The Kinetics of Systems of Planetesimals
Abstract
For the late stages of the planetary formation, a description in terms of intrinsic variales is necessary to take into account the degeneracy of the Keplerian motion. We define a kinetic formalsim relevant to such structures where we assume particles distributed randomly only according to their longitudes. Two main effects come out naturally: (1) a diffusion in phase space due to resonances and which account for instantanous chances in orbital elements of two particles undergoing a collision (2); a secular pertubation potential which governs the precession of the degenerate variables, namely, the longitudes of perihelion and ascending node. We derive analytically this potential under Hill's approximation. When the number of bodies within the cloud is small, this precession is not a simple rotation of angle variables; thus, there exist equilibrium positions in phase space that prevent averaging schemes. Finally, the diffusion operator is applied to some special cases to recover the classical results of Hornung, Pellat & Barge (1985) and to derive the exact logarithmic function that comes out in the FokkerPlanck approach.
 Publication:

The Astrophysical Journal
 Pub Date:
 February 1995
 DOI:
 10.1086/175218
 Bibcode:
 1995ApJ...439..800L
 Keywords:

 Kinetics;
 Planetary Evolution;
 Planetary Nebulae;
 Planetary Systems;
 Protoplanets;
 Diffusion;
 Equations Of Motion;
 FokkerPlanck Equation;
 Kepler Laws;
 Kinetic Equations;
 Three Body Problem;
 Astrophysics;
 ISM: PLANETARY NEBULAE: GENERAL;
 STARS: PLANETARY SYSTEMS