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f and g series solutions to a post-Newtonian two-body problem with parameters β and γ

Song-He Qin, Jing-Xi Liu, Ze-Hao Zhong, Yi Xie

Abstract


Classical Newtonian f and g series for a Keplerian two-body problem are extended for the case of a post-Newtonian two-body problem with parameters β and γ. These two parameters are introduced to parameterize the post-Newtonian approximation of alternative theories of gravity and they are both equal to 1 in general relativity. Up to the order of 30, we obtain all of the coefficients of the series in their exact forms without any cutoff for significant figures. The f and g series for the post-Newtonian two-body problem are also compared with a Runge-Kutta order 7 integrator. Although the f and g series have no superiority in terms of accuracy or efficiency at the order of 7, the discrepancy in the performances of these two methods is not quite distinct. However, the f and g series have the advantage of flexibility for going to higher orders. Some examples of relativistic advance of periastron are given and the effect of gravitational radiation on the scheme of f and g series is evaluated.


Keywords


gravitation – celestial mechanics – binaries: general

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DOI: http://dx.doi.org/10.1088/1674%E2%80%934527%2F16%2F1%2F016

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Print ISSN: 1674-4527

Online ISSN: 2397-6209