Equation Icon  dP-τ1Θ 2m1m2-- dτ = − ε r2 [4(⃗n12 ⋅⃗v1) − 3(⃗n12 ⋅⃗v2)] 12 [ + ε4m1m2-- − 9(⃗n ⋅⃗v )3 + 1-v2(⃗n ⋅⃗v ) + 6(⃗n ⋅⃗v )(⃗n ⋅⃗v )2 r212 2 12 2 2 1 12 2 12 1 12 2 2 ⃗ 2 2 − 2v1(⃗n12 ⋅⃗v1) + 4(⃗v1 ⋅⃗v2)(⃗n12 ⋅V ) + 5v2(⃗n12 ⋅⃗v2) − 4v2(⃗n12 ⋅⃗v1) ] m1- m2- + r (− 4(⃗n12 ⋅⃗v2) + 6(⃗n12 ⋅⃗v1)) + r (− 10(⃗n12 ⋅⃗v1) + 11 (⃗n12 ⋅⃗v2)) [ ( 12 ) (12 ) + ε6m1m2-- − 3v4 + 2v2v2 + 4v4 (⃗n ⋅⃗v ) + 5-v4+ 3v2v2 + 7v4 (⃗n ⋅⃗v ) r12 2 1 1 2 2 12 1 8 1 2 1 2 2 12 2 ( 2 2) ( 2 2) + 2v1 + 4v2 (⃗n12 ⋅⃗v1)(⃗v1 ⋅⃗v2) − 2v1( + 8v2 (⃗n12)⋅⃗v2)(⃗v1 ⋅⃗v2) ( 2 2) 2 3-2 2 3 + 3v1 + 12v2 (⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2) − 4v1 + 12v2 (⃗n12 ⋅⃗v2) 2 2 3 + 2(⃗n12 ⋅⃗v2)(⃗v1 ⋅⃗v2) − 6(⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2) (⃗v1 ⋅ ⃗v2) + 6(⃗n12 ⋅⃗v2) (⃗v1 ⋅⃗v2) 15- 4 45- 5 − 2 (⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2) − 8 (⃗n12 ⋅⃗v2) { ( ) + m1- − 42v21 − 117-v22 (⃗n12 ⋅⃗v1) + 60 (⃗n12 ⋅⃗v1)3 r12 4 ( 137 37 ) 297 + ---v21 +---v22 (⃗n12 ⋅⃗v2) + ---(⃗n12 ⋅⃗v1)(⃗v⋅⃗v2) 4 2 4 219- 2 − 4 (⃗n12 ⋅⃗v2)(⃗v⋅⃗v2) − 151 (⃗n12 ⋅⃗v1) (⃗n12 ⋅ ⃗v2) } + 109(⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2)2 − 23(⃗n12 ⋅⃗v2)3 + m2-{ − (13v2 + 18v2) (⃗n ⋅⃗v ) + (17v2 + 25v2) (⃗n ⋅⃗v ) r12 1 2 12 1 1 2 12 2 + 26 (⃗n ⋅⃗v )(⃗v ⋅ ⃗v ) − 28 (⃗n ⋅⃗v )(⃗v ⋅⃗v ) + 2(⃗n ⋅⃗v )2(⃗n ⋅⃗v ) 12 1 1 2 2 12 2 13} 2 12 1 12 2 + 16 (⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2) − 20(⃗n12 ⋅⃗v2) m2 ( 33 13 ) m m ( 35 17 ) + -21 ---(⃗n12 ⋅⃗v1) −---(⃗n12 ⋅⃗v2) − --12--2 --(⃗n12 ⋅⃗v1) + --(⃗n12 ⋅⃗v2) r12( 4 2 ) ] r12 4 4 m22 23 + r2- − 12(⃗n12 ⋅ ⃗v1) +-2-(⃗n12 ⋅⃗v2) 12 + 𝒪 (ε7). (147 )