Numerical evidence on the chaotic nature of the 3/1 mean motion commensurability

Details Numerical evidence on the chaotic nature of the 3/1 mean motion commensurability Numerical evidence on the chaotic nature of the 3/1 mean motion commensurability

May 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995icar..115...60m&link_type=abstract

Icarus (ISSN 0019-1035), vol. 115, no. 1, p. 60-65

Mathematics

39

Chaos, Nonlinearity, Numerical Integration, Orbital Mechanics, Orbital Resonances (Celestial Mechanics), Asteroids, Eccentricity, Mathematical Models, Meteorites, Rendezvous Trajectories

Scientific paper

In this paper we examine some realistic numerical integrations of objects in the 3/1 commensurability. We show that, as pointed out by the analytic model in Moons and Morbidelli (1995), the dynamics in the 3/1 commensurability is strongly chaotic due to the overlapping of secular resonances. As a consequence, the eccentricity of bodies in the 3/1 commensurability can increase to e approximately equal to 1 on a time scale of 1 Myr. This causes the 3/1 resonant asteroids to cross the orbit of the Earth and, possibly, to fall into the Sun. Therefore the 3/1 resonance is an active transport route of meteorites to the Earth. However, the collisions with the Sun can get rid of most potential meteorites before their encounter with the Earth.

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