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

3PN accurate conservative dynamics
3PN accurate orbital dynamics, namely, r, ˙r, φ, and ˙ φ, explicitly in terms of u,
n, and et using explicit expressions for the PN orbital elements ar, er, eφ, k,
f4φ, f6φ, g4φ, g6φ, i6φ, h6φ, g4t, g6t, f4t, f6t, i6t, and h6t of the GQKR (MGS).
PN orbital elements, given in terms of E and L, can easily be expressed in
terms of n and et with the help of the following 3PN accurate relations for
−2E and −2EL2 :
−2E = (GMn) 2/3
ξ 2
5184
18
(1 − e 2 t )3/2
1 + ξ2/3
12
(15 − η) + ξ4/3
24
− 4995 − 6075η − 450η 2 − 35η 3 +
15 − 15η − η 2 +
864
1 − e 2 t
2 2
11520 − 15968η + 123π η + 2016η ,
24
1 − e 2 t
(5 − 2η)
(15 + 23η − 20η 2 ) +
+
BRI-IHP06-I – p.117/??