Speaker
Description
We consider the implications of the extension's of Newton's law of
gravitation as proposed in the framework of the Bolyai-Lobachevski hyperbolic geometry. In particular, we focus on the negatively-curved hyperbolic space, $H^3$, and we investigate the generalisations of Newton's inverse-square law of the gravitational force in this geometry, its properties, and its physical implications. We obtain the solutions of the two-body problem in the non-Euclidian hyperbolic Newtonian gravity by considering that the absolute space of Newton is of the Bolyai-Lobachevski type. The equations of the planetary orbits, as well as the generalization of Kepler's third law are derived. The perturbations of the orbits are also analyzed, and the expression of the perihelion precession of the planets is obtained.