DFT for solar system

In the solar system, our analogue for electrons and nuclei are the planets and the sun, respectively. Planets have nonnegligible interactions with each other and the sun, but the force exerted on the sun by the planets can be safely approximated as 0. If solving for the probability distribution of the planets, we can use a Kohn-Sham-like approach to eliminate the need to solve for individual body-body interactions between the planets themselves. The Hamiltonian for quasiparticles this system (to replace that of the planets’ Hamiltonian) would need to include kinetic energy, the gravitational field of the sun, a Hartree-like potential from the average gravitational field created by the planets’ distribution, and perhaps an XC-like potential that comes from a functional of the planetary density distribution.