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No, if moon wouldn't spin you would see different side of it depending on its position in its orbit around Earth, not depending on your position in earth.
Originally posted by AgentSmith
I thought if it didn't spin at all you would see a different face of it at different points around the Earth, the same every time.
I.e. directly opposite from your location you would see the opposite side.
Actually satellites and probes use reaction/momentum wheels for precise pointing. (especially good thing with those is they don't consume rocket fuel)
Originally posted by Off_The_Street
For example, if the satellite's job were to keep a camera pointed toward the earth, its attitude would be fine-tuned by small thrusters so that it would appear stationary from the Earth (which, of course, means it would have one rotation per revolution, but we've already beat that one to death!).