First, we show the independence of the body zone radius in the 0.5 PN field. Returning back to the derivation of the 1 PN with care for the dependence (see Equation (128)), we get
In the similar manner we split as and obtain from the definition of . Thus from the fact that , we find that the 0.5 PN momentum-velocity relation does not depend on : . Finally evaluating the surface integrals in the general form of equations of motion using the “renormalized” (barred) moments, we find that the equations of motion are independent of as was expected.
As remarked in Section 4.5 from now on we use the same symbol for the renormalized moments as for the “bare” moments henceforth as before for notational simplicity.
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 2.0 Germany License.