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If we consider the sun to be the nucleus, then the planets could be considered the electrons. The moons can be approximated to be non existant. However, they could be included in the exchange correlation potential and the average, static distribution potential (V_H). The interaction between them is not the electrostatic but the gravitational interaction. The problem is that there are no quantum quantum numbers for the orbits of planets, so interactions would not be the same.
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