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On the moon's surface, lunar astronauts placed a corner reflector, off which a laser beam is periodically reflected. The distance to the moon is calculated from the round-trip time. What percent correction is needed to account for the delay in time due to the slowing of light in the earth's atmosphere? Assume the distance to the moon is precisely 3.84 x 10⁸ m, and the earth's atmosphere (which varies in density with altitude) is equivalent to a layer 30.0 km thick with a constant index of refraction n = 1.000293.

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