# How to find the terms of Post-Newtonian approximation?

I am studying the Damour paper on the Post-Minkowskian approximation to the 2 bodies problem in General Relativity (paper) but can't really understand the explanation of the previous state of the art, namely the Post-Newtonian approximation: a way to "perturbe" the Newtonian flat space-time assuming small velocities.

I understand that, once is established that the two momentums $$I_R$$ and $$I_\phi$$ are the same in the real and effective scenario, one has to look for a map $$f$$ that connects the real and effective energies: $$E^{eff}=f(E^{real})$$ and this map will be expanded in a series of $$\frac{1}{c^2}$$. In the paper the $$\alpha_i$$ are the coefficients of this series. How does one calculate them?

Edit: if anyone is still interested, I found another interesting paper from 1998 by Buonanno and Damour, and chapters 2, 3 and 4 cover the subject, so question solved.