Epicycles and Poincar\'{e} Resonances in General Relativity
General Relativity and Quantum Cosmology
2011-05-10 v1
Abstract
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.
Cite
@article{arxiv.1011.3973,
title = {Epicycles and Poincar\'{e} Resonances in General Relativity},
author = {G. Koekoek and J. W. van Holten},
journal= {arXiv preprint arXiv:1011.3973},
year = {2011}
}
Comments
24 pages, 4 figures