gauge for the time coordinate along the worldline ${\cal L}_A$. We shall call “standard worldline data” the case where this freedom is used to satisfy the following constraints: (i) $\forall A\, ,\forall T_A\, ,M_a^A(T_A)=0$ (which means identifying the origin of all local coordinate systems with the relativistic mass centers of the bodies), (ii) $\forall A\, ,
\forall T_A\, , {\bar W}^A_\alpha(T_A,0)=0$ (the so called weak effacement condition for the external gravitational potential in the local frames). Note that we still leave unconstrained the orientation of the local frame axes which can undergo a slow rotation described by the matrix $R^i_{A a}(T)$. In the case of the standard worldline data, Eq. (\[eleven\]) simplifies to the form $$\begin{aligned}
  m^{\rm standard}(t) &=& \sum_A \biggl\{ M^A\left[1+{1 \over 2c^2}
   \left( v_A^2- G_{A}^{\prime}\right)\right] \nonumber \\
 & & + {1 \over 2c^2} \sum_{l \geq 2} {2l+1
   \over l!} M^A_L G_L^A  \biggr\} + {\cal O}(4) \; , \label{twelve}\end{aligned}$$ where $G_{A}^{\prime} = \sum_{B \neq A} G^{B/A} = \sum_{B \neq
A} w^B(z_A) + {\cal O}(2)$ \[$G_A' = -G_A''$ for standard data\] denote the value on the central worldline ${\cal L}_A$ of the Newtonian potential generated by all the other bodies \[$
w^B(z_A) = \sum_{l \geq 0} {(-)^l \over l!} G 