the total mass-energy. Note, however, that he always used it in the global coordinate system. Our definition is written in the local system $X_A^\alpha$, but we use for $W(T,X)$ the [*total*]{} potential in the local frame, containing both internally and externally (including inertially) generated contributions. By using the expressions (4.15) of [@dam2] for the tidal expansion of $W(T,X)$ we find (in any worldline gauge) the following relation between the Blanchet-Damour mass and the Fock one: $$M^A  = M^A_F - {1 \over 2c^2} \sum_{l} {2l+1 \over l!} M^A_L
  G_L^A + {\cal O}(4) \; . \label{thirteen}$$ Thus in the case of standard data we can rewrite our previous formula (\[twelve\]) in the following form $$m^{\rm standard}(t) = \sum_A M^A_F\left[1+{1 \over 2 c^2}\left(
   v_A^2- G_{A}^{\prime}\right)\right] + {\cal O}(4) \; .
 \label{fourteen}$$ Let us, however, emphasize again that it is only the Blanchet-Damour mass $M^A$ which is directly observable as a gravitational mass determining the orbital motion of satellites of body $A$. The Fock mass $M^A_F$ is just a mathematical construct.

Center-of-mass integral and linear momentum
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The Blanchet-Damour post-Newtonian dipole mass moment $m_i(t)$ of the whole system [@bd] can be written as $$\begin{aligned}
 m_i(t) &=& \int d^3x \,x^i \sigma(x) \label{fifteen} \\
 & & 