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Orbital stability of compact three-planet systems

Published onAug 03, 2020
Orbital stability of compact three-planet systems

We explore the orbital dynamics of systems consisting of three planets, each as massive as the Earth, on coplanar, initially circular, orbits about a one solar mass star. The initial semimajor axes of the planets are equally-spaced in terms of their mutual Hill radius, which is equivalent to a geometric progression of orbital sizes for small, equal-mass, planets. Our simulations explore a wide range of spacings of the planets and were integrated for virtual times of up to 10 billion years or until the orbits of any pair of planets crossed. We analyze the general trend of increasing stability for more widely-spaced planets, the destabilizing effects of mean motion resonances, the dependence of lifetimes on initial starting longitudes, and the magnitude of differences in lifetimes of initially very similar systems caused by deterministic chaos. We find the same general trend of system lifetimes increasing exponentially with separation between orbits seen by previous studies of systems of three or more planets, and our results also show sensitivity of lifetimes to initial conditions that has not been previously detected. Substantial shifts in the initial planetary longitudes cause a scatter of roughly a factor of two in system lifetime, whereas the shift of one planet's initial longitude by 100 meters has smaller affects the time to orbit crossing, especially for systems with short lifetimes.

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