One common solution to the singularity and perihelion problems

TL;DR

This paper proposes a unified approach to address the singularity and perihelion problems in planetary motion by modifying Newton's gravity based on a new mathematical model derived from classical mechanics.

Contribution

It introduces a novel mathematical model of a material point in spacetime and modifies Newton's gravity to solve two longstanding issues in celestial mechanics.

Findings

Addresses singularity problem in gravitational models

Provides a new mathematical framework for planetary motion

Suggests a modified gravity concept to resolve perihelion precession

Abstract

Based on the kinetic energy theorem, as one of the fundamental theorems from the classical mechanics, throughout the first part of the article an attempt has been made to derive the mathematical model of a material point motion in the three-dimensional spatial subspace of the integral four-dimensional space-time continuum and in the field of action of an active force F. Accordingly, with a view to surmounting the singularity problem on the one hand, as well as the moving perihelion problem of the planets on the other, as two acutely vexed questions within Newton's gravity concept, the paper ends with modification of Newton's gravity concept itself.