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physical shape of the bodies remains the same in all frames. The non-rotating-spheroid frame has physics whose cause lies outside the system, responsible for the oblateness of the spheroid. The non-rotating-sphere frame does not, which makes it privileged in that it doesn't require external causes.
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elastic bodies are in space and distant from each other such that the interaction between them can be ignored, and whose only relative motion is a uniform rigid rotation around the line joining the centers of both bodies (like spinning wheels around an
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Einstein's Space-Time: An
Introduction to Special and General Relativity
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explain these inertial-gravitational effects without an external cause.
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352:Gilson, James G. (September 1, 2004),
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