Mathematics

Kepler's two-body problem concerns the study of planetary motion around the sun and was solved analytically by Newton, who found a rigorous proof of the three Kepler’s laws. This apparently simple problem after a deeper study reveals to encode the very deep heart of the Euclidean Geometry.  More specifically, many mathematicians tried to formulate and solve similar problems on spaces with curvature (i.e., Riemannian manifolds) and they noticed that is was impossible to obtain an analogous of Kepler’s laws with these different Geometries.  Recently, this problem has been studied in the sub-Riemannian setting, namely on the Heisenberg group. In this talk, I will recall the main features of the classical problem and then I will expose this last new formulation and discuss a few results about it.