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

• 来源期刊: 天文和天体物理学研究
• 年，卷（期）: 2016,（1）
• 页码范围: 135-144
• 页数: 10页
• 语种: 英文
• DOI: 10.1088/1674-4527/16/1/016

摘要

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 parameters3 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.