A geometric method to locate Neptune: https://arxiv.org/abs/2102.04248
Siddharth Bhatnagar, Jayanth P. Vyasanakere, Jayant Murthy
We develop a direct geometric method to determine the orbital parameters and mass of a planet, and we then apply the method to Neptune using high-precision data for the other planets in the solar system. The method is direct in the sense that it does not involve curve fitting. This paper, thereby, offers a new pedagogical approach to orbital mechanics that could be valuable in a physics classroom.
Comments: Accepted for publication in American Journal of Physics