ON THE ORIGIN OF THE PLANETARY SPIN BY ACCRETION OF PLANETESIMALS .2. COLLISIONAL ORBITS AT THE HILL SURFACE

The structure of the totality of orbits starting at the Hill surface is investigated numerically and systematically in the framework of the planar-restricted three-body problem. We have obtained the following results. (1) The qualitative features of the totality of orbits at the Hill surface are clarified. (2) A general formula for the collisional probability as a function of the mass ratio μ, radius R, and Jacobi constant C is obtained for μ ≤ 10-4, 2 × 10-5 ≤ R < 2 × 10-4, and the range of C corresponding to Γ ≤ 2, where Γ is the Jacobi constant for the Hill problem of the restricted three-body problem. The collisional probability is also given as a function of the velocity at the Hill surface. (3) The relative collisional probability as a function of (a,e) is obtained for 0.86 ≤ a ≤ 1.14 and 0.0 ≤ e ≤ 0.1. © 1991.