Other
Scientific paper
Jul 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007dda....38.1505b&link_type=abstract
American Astronomical Society, DDA meeting #38, #15.05
Other
Scientific paper
The relationship between the boundaries for Hill and Lagrange stability in orbital element space is modified in the case of resonantly interacting planets. Hill stability requires the ordering of the planets to remain constant while Lagrange stability also requires all planets to remain bound to the central star. The Hill stability boundary is defined analytically, but no equations exist to define the Lagrange boundary, so numerical experiments are needed. To explore the effect of resonances, we consider orbital element space near the conditions in the HD 82943 and 55 Cnc systems. For each of those systems, we use simulations of the dynamical evolution of 1000 cases over 106 years, with initial conditions distributed over the range of observational uncertainty, to identify the Lagrange-stability boundary. The observational errors are large enough that non-resonant configurations are included in our sets of integrated cases. Previous studies have shown that, for non-resonant systems, the two stability boundaries are nearly coincident. Hill stability formulae are not applicable to resonant systems, so our investigation shows how the two boundaries diverge in the presence of a mean-motion resonance, while confirming that the Hill and Lagrange boundaries are similar otherwise. In resonance the region of stability is larger than the domain defined by the analytic formulae for Hill stability. Moreover, the expansion is greater in the 2:1 resonance (HD 82943) than for the 3:1 case (55 Cnc).
Barnes Rory
Greenberg Richard
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