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The Newtonian equations of motion for two-point masses $m$ and $m^{\prime}$ are derived from the following Lagrangian:

$$L = \frac{1}{2}m\mathbf{v}^{2} + \frac{1}{2}m^{\prime}\mathbf{v}^{\prime \, 2} + \frac{Gmm^{\prime}}{R} \, ,$$ where $R = |r - r^{\prime}|$. In Damour, T.; Deruelle, N. (1985), “General relativistic celestial mechanics of binary systems. I. The post-Newtonian motion”, it's stated the center-of-mass integral is:

$$\mathbf{K} = m \mathbf{r} + m^{\prime} \mathbf{r}^{\prime} - t \mathbf{P}_{N} \, .$$ Where does the term $t\mathbf{P}_{N}$ come from?

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  • $\begingroup$ The title of the paper explicitly told you that it is going to handle GR corrections. It is post-Newtonian. Have you learnt about that? $\endgroup$
    – naturallyInconsistent
    Commented Dec 7, 2023 at 15:21
  • $\begingroup$ I didn't learn it, I don't know where $K_n$ comes from. Incidentally, isn't this a classical problem? I can only assume it might come from Galilean transformations. $\endgroup$
    – MicrosoftBruh
    Commented Dec 7, 2023 at 15:36
  • $\begingroup$ Look, the title already told you that they are interested in General Relativity. Why do you think Galilean transformations would be relevant? $\endgroup$
    – naturallyInconsistent
    Commented Dec 7, 2023 at 15:43
  • $\begingroup$ Where does the term $t\mathbf P_N$ come from? Isn’t it just due to the uniform motion of the center of mass? $\endgroup$
    – Ghoster
    Commented Dec 7, 2023 at 17:14

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