Secular motion around synchronously orbiting planetary satellites.

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.

[1]  M. Lara,et al.  Dynamic Behavior of an Orbiter around Europa , 2005 .

[2]  J. Palacián,et al.  The Keplerian regime of charged particles in planetary magnetospheres , 2004 .

[3]  A. Roy,et al.  A Hill Problem with Oblate Primaries and Effect of Oblateness on Hill Stability of Orbits , 2001 .

[4]  D. Scheeres,et al.  Stability Analysis of Planetary Satellite Orbiters: Application to the Europa Orbiter , 2001 .

[5]  M. A. Vashkov'yak,et al.  Stability of periodic solutions for Hill’s averaged problem with allowance for planetary oblateness , 2001 .

[6]  G. Schubert,et al.  Europa's differentiated internal structure: inferences from two Galileo encounters. , 1997, Science.

[7]  Shannon L. Coffey,et al.  Frozen orbits for satellites close to an Earth-like planet , 1994 .

[8]  M. Burṥa.  Figure and Dynamic Parameters of Synchronously Orbiting Satellites in the Solar System , 1989 .

[9]  J. Sanders,et al.  The constrained normal form algorithm , 1988 .

[10]  Bruce R. Miller,et al.  The critical inclination in artificial satellite theory , 1986 .

[11]  R. Cushman.  Reduction, Brouwer's Hamiltonian, and the critical inclination , 1983 .

[12]  M. L. Lidov,et al.  Integrable Cases in the Problem of the Evolution of a Satellite Orbit under the Joint Effect of an Outside Body and of the Noncentrality of the Planetary Field , 1974 .

[13]  André Deprit,et al.  Canonical transformations depending on a small parameter , 1969 .

[14]  R. Broucke.  Long-Term Third-Body Effects via Double Averaging , 2003 .