As gravitational interactions are much more significant, I would change the electron density to a mass density. I would opt towards a multiscale approach as well. For the length- and timescale of the planets, as satellites around the sun, just like in the Kohn Sham equation we can think of quasi planets. For a gravitational Kohn Sham equation we’d have: A term for the kinetic energy of the quasi planets, a term that stresses that these are subject to the gravitational potential of the sun, an interaction term describing how the quasiplanets interact with one another through the interaction with the average static distribution of all the other quasi planets and a exchange-correlation potential to glue everything together. We can do the same on the length- and timescale of moons or even meteors and smaller debree around planets, taking these as quasi particles now, and not the planets.