ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Previous work by the authors [B. M. Barker and R. F. O'Connell, Phys. Rev. D 12, 329 (1975); 14, 861 (1976); B. M. Barker, G. G. Byrd, and R. F. O'Connell, Astrophys. J. (in press); B. M. Barker and R. F. O'Connell, Gen. Relativ. Gravit. (to be published)] on the post-Newtonian (order c−2) gravitational two-body problem with spin and parametrized post-Newtonian parameters γ and β was concerned with the relative position r=r1−r2. Here this work is completed by finding the individual positions r1 and r2, which is necessary for the interpretation of certain binary-system observations. First the center of inertia rCI is found. This makes it possible to obtain the positions r1 and r2 and the center of mass rCM as a function of the relative position r, relative velocity v, and spin angular momenta S(1) and S(2) of the two bodies. Thus, if a solution r=r(t) exists, then solutions r1=r1(t) and r2=r2(t) also exist. The final results are given in a very general coordinate system specified by four arbitrary dimensionless parameters. In particular, the spin-orbit potential energy terms VS1 and VS2 are given without going to a frame of reference where the total momentum is zero.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.527600
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