The force law for the dynamic twobody problem on the second postNewtonian approximation of general relativity.
Abstract
We calculate the force between two wellseparated bodies in a fully dynamic system of two extended bodies up to and including the second postNewtonian approximation (PNA). We use the iteration procedure as formulated by Anderson and Decanio in a version whose divergences have been pushed to the third PNA. We show the following, (i) The force law assumes the “Newtonian form” if a second approximation in 1/(separation of the bodies) is made; (ii) the mass terms appearing in the force law are the (Tolman) masses of the individual bodies expanded up the second PNA; the interal masses equal the (passive and active) gravitational masses of the bodies in order considered; they are all constants of the motion; (iii) the selffields of the bodies vanish in the second PNA; hence there is no Nordvedt effect in the second PNA; (iv) the compactness of the bodies, i.e., (gravitational radius)/(body size), does not appear in the force law; only the relation between mass and the matter variables is changed in the PNA as compared with the corresponding Newtonian result.
 Publication:

General Relativity and Gravitation
 Pub Date:
 February 1982
 DOI:
 10.1007/BF00756922
 Bibcode:
 1982GReGr..14..181B
 Keywords:

 Gravitation Theory;
 Relativity;
 Two Body Problem;
 Binary Stars;
 Flow Charts;
 Iteration;
 Astrophysics;
 Relativity Theory:TwoBody Problem