title: Secular motion around synchronously orbiting planetary satellites.
abstract: We investigate the secular motion of a spacecraft around the natural satellite of a planet. The satellite rotates synchronously with its mean motion around the planet. Our model takes into account the gravitational potential of the satellite up to the second order, and the third-body perturbation in Hill's approximation. Close to the satellite, the ratio of rotation rate of the satellite to mean motion of the orbiter is small. When considering this ratio as a small parameter, the Coriolis effect is a first-order perturbation, while the third-body tidal attraction, the ellipticity effect, and the oblateness perturbation remain at higher orders. Then, we apply perturbation theory and find that a third-order approach is enough to show the influence of the satellite's ellipticity in the pericenter dynamics. Finally, we discuss the averaged system in the three-dimensional parametric space, and provide a global description of the flow.
authors.affiliation: Ephemerides Department, Real Observatorio de la Armada, 11 110 San Fernando, Spain. mlara@roa.es
authors.forename: Martin
authors.initials: M
authors.lastname: Lara
authors.forename: Juan F
authors.initials: JF
authors.lastname: San-Juan
authors.forename: Sebastián
authors.initials: S
authors.lastname: Ferrer