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