  The chaotic nature of planet dynamics in the solar system suggests the
relevance of a statistical approach to planetary orbits. In such a statistical
description, the time-dependent position and velocity of the planets are
replaced by the probability density function (PDF) of their orbital elements.
It is quite natural to set up this kind of approach in the framework of
statistical mechanics. In the present paper I focus on the collisionless
excitation of eccentricities and inclinations by gravitational interactions in
a planetary system, the prototype of such a dynamics being the future planet
trajectories in the solar system. I thus address the statistical mechanics of
the planetary orbits in the solar system and try to reproduce the PDFs
numerically constructed by Laskar (2008). I show that the microcanonical
ensemble of the Laplace-Lagrange theory accurately reproduce the statistics of
the giant planet orbits. To model the inner planets I then investigate the
ansatz of equiprobability in the phase space constrained by the secular
integrals of motion. The eccentricity and inclination PDFs of Earth and Venus
are reproduced with no free parameters. Within the limitations of a stationary
model, the predictions also show a reasonable agreement with Mars PDFs and that
of Mercury inclination. The eccentricity of Mercury demands in contrast a
deeper analysis. I finally revisit Laskar's random walk approach to the time
dependence of the inner planet PDFs. Such a statistical theory could be
combined with direct numerical simulations of planet trajectories in the
context of planet formation, which is likely to be a chaotic process.
