An approximate superposition method to obtain a planet's orbit

Abstract

We demonstrate that the deviation produced by one celestial object on the Keplerian orbit of another around the Sun is largely independent of the presence of the remaining ones. Hence, to calculate the net deviation of an object from its Keplerian orbit, we superpose the deviations produced by every other object. We show that this method will be useful when dealing with a system containing a large number of objects. As a demonstration, we apply our method to the Solar System, with a particular focus on the orbit of Uranus.