Nonlinear Dissipative Forces in Celestial Motion Using the Method of Multiple Scales

TL;DR

This paper introduces a covariant model of nonlinear dissipative forces, like gravitational friction, affecting celestial motion, and uses the method of multiple scales to analyze their impact on planetary precession within general relativity.

Contribution

It develops a modified metric incorporating dissipative forces and applies the method of multiple scales to analyze their effects on planetary precession, providing a new approach in relativistic celestial mechanics.

Findings

Constrained medium density near Mercury to approximately 1.12 x 10^{-10} kg/m^3.

Reproduced classical relativistic perihelion precession predictions.

Provided a covariant description of dissipative forces in planetary motion.

Abstract

This paper investigates the influence of nonlinear dissipative forces, specifically Gravitational Friction (GF), on the precession of celestial bodies within the framework of general relativity. We derive a modified line element by introducing a density-dependent term to model interactions between planetary bodies and the low-density interplanetary medium, providing a covariant description of dissipative forces in planetary motion. The resulting metric modification leads to corrections in the perihelion precession of Mercury, also reproducing the classical relativistic predictions. Utilizing the method of multiple scales, we analyze perturbative effects induced by GF. Using this model, we successfully constrain the medium density near Mercury to approximately $\rho_0 \approx 1.12 \times 10^{-10} \, \text{kg/m}^3$. These findings offer a new approach for incorporating dissipative mechanisms into general relativity, with potential applications in other astrophysical systems.