The planets revolve around the Sun due to its spacetime curvature of gravity. Does the same apply to the satellites of the planets?
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11$\begingroup$ Yes ${}{}{}{}{}$ $\endgroup$– John RennieCommented Nov 16, 2018 at 17:54
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$\begingroup$ @JohnRennie That looks like an answer. $\endgroup$– AvantgardeCommented Nov 16, 2018 at 22:52
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$\begingroup$ No ${}{}{}{}{}$ $\endgroup$– John RennieCommented Nov 18, 2018 at 18:26
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1 Answer
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Yes, except that, for the Moon, the curvature due to the Sun is as important than the curvature due to the Earth. Even in Newtonian gravity, the Sun pulls about twice as hard on the Moon as the Earth does! This is because, even though the Sun is a lot further away from the Moon than the Earth is, it is so much more massive than the Earth.
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$\begingroup$ Please do not confuse GR curvature with Newtonian force. Whereas the latter goes as $1/r^2$, the former goes as $1/r^3$. So for Moon spacetime curvature due to Sun is much smaller than the one due to Earth: 200 times so. A direct effect of curvature can only seen in tides: you had to compare Earth tides on Moon with Sun tides. $\endgroup$ Commented Nov 17, 2018 at 16:02
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$\begingroup$ You are correct that our Moon is the only moon in the Solar System that would stay with the Sun, if the host planet is towed away. However your explanation could be improved. The Sun also s more massive than Jupiter, but if you tow away Jupiter, all its moons would follow it and part with the Sun despite its mass. Our Moon is not a true satellite, bud more of a companion rotating around the Sun with the Earth more so than just rotating around the Earth. $\endgroup$ Commented Nov 18, 2018 at 17:58
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$\begingroup$ @ElioFabri The Newtonian gravity follows directly from the Schwarzschild time dilation, so the answer appears correct. Perhaps by "curvature" you mean something more spacific. $\endgroup$ Commented Nov 18, 2018 at 18:04
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$\begingroup$ @safesphere "Perhaps by 'curvature' you mean something more spacific." Surely I do. In GR curvature has a precise meaning. In pop science it's very common to read that "gravity is due to spacetime curvature" but this is wrong. You may feel gravity in several situations where there is no spacetime curvature. G. Smith appears to take implication curvature --> gravity too literally. $\endgroup$ Commented Nov 19, 2018 at 11:00
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$\begingroup$ @safesphere "our Moon is the only moon in the Solar System that would stay with the Sun, if the host planet is towed away." Do yo have some calculation available? I guess that it all depends on how Earth is accelerated. If acceleration is gentle enough, I would say Moon would follow it. $\endgroup$ Commented Nov 19, 2018 at 11:02