To study the many-body system of gravitationally interacting planets and the Sun using Density Functional Theory (DFT) and the Kohn-Sham method, you would start by modeling the gravitational potential created by the Sun and planets as an effective potential. In this adapted DFT framework, the mass densities of the celestial bodies would replace the electron densities typically used in quantum systems. The Kohn-Sham method would then allow you to simplify the problem by mapping this complex gravitational system onto a set of non-interacting particles moving under this effective potential. This approach could facilitate calculations of orbital dynamics and stability in a manner analogous to how DFT is used for electronic systems