Abstract
THE equations of motion of two gravitating particles have been given by Milne1; they are second-order differential equations in (t1, P1), (t2, P2), the epochs and vector positions of the two particles as measured by a fundamental observer, O. From their derivation, the equations are invariant for Lorentz transformations from one fundamental observer to another. There are eight variables, four for each particle, but only six differential equations—since Milne's equations (45′) and (46′) may be deduced from (45) and (46). Thus a further relation is needed in order to integrate the equations.
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References
Milne, Proc. Roy. Soc., A, 160, 12 (1937).
Schild, Phys. Rev., 66, 340 (1944).
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CAMM, G. The Two-body Gravitational Problem in Kinematical Relativity. Nature 155, 754–755 (1945). https://doi.org/10.1038/155754a0
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DOI: https://doi.org/10.1038/155754a0
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