Loss of mass energy from the galaxy, whether by gravitational radiation or otherwise, should cause the galaxy to expand. Observations of stellar motions near the sun imply that the rate of radiation averaged over the last {~}10⁸ yr must be less than 200M_ yr^-1. Studies based on the 21-cm line have already yielded some evidence for galactic expansion, which could be a consequence of mass loss.
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Sciama et al. (1969) studied this question.
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