Applying the Kohn-Sham method to the gravitational attraction of the planets and the sun would perhaps give something like this:
– The planets are not subject to any direct body-to-body gravitational interaction
– The planets move in a gravitational field that consists of
– The gravitational field of the sun
– The average gravitational field caused by all planets
– An additional field that compensates for the lack of planet-to-planet interactions.
– The energy of a planet is the sum of its kinetic energy, its potential energy in the combined gravitational fields. The additional field is a functional of the density of planets in the system.