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We extend a theorem by Darwin on the deformation invariance of Tr |, the trace of the earth's inertia tensor, and clarify some obscure points in the geophysical literature on the subject. By combining the possibility of changes in Tr | with results obtained by Lambeck and Cazenave (1973a) on the contribution of atmospheric winds to seasonal variations in the length of day, we (1) reduce by a factor of 3 Nordtvedt and Will's (1972) upper limit on the spatial gradient of the gravitational ‘constant’ G across the earth's orbit, predicted by preferred frame theories of gravitation, and (2) find that the seasonal changes in the geopotential, deduced by Kozai (1970), are an order of magnitude too large.
Rochester et al. (Sun,) studied this question.