 90 or 270 deg.