Integrable cases of the planetary three-body problem with first-order resonance

Details Integrable cases of the planetary three-body problem with first-order resonance Integrable cases of the planetary three-body problem with first-order resonance

Jul 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992kosis..30..455s&link_type=abstract

Kosmicheskie Issledovaniia (ISSN 0023-4206), vol. 30, no. 4, p. 455-461.

Physics

Equations Of Motion, Neptune (Planet), Orbital Resonances (Celestial Mechanics), Pluto (Planet), Solar Orbits, Three Body Problem, Asteroids, Motion Stability, Solar System

Scientific paper

Motion stability in the general and restricted elliptical planetary three-body problems is investigated in the case of first-order resonance. Equations of body motion near the resonance surface are obtained and analytically integrated in quadratures. The stability of the body motion near the resonance surface is analyzed. The conditionally periodic time dependence of the body motion with a two-frequency basis is established. An analytical condition is obtained for resonance phase libration. The results of the study are applied to the motion of planets (Neptune - Pluto) and asteroids (Thule, and Hilda and Hecuba families) in the solar system.

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