We know that the potential by which the object will interact will be gravity. With this knowledge we would write the problem as sums of single body interactions while keeping the sun stationary. The external potential will be the interaction with the stationary sun. We will also need the kinetic energy of the planets. Then we will have to construct the Hartree term (the interaction between the average static distribution of all the other planets and any given planet). And then we need the unknown external correlation functional.