Dynamics of Systems of Two Close Planets

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.