Nonlinear Sciences – Chaotic Dynamics
Scientific paper
Dec 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005chaos..15d3101l&link_type=abstract
Chaos, Volume 15, Issue 4, pp. 043101-043101-11 (2005).
Nonlinear Sciences
Chaotic Dynamics
Nonlinear Dynamics And Chaos, Chaotic Dynamics, Solar System Objects
Scientific paper
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.
Ferrer Sebastián
Lara Martin
San-Juan Juan F.
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