Astronomy and Astrophysics – Astronomy
Scientific paper
Jun 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006dda....37.1103g&link_type=abstract
American Astronomical Society, DDA meeting #37, #11.03; Bulletin of the American Astronomical Society, Vol. 38, p.672
Astronomy and Astrophysics
Astronomy
Scientific paper
Stability of a planetary system can be defined in many ways. Two meaningful definitions, defined in the context of a system consisting of one star and two planets, are Lagrange stability and Hill stability. Lagrange stability requires that the planets remain bound to the star, conserves the ordering of the distance from the star, and limits the variations of orbital elements like semi-major axis and eccentricity. Hill stability is less stringent: It only requires that the ordering of the planets remain constant; the outer planet may escape to infinity. A region in orbital element space that is guaranteed to be Hill stable has been described analytically (Marchal and Bozis 1982, Gladman 1993), although Hill stable orbits may lie outside that region as well. No analytic criteria describe Lagrange stability, although it must be a subset of the Hill-stable space, by definition. We compare these analytical constraints with results of numerical integration of 1000 hypothetical planetary systems similar to the extra-solar systems 47 UMa and HD 12661 that had been performed by Barnes and Quinn (2004). All the results are consistent with the analytic constraint on Hill stability. Moreover, the numerically determined boundary for Lagrange stability lies close to the analytic boundary for Hill stability. This result is doubly interesting because the analytic limit was not developed for the Lagrange definition, and did not even define the boundary of Hill stability. Yet this agreement may have a practical application, if borne out by subsequent studies: It suggests an analytic formulation that may describe the criterion for Lagrange stability. This study also confirms that the planets in both the 47 UMa and the HD 12661 systems are about as closely packed as they can be, a result that, if generally true, may have important implications for planet formation.
Barnes Robin
Greenberg Richard
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