Numerical implementation of a new gravitational force derived within Spacetime Algebra

Spacetime Algebra (STA) has proved to be a powerful tool for the study of a number of physics' theories. Many concepts in physics arise naturally from its geometric structure, which allows a simple and coordinate-free formulation of physics. Motivated by its uncomplicated description of the electromagnetic theory, in this work we derive a gravitational force within this framework, which consists of a Newtonian term and an additional vxL term, and implement it on 200 test particles orbiting around the Milky Way. By additionally implementing a standard Newtonian force, we compare the orbits generated by both forces and conclude that the extra term causes orbit precession. In this way, the STA formulation of gravity might prove advantageous over the Newtonian theory, given that it seems to be able to properly describe precession.