Epicycles and Poincaré Resonances in General Relativity

Details Epicycles and Poincaré Resonances in General Relativity Epicycles and Poincaré Resonances in General Relativity

2010-11-17

arxiv.org/abs/1011.3973v1

Phys.Rev.D83:064041,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, 4 figures

Scientific paper

10.1103/PhysRevD.83.064041

The method of geodesic deviations provides analytic approximations to geodesics in arbitrary background space-times. As such the method is a useful tool in many practical situations. In this note we point out some subtleties in the application of the method related to secular motions, in first as well as in higher order. In particular we work out the general second-order contribution to bound orbits in Schwarzschild space-time and show that it provides very good analytical results all the way up to the innermost stable circular orbit.

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