Lyapunov Exponent Criterion for Stability of Planetary Orbits in Binary Systems

Details Lyapunov Exponent Criterion for Stability of Planetary Orbits in Binary Systems Lyapunov Exponent Criterion for Stability of Planetary Orbits in Binary Systems

Jan 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011aas...21741505m&link_type=abstract

American Astronomical Society, AAS Meeting #217, #415.05; Bulletin of the American Astronomical Society, Vol. 43, 2011

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The existence of planets in stellar binary systems is now well-confirmed by many observations. Stability of planetary orbits in these systems has extensively been studied and some attempts have been made to establish stringent stability criteria for the orbits. In this paper, we contribute to the ongoing work on the stability criteria in binary systems by introducing a Lyapunov exponent criterion. We have computed the Lyapunov exponents, the Lyapunov dimension and the time series spectra for planets in binary system. The obtained results demonstrate when a system becomes unstable by orbital energy criterion and the method of Lyapunov exponents provides a quantitative classification scale to characterize the instability. By applying the maximum Lyapunov exponent to the parameter space, which covers mass and distance ratios for the considered binary systems, we determined regions of stability and used the time series spectra and the Lyapunov dimension to illustrate the reasons behind the stability. Specific applications of the criterion to binary systems with known planets will also be discussed.

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