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The restricted two-body problem and the Kepler problem in the constant curvature spaces. (English) Zbl 1137.70339
Summary: In this work we carry out the bifurcation analysis of the Kepler problem on $$S^3$$ and $$L^3$$, and construct the analogues of Delaunay variables. We consider the problem of motion of a mass point in the field of moving Newtonian center on $$S^2$$ and $$L^2$$. The perihelion deviation is derived by the method of perturbation theory under the small curvature, and a numerical investigation is made, using the anologuous problem with rigid body dynamics.

##### MSC:
 70F05 Two-body problems 37N05 Dynamical systems in classical and celestial mechanics
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