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We can shield a change from electric fields by a putting it inside a hollow conductor.Can we shild a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?

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No, because gravitational force between two point mass bodies is independent of the interventing medium between them. It is due the above reason, we cannot shiled a body from the gravitational influence of nearby matter by putting it either inside a hollow sphere or by some other means.

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