Now let us derive the Newtonian mass-energy relation first. From Equations (102, 103) and the time component of Equation (110), we have
Second, from Equation (91) with Equations (102) and (103) we obtain at the lowest order. Thus we have the Newtonian momentum-velocity relation from Equation (86) (we set ).
Substituting Equation (104) with the lowest order into the general form of equations of motion (111) and using the Newtonian momentum-velocity relation, we have for star :9 emanating from , , and . We used and . For details see Figure 3).
In the above equation, by virtue of the angular integral the first term (which is singular when the zero limit is taken) vanishes. The third term vanishes by letting go to zero. Only the second term survives and gives the Newtonian equations of motion as expected. This completes the Newtonian order calculations.
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