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E. T. Bell & 2-body problem in GR



In "Mathemaics. Queen & Servant of Science" E. T. Bell writes the
following about the two body problem in general relativity:
"The most promising attempt was that (1937) by Levi-Civita. It predicted

an effect on the motions of binary stars that should have been
observable. However, before any observations were attempted, H. P.
Robertson (1903-) found (1938) a mistake in the elaborate calculations,
causing the abandonment of the whole."
Does anyone have any information, preferably references, either about
the work of Levi-Civita or the work of Robertson or both ? Has this two
body problem been solved later ?