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So it will take a second before it gets there but once it gets there the wave of shadow will appear to move across the moon faster than the speed of light?
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No, at exactly the speed of light. Darkness is the absence of light. Before you put your hand in front of the light beam there was light traveling to the moon at the speed of light. When you put your hand in front of the light beam you stopped the flow of light, but there was already light on its way inbetween the source and the moon, traveling at the speed of light. The shadow will not exist until all this light reaches the moon.