Dynamics of Systems of Two Close Planets

Abstract

In connection with the study of newly formed protoplanetary embryos in the early Solar System, we study the dynamics of a pair of interacting planets orbiting a Sun. By examining the topological stability of the three-body problem, one finds that for initially circular planetary orbits the system will be Hill stable (that is, stable against close approaches for all time) if the fractional orbital separation Δ > 2.4(μ1 + μ2)1/3, where μ1 and μ2 are the mass ratios of the two planets to the Sun. The validity of this stability condition is supported by numerical integrations. The chaotic dynamics of these systems is investigated. A region of bound chaos exterior to the Hill-stable zone is demonstrated. The implications for planetary accretion, the current Solar System, and the pulsar planet system PSR 1257 + 12, are discussed. © 1993 Academic Press. All rights reserved.