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arXiv · 2504.13239

The first-order orbital equation

Maurizio M. D'Eliseo
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Abstract

We derive the first-order orbital equation employing a complex variable formalism. We then examine Newton's theorem on precessing orbits and apply it to the perihelion shift of an elliptic orbit in general relativity. It is found that corrections to the inverse-square gravitational force law formally similar to that required by general relativity were suggested by Clairaut in the 18th century.

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Maurizio M. D'Eliseo. 2025-04-17. The first-order orbital equation. https://arxiv.org/abs/2504.13239

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