First the charge density should change to a mass density. Now we can create the Kohn-Sham hamiltonian. It has a kinetic energy, Hartree potential, external potential and an exchange correlation potential. The kinetic energy term can be determined by the momentum of a body with a mass. The Hartree energy is the average pull a planet feels from all the other planets. The external potential is the gravitational energy generated by the sun. Now we just need to find the exchange correlation for gravity based on the mass density.