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

3PN accurate conservative dynamics
The angular motion, described in terms of φ and ˙ φ, is given by
φ(λ, l) = λ + W (l) ,
λ = (1 + k)l ,
k = 3ξ2/3
1 − e2 ξ
+
t
4/3
4(1 − e2 t )2
2
78 − 28η + (51 − 26η)et +
ξ2 128(1 − e2 t )3
18240 − 25376η + 492π 2 η + 896η 2 +
(28128 − 27840η + 123π 2 η + 5120η 2 )e 2 t + (2496 − 1760η + 1040η 2 )e 4 t
+ 1920 − 768η + (3840 − 1536η)e 2
t 1 − e2 t ,
W (l) = WN + W1PN + W2PN + W3PN ,
WN = v − u + et sin u ,
W1PN = 3ξ2/3
1 − e 2 t
(v − u + et sin u) ,
BRI-IHP06-I – p.122/??