Astronomy and Astrophysics – Astrophysics
Scientific paper
Jun 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004a%26a...420..751g&link_type=abstract
Astronomy and Astrophysics, v.420, p.751-762 (2004)
Astronomy and Astrophysics
Astrophysics
1
Celestial Mechanics, Methods: N-Body Simulations, Methods: Numerical
Scientific paper
In this paper we construct two models for the motion of a particle under the gravitational attraction of Sun, Jupiter, Saturn and Uranus, that can be seen as a generalization of the well known Restricted Three-Body Problem (RTBP). Both models are obtained by computing quasi-periodic solutions - with two basic frequencies - of a suitable N-body problem. The first model is based on a quasi-periodic solution of the planar Sun-Jupiter-Saturn Three-Body problem, that tries to approach the real motion of Jupiter. The second model is based on a quasi-periodic solution of the Sun-Jupiter-Saturn-Uranus Four-Body problem. In both cases, we derive the equations of motion for a particle under the gravitational attraction of these bodies as a quasi-periodic time-dependent perturbation of the well-known RTBP.
Gabern F.
Jorba À.
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