On the Moon\\\'s surface, lunar astronauts placed a corner reflector, off which

Question

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. The Earth's atmosphere slows down light. Assume the distance to the Moon is precisely 3.84 × 108 m, and Earth's atmosphere (which varies in density with altitude) is equivalent to a layer 35.0 km thick with a constant index of refraction n = 1.000293. What is the difference in travel time for light that travels only through space to the moon and back and light that travels through the atmosphere and space?

Explanation / Answer

The speed of light in space is 3e8 m/s

travel time t1 = 2*3.84e8/3e8 = 2.56 s

The speed of light in atmosphere = c/n = 3e8/1.000293 =299912126 m/s

travel time t2 = 2*(3.84e8-35000)/3e8 + 2*35000/299912126

= 2.56000006837 s

difference in time = t2- t1

= 6.837 *10^-8 s

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