Towards an Alternative Gravitational Theory

TL;DR

This paper explores a novel gravitational theory based on Spiric curves, generalizing Cassini ovals, and demonstrates that planetary orbits can be derived as special cases within this new framework.

Contribution

It introduces a new gravitational model using Spiric curves, extending classical orbital theories and providing a potential alternative to Keplerian dynamics.

Findings

Elliptical orbits emerge as special cases in the Spiric gravitational framework.

The formalism generalizes classical planetary trajectories.

Initial steps towards a broader Spiric-based gravitational theory.

Abstract

In 1680 Cassini proposed oval curves as alternative trajectories for the visible planets around the sun. The Cassini ovals were of course overshadow by the Kepler's first law (1609), namely the planets move around the sun describing conic orbits. Here we describe the possibility that the Cassini's idea works at larger or smaller scales. Indeed, we consider the Spiric curves (which are a generalization of the Cassini oval) and present the first steps towards a Spiric gravitational theory. We show that from our formalism an ellipse associated with a planet can be obtained as a particular case.