11 of 13 ogen Physics On the Moon\'s surface, lunar astronauts placed a comer re

Question

11 of 13 ogen Physics On the Moon's surface, lunar astronauts placed a comer reflector, off which a laser beam is periodically reflected. The distance to the Moon is calculated from the round-trip time. The Earth's at down light. Assume the distance to the Moon is precisely 3.84 x 108 m, and Earth's atmosphere (which varies in density with altitude) is equivalent to a layer 350 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? tmosphere slows Number

Explanation / Answer

t = time taken when travel only in space = 2 x distance of moon / speed of light = 2 x 3.84 x 108 / 3 x 108 = 2.56 sec

c' = speed of light in atmosphere = c/n = (3 x 108)/1.000293 = 2.999 x 108 m/s

t' = time taken through atmosphere and space = 2 x distance of atmosphere / c' + 2 x distance in space/c

t' = 2 x 35000/(2.999 x 108 ) + 2 (3.84 x 108 - 35000)/(3 x 108) = 2.5600000778 sec

difference in time = 2.5600000778 - 2.56 = 7.78 x 10-8 sec

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