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> the bulge on the Earth induced by the Sun exerts a torque on the Sun

There's a further point here, though. The torque exerted on the Moon by the bulge is constant over time, because the position of the Moon relative to the bulge is constant (the bulge "leads" the Moon by a constant angle which is the result of a balance between the torque on the bulge exerted by the Moon and the pull on the bulge exerted by the Earth's spin). But the position of the Sun relative to the bulge is not constant: it goes through a complete cycle over the course of a month. So it seems to me that, at least to first order, the net torque of the bulge on the Sun over the course of a month should cancel out, so there will be no net exchange of angular momentum between the Earth's spin and the Sun-Earth orbit.



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