Abstract

We report on our development of a highly accurate symplectic integration system which (a) works in jacobi coordinates, and (b) simultaneously calculates the evolution of the tangent equations. This enables us to rapidly and accurately integrate (symplectically) arbitrary system configurations (e.g. planets in multi-stellar systems) while rigorously investigating their stability via measures of the Lyapunov exponent (and related MEGNO indicators). We demonstrate this integration scheme by mapping out the possible stable configurations of planet-satellite system in circumbinary orbits around a pair of stars, and illustrate the implications for known Kepler circumbinary planets. We go on to illustrate further novel applications of our integrator, including to the evolution of evolved planetary systems around white dwarfs.

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