Massive identification of asteroids in three-body resonances

Abstract

An essential role in the asteroidal dynamics is played by the mean motion resonances. Two-body planet-asteroid resonances are widely known, due to the Kirkwood gaps. Besides, so-called three-body mean motion resonances exist, in which an asteroid and two planets participate. Identification of asteroids in three-body (namely, Jupiter-Saturn-asteroid) resonances was initially accomplished by D. Nesvorný and A. Morbidelli (1998), who, by means of visual analysis of the time behaviour of resonant arguments, found 255 asteroids to reside in such resonances. We develop specialized algorithms and software for massive automatic identification of asteroids in the three-body, as well as two-body, resonances of arbitrary order, by means of automatic analysis of the time behaviour of resonant arguments. In the computation of orbits, all essential perturbations are taken into account. We integrate the asteroidal orbits on the time interval of 100000 yr and identify main-belt asteroids in the three-body Jupiter-Saturn-asteroid resonances up to the 6th order inclusive, and in the two-body Jupiter-asteroid resonances up to the 9th order inclusive, in the set of ∼ 250000 objects from the "Asteroids -Dynamic Site" (AstDyS) database. The percentages of resonant objects, including extrapolations for higher-order resonances, are determined. In particular, the observed fraction of pure-resonant asteroids (those exhibiting resonant libration on the whole interval of integration) in the three-body resonances up to the 6th order inclusive is ≈ 0.9% of the whole set; and, using a higher-order extrapolation, the actual total fraction of pure-resonant asteroids in the three-body resonances of all orders is estimated as ≈ 1.1% of the whole set.

Habitability Properties of Circumbinary Planets

“…(On the three-body resonances in the Solar system, see Smirnov & Shevchenko 2013). Besides, a plausible orbital architecture of CBP can be expected to resemble that observed in the satellite system of the Pluto-Charon binary, where Styx, Nix, Kerberos, and Hydra all move in the orbits close to integer resonances with the Pluto-Charon binary (Buie et al, 2013;Brozović et al, 2015), and the system is dynamically closely-packed.…”

The Laplace resonance in the Kepler-60 planetary system

“…The overlap of two-body and three-body MMRs has been identified as a source of deterministic chaos in the Outer Solar system and in the asteroid belt (e.g. Murray & Holman 1999;Guzzo 2006;Smirnov & Shevchenko 2013). The best-studied and known example of the three-body MMR is the Laplace resonance of the Galilean moons.…”

Atlas of three body mean motion resonances in the Solar System

“…In particular, both borders of the main asteroid belt exhibit chaotic diffusion due to the superposition of several weak two-body and TBRs (Murray and Holman, 1997;Morbidelli and Nesvorný, 1999). More recently, Smirnov and Shevchenko (2013) in a massive numerical integration of 249,567 asteroids by 10 5 years and looking at the time evolution of the critical angles, identified thousands of asteroids in TBRs with Jupiter and Saturn, concluding there are more asteroids in TBRs than in two body resonances.…”