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The restricted two-body problem in constant curvature spaces

Authors:	Alexey V Borisov Ivan S Mamaev

Institution:	(1) Institute of Computer Science, Udmurt State University, 1 Universitetskaya str., 426034 Izhevsk, Russia

Abstract:	We perform the bifurcation analysis of the Kepler problem on $\mathbb{S}^{3}$ and $\mathbb{H}^{3}$ . An analog of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of a Newtonian center moving along a geodesic on $\mathbb{S}^{2}$ and $\mathbb{H}^{2}$ (the restricted two-body problem). For the case of a small curvature, the pericenter shift is computed using the perturbation theory. We also present the results of numerical analysis based on an analogy with the motion of a rigid body.

Keywords:	Kepler problem Bifurcation analysis Perihelion shift Delaunay variables Restricted two-body problem
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