Statistics – Applications
Scientific paper
Jan 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004iaus..219..820z&link_type=abstract
Stars as suns : activity, evolution and planets, Proceedings of the 219th symposium of the International Astronomical Union held
Statistics
Applications
1
Scientific paper
In a multiple planet system when the pericenters of the two planets are locked into alignment or anti-alignment we call these two planets are in apsidal secular resonance. The configuration apsidal alignment or anti-alignment can avoid close encounters between the planets thus it is believed that apsidal secular resonance can stabilize the interacting planets. For the 10 confirmed multiple planetary systems (GJ876 47UMa HD82943 HD12661 HD168443 HD37124 HD38529 HD74156upsiloAndromedae and 55 Cancri) the best-fit orbital parameters show 5 pairs of planets are in apsidal resonance: GJ876 (apsidal alignment due to 2:1 mean motion resonance) 47UMa (apsidal alignment) HD82943 (both apsidal alignment and 2:1 mean motion resonance) HD12661(anti-apsidal alignment) and the outer two planets of upsiloAndromedae (apsidal alignment). Here we report our studies on the occurrence and stability of apsidal resonance. We find the occurrence of apsidal secular resonance depends only on the mass ratio semi-major rate and eccentricity rate between the two planets. Analytical relations between these quantities and the resonance angles are derived. The dynamical stability the planets in apsidal secular resonance with and without disk-generated torque are studied with applications to the extrasolar planetary systems.
Sun Yi-Sui
Zhou Ji-Lin
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