Corrected Newtonian potentials in the two-body problem with applications

TL;DR

This paper analytically studies various corrected Newtonian potentials, describing their behavior, stability, and applications to satellite and planetary motion, with potential relevance to galactic phenomena.

Contribution

It provides a comprehensive description of corrected potentials, including new models derived from continued fractions and logarithmic corrections, and analyzes their stability and applicability.

Findings

Continued fractional potential U2 has stable circular orbits.

Potential models can be tuned to match observational data.

Applications include satellite motion and galactic phenomena.

Abstract

The paper deals with an analytical study of various corrected Newtonian potentials. We offer a complete description of the corrected potentials, for the entire range of the parameters involved. These parameters can be fixed for different models in order to obtain a good concordance with known data. Some of the potentials are generated by continued fractions, and another one is derived from the Newtonian potential by adding a logarithmic correction. The zonal potential, which models the motion of a satellite moving in the equatorial plane of the Earth, is also considered. The range of the parameters for which the potentials behave or not similarly to the Newtonian one is pointed out. The shape of the potentials is displayed for all the significant cases, as well as the orbit of Raduga-1M 2 satellite in the field generated by the continued fractional potential U3, and then by the zonal one. For the continued fractional potential U2 we study the basic problem of the existence and linear stability of circular orbits. We prove that such orbits exist and are linearly stable. This qualitative study offers the possibility to choose the adequate potential, either for modeling the motion of planets or satellites, or to explain some phenomena at galactic scale.