For this, we would treat the Sun as the nucleus and the planets as electrons (ignoring moons and asteroids), all of which would interact with each other. However, we apply the Born–Oppenheimer approximation and retain only the interactions with the Sun.
We then introduce an external gravitational field that mimics the interactions we just neglected.
This external field does not exist physically but serves as a way to account for all the interactions using a single effective term. Using this we have turned a many-body problem into a lot of single body problems wxhich are easier to solve.