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 30.0 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

given distance d = 3.84 X 108 m

C = 3 X 108 m/s

D = 30 km

n = 1.000293

the time taken for the round trip is t

t = 2 d / C

t = 2 X 3.84 X 108 / 3 X 108

t = 2.56 sec

and distance D = 30 km

the distance through atmosphere is = 2 X D

= 2 X 30 X 1000

= 60000 m

V = C / n

V = 3 X 108 / 1.000293

V = 2.99 X 108 m/s

th etime in the atmosphere is T

T = 2 D / V

T = 2 X 30000 / 2.99 X 108

T = 2.00 X 10-4 sec

and for the space d ' = 3.84 X 108 - 60000

= 3.8394 X 108 m

but velocity of light is C = 3 X 108 m/s

t = 2 X 3.8394 X 108 / 3 X 108

t = 2.5596 sec

the total time is = 2.5596 + 2 X 10-4

= 2.5598 sec

the difference time is = 2.5598 - 2.56

= - 2 X 10-4 sec

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