On the relation between resonance and instability in planetary systems

Details On the relation between resonance and instability in planetary systems On the relation between resonance and instability in planetary systems

Jul 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..27..305h&link_type=abstract

Celestial Mechanics, vol. 27, July 1982, p. 305-322.

Physics

20

Orbit Perturbation, Orbital Mechanics, Planetary Orbits, Planetary Systems, Resonance, Solar Orbits, Asteroids, Circular Orbits, Elliptical Orbits, Equations Of Motion, Four Body Problem, Hamiltonian Functions, Motion Stability, Perturbation Theory, Three Body Problem

Scientific paper

The factors which affect the linear stability of a planetary system are studied, and the mechanism by which instabilities are generated because of the existence of resonances is emphasized. The case of a planetary system with two planets revolving around the sun in the same direction is considered, and the results are extended to the case of three planets, pointing out the reasons for the greater instability in the latter case. Planetary systems with elliptic orbits are also studied and the qualitative differences from the circular case are demonstrated. Finally, the results are extended to retrograde motion. Numerical examples are given.

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