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I understand that matter will gravitate toward matter. (ex: Earth gravitates a satellite toward it, and the satellite toward Earth.)

Does this always apply, regardless of distance? 

Take two atoms, the farthest apart in the universe. Do they gravitate toward each other, but at an infinitesimal rate? (And actual position displacement is likely in a different direction, due to stronger/closer forces)

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Any mass/energy will interact with the gravitational field.

The gravitational field at an atoms position will be the combined result of all the mass/energy of the universe at that position, but the strength falls with distance from the gravitational sources.

The coupling to gravity is so very small with respect to other forces acting on an atom, it is ignored when solving problems, except gravitational ones for aggregates of atoms.

So yes, atoms interact with other atoms gravitationally, as a function of the distance, but the strength of the interaction is infinitesimally small.

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What about distances greater than the distance of galaxies with a recession speed equal light speed? –  Georg Apr 15 '11 at 8:45
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@Georg: In classical GR, after the curvature is established in spacetime, there is no interaction necessary between the particles for them to "feel" some kind of gravitation, even if they start to separate with lightspeed. However any further change in their positions will need gravitational waves to propagate (at the speed of light). –  BjornW Apr 15 '11 at 9:07
    
@Bjorn , that sounds as if after establishing of curvature one could remove the masses? Of course not. That galaxy just vanishing at lightspeed should cause no longer some gravity here. But that galaxy is no longer "in our univers" , right? –  Georg Apr 15 '11 at 9:43
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@Georg: yes you could remove the masses and you wouldn't notice it until the gravitational field has propagated to you and that goes with the speed of light. Now mass-energy can't just disappear of course, but a mass configuration can change and the gravitational waves will propagate this information. –  BjornW Apr 15 '11 at 12:30
    
In a General Relativity framework, even if the galaxies were receding from us with close to the speed of light ( cannot reach it), a "gravitational wave camera" would see the gravitational picture in the way we see the night sky : time projections . The time projected gravitational waves from the universe will deform the space where an atom is and it will interact with the field of the atom . The coupling strength will be infinitessimaly small. –  anna v Apr 15 '11 at 15:56

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