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.
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.