Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH

Evoln of orbital elements under GRR
3PN accurate expressions for the mean motion n, eccentricity et
and semi-major axis ar read are listed. Let us use the example of n
to outline the procedure adopted for the computation of orbital
elements in more detail. The expression for n is symbolically written
as
n = n(E, J).
Differentiating with respect to t one obtains
dn
dt = γ1(et, ζ, ν) dE
dt + γ2(et, ζ, ν) d|J|
dt ,
where γ1 and γ2 are PN expansions in powers of ζ. Now we use the
balance equations,
dE
dt
d|J|
dt
= − dE
dt ,
= − dJ
dt .
BRI-IHP06-I – p.83/??