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

3PN accurate conservative dynamics
Radial motion, defined by r(l, n, et) and ˙r(l, n, et), reads (both in the
compact and in the 3PN expanded form) 5
r = S(l, n, et) = ar(n, et)[1 − er(n, et) cos u] = rN + r1PN + r2PN + r3PN ,
rN =
GM
n 2
r1PN = rN ×
r2PN = rN ×
r3PN = rN ×
1/3
(1 − et cos u) ,
ξ 2/3
6(1 − et cos u) [−18 + 2η − (6 − 7η)et cos u] ,
ξ 4/3
−72(4 − 7η) + 72 + 30η + 8η 2 − i
72(1 − e2 t )(1 − et cos u)
(72 − 231η + 35η 2 )et cos u (1 − e 2
t ) − 36(5 − 2η)(2 + et cos u) 1 − e2 t
− 2
3
ξ 2
(1 − e 2 t )2 (1 − et cos u)
87 437
+ η −
16 144 η2 + 49
1296 η3
· · · · · · · · · · ··
− 70
3
+ 56221
840
× et cos u
η − 123
64 π2 η − 151
36 η2 + 2
81 η3 +
BRI-IHP06-I – p.120/??