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Yes it does, although it become unnoticeable after a point. Newton's law of universal gravitation states Force = G * (m1*m2)/d2. Where G is the gravitation constant, m1 and m2 are the mass for the respective objects and d is the distance, squared. The effects grow weaker the farther the object is, to the point it doesn't matter, but as long as Force isn't zero --which it truly can't be -- a force is acted on the object(s).

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