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Sun as the fixed nucleus since its so much heavier (kind of born-oppenheimer), so its gravity is V_ext, planets are the electrons and ρ is their mass density. Kohn-Sham would then be non interacting planets in an effective potential = sun + hartree-like gravity of the averaged mass of the others + xc (no exchange since planets arent identical, but correlation yes, resonances etc), and iterate till self consistent. Problem is DFT gives the ground state and for gravity thats everything collapsed onto the sun, and with 8 planets of different masses youd just solve newton directly anyway.
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