Open Access Open Access  Restricted Access Subscription Access

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


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.


gravitation – celestial mechanics – binaries: general

Full Text:




  • There are currently no refbacks.

Print ISSN: 1674-4527

Online ISSN: 2397-6209