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How general relativity explains tides using spacetime curvature? and if the full moon can affect water, inside the international space station did the ever observe small things like water droplets move towards the moon or the entire station move to a path closer to moon? even on earth when the full moon arises why we cant see least any small objects which have less density than water but higher than the atmospheric air move towards the moon. i know that there were two tides can be seen cause earth moves towards the moon so may be that's the case we don't see small items moving up cause the earth is moving with those too. just need a clarification.

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    $\begingroup$ Why do you think it explains it any differently from Newtonian gravity? Newtonian gravity is a valid limit of general relativity in situations where the relativistic effects are neglegible, what reason do you have to believe they aren't in this case? $\endgroup$
    – ACuriousMind
    Oct 8, 2021 at 15:23
  • $\begingroup$ Related. $\endgroup$
    – J.G.
    Oct 8, 2021 at 15:38
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    $\begingroup$ @ACuriousMind Not all Newtonian and post-Newtonian theories of gravity necessarily have the same predictions about tides. Famously, Whitehead's theory was problematic there (though that's been debated). Vector-tensor theories are surprisingly sensitive re: tides, too. $\endgroup$
    – J.G.
    Oct 8, 2021 at 15:42
  • $\begingroup$ Re, "or the entire station move to a path closer to moon ?" That phenomenon is called perturbation, and I don't know this for a fact, but I strongly suspect that it's measurable. $\endgroup$ Oct 8, 2021 at 15:50
  • $\begingroup$ P.S.: Water in the Earth's oceans does not "move toward the moon." It experiences a daily cycle of very small changes in its weight as the Earth rotates in the presence of the gravitational attraction from the Moon and Sun. Those cyclic changes constitute a forcing function that causes the water in the oceans to slosh around in complex ways. The complexity is due to the shapes of the various ocean basins and bays around the world. $\endgroup$ Oct 8, 2021 at 15:57

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In Newtonian gravity tides occur because the force of gravity acting on one side of an extended object is different than on the other side. For the Earth-Moon system, the gravitational pull of the Moon on the near side of the Earth is stronger than on the far side. This force difference causes a relative acceleration between the two sides.

Internal forces (like the gravity of the Earth itself or internal stress/strain of a steal beam) hold extended objects together. In the case of the Earth-Moon system, the Earth slightly "flexes" under the tide of the Moon. In a more extreme situation the extended object could be ripped apart by a very strong tidal force.

Effectively, the same thing happens in general relativity (GR). Because GR formulates gravity as spacetime curvature, the effect can be stated in those terms. Moving objects follow geodesics of the spacetime. Each part of an extended object would travel on its own geodesic. There's a common calculation in GR to find the geodesic deviation between two nearby geodesic paths. It tells the relative acceleration between the two paths.

Since Newtonian gravity is a good approximation to GR for weak gravitational fields, we would need a highly precise experiment to measure any deviations from the Newtonian predictions in the Earth-Moon system.

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  • $\begingroup$ that cleared up. thanks a lot . $\endgroup$ Oct 13, 2021 at 5:38

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