The orbit of every single celestial body can be resolved with the Kohn-Sham method. The Kohn-Sham hamiltonian for the earth would consist of a term with the kinetic energy for the earth, a term with the gravitational interaction with the sun, which using the BO approximation doens’t move (similar the the nuclei in solids), a term with the interaction with the statistical average of the location of the other celestial bodies. And a term that is the Exchange potential, this is the derivative of the Exchange functional in respect to the path of earth. Then using the Hamiltonian equations of motion you can find the movement of the earth, the single particle path. Then do this for all other planets aswell.