Planetary orbital precession in pseudo-Newtonian potentials: reproduction of the general relativity orbital effect

In this paper, pseudo-Newtonian potentials are used to study the problem of orbital precession. The precession rates are found to have the same dependence on GM/cL, where M is the mass of the star and L the angular momentum per unit mass of the planet, comparable to the result obtained in Einstein's general relativity (GR). Moreover, a specific form of pseudo-Newtonian potential (i.e. equation (16) in the text) is constructed to have the same precession rate with the GR result to the lowest order. Finally, we give a brief discussion for this potential form, as well.