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May 17, 2022 at 15:27 comment added AstoundingJB Yes, definitely. This is the quasi-Newtonian approximation, where you are using a relativistic theory but basically neglecting everything $\mathcal{O}(v/c)$, which implies that the source is moving according to Newton's laws. In the post-Newtonian expansion, you start considering the first order terms in $v/c$(squared), which is appropriate for describing also the motion of the source, especially in a binary system. An excellent reference is the Living review by Luc Blanchet.
May 17, 2022 at 14:19 comment added Jiaxiang Zhu I see. So the quadrupole formula is actually a good approximation for binary neutron stars. I've read some references and some of them mention Post-Newton corrections for the early stage of merge. Is it connected with my problem?
May 17, 2022 at 14:13 history answered AstoundingJB CC BY-SA 4.0