Gabriela-Ana Nadabaică
Alexandru Ioan Cuza University, Iaşi, Romania

In the context of a perturbed two body problem, in which the keplerian motion of the small object (the satellite) is perturbed by the oblateness of the central body (the asteroid) and the attraction of a third body (the Sun), we discuss the long-term evolution of the inclination and the longitude of the ascending node of a satellite orbiting an oblate body. To this end, we provide an analytical study describing the location of the Laplace plane as a function of several parameters, such as the magnitude of the forces involved, the distance from the oblate body, the obliquity of the Sun’s orbit. This plane, also called the invariable plane, has its normal vector located between the normal vector of the equatorial plane and the normal vector of the Sun’s orbital plane. The analytical study is complemented by numerical tests in which there are propagated several orbits within the context of both Cartesian and Hamiltonian approaches.