This is shown to make the retrograde contribution to the perihelion precession,


 60- 7- (3-20)
 a(l e2)

where a is the semi-i i' ',r axis of the orbit, e is its eccentricity, and re = e2/m, the

classical radius of the particle.

 From Eq. (3-17)

 hoo =2GM (3-21)

and this leads to


 1 a2 (GM>
 Rlioo = hooij = i (3-22)

Then with this, FNC can be rewritten in the form


 FNCei e2RC,, ,,, (3-23)
 3

which shows directly that the damping effect comes from the curvature of space-

time. FNC may be written in another form by making use of the undamped

equation of motion

 = GM) (3-24)

as the first approximation. Then, one gets

 2 2"
 FNC e= er, (3-25)


which is in agreement with the flat spacetime theory. From this, an integration by

parts gives

 AEorbit = -22 bit dt, (3-26)
 3 orbit
which expresses either the total energy loss for an unbound orbit or the loss in

one period for a bound orbit. This would be identical with the effect from the

traditional damping term of Eq. (3-6) which is used for accelerations caused by