Elementary Solution of Kepler Problem (and a few other problems)

TL;DR

This paper introduces a straightforward method to solve several orbital mechanics problems, including Kepler's problem, a modified Kepler problem with an additional inverse square potential, and a linear force problem.

Contribution

It provides a simple, unified approach to solving multiple classical orbital problems that are typically more complex to analyze.

Findings

Derived explicit solutions for Kepler and modified Kepler problems.

Extended method to include linear force orbital problems.

Simplified the solution process for these classical problems.

Abstract

We present a simple method to obtain the solution of a few orbital problems: the Kepler problem, the modified Kepler problem by the addition of an inverse square potential and linear force.