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If you take the Earth-Moon system, from what I understand, the Moon for instance is in free fall towards the Earth-Moon center of mass. However Einstein's equivalence principle says that a body in free fall is in inertial motion. Then why does the Moon (and any binary system in general) emit gravitational waves?

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However Einstein's equivalence principle says that a body in free fall is in inertial motion.

This holds in the limit of a small body (a "test mass."). It is not true except in that limit, and for exactly the reason you've expressed.

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  • $\begingroup$ Small as in small radius or small mass? If the former then gravitational radiation is a function of the radii of two bodies? $\endgroup$ – Opt Dec 12 '19 at 3:52
  • $\begingroup$ @Opt: It's complicated, but basically both, and you also need an energy condition. You need a small mass so that radiation is negligible. You need a small radius because otherwise it's not clear what is meant by the world-line. For a simplified pedagogical discussion, see sec. 8.1.3 of my GR book, which is free online at lightandmatter.com/genrel . $\endgroup$ – user4552 Dec 12 '19 at 4:19

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