Towards an alternative 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 overshadowed 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.