The Finsler geometry of the rotating Kepler problem (Q2875438)

The rotating Kepler's problem arises as a limiting case of the restricted 3-body problem when the mass of one of the primaries converges to zero. The authors prove that the bounded components of the regularized planar Kepler problem in a rotating frame are fiberwise convex (Theorem A). Hence, the rotating Kepler problem has a Cartan structure (the structure of a Legendre dual to a Finsler metric). The second main result of the paper states that for the rotating Kepler problem there are regions in which the flag curvature is negative (Observation B). In the appendix, the authors give a MAPLE program to numerically calculate the flag curvature of a Cartan metric.