For the late stages of the planetary formation, a description in terms of intrinsic variables is necessary to take into account the degeneracy of the Keplerian motion. We define a kinetic formalism 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 accounts for instantaneous changes in orbital elements of two particles undergoing a collision (2); a secular perturbation 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 Fokker-Planck approach.
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