Question

During the Apollo XI Moon landing, a retroreflecting panel was erected on the Moon's surface. The speed of light can be found by measuring the time it takes a laser beam to travel from Earth, reflect from the panel, and return to Earth. If this interval is found to be 2.51 s, what is the measured speed of light? Take the center-to-center distance from Earth to Moon to be 3.84 X 10⁸ m. Assume that the Moon is directly overhead and do not neglect the sizes of the Earth and Moon. (Assume the radius of the Earth and the Moon are 6380 km and 1740 km respectively.)

Answer 1

Find the radius of the earth and the radius of the moon. Then subtract the sum of those from the center to center distance given. That will tell you the actual distance the light traveled surface to surface. If the return time for the light to return after being reflected was 2.51 seconds, then the time it took to reach the moon was half of that, 1.255 seconds. All that you have to do after that is plug the distance traveled one way and time traveled one way into the distance formula, d = r t and solve for r.

d = r t
d/t = r

radius of earth ? 6.39 x 10^6 m
radius of moon ? 1.74 x 10^6 m

sum of earth's and moon's radii ? 8.13 x 10^6 m

distance traveled surface to surface by light from earth to moon ? 3.84 x 10^8 - 8.13 x 10^6 ? 3.76 x 10^8 m

r = d/t
r ? (3.76 x 10^8 m) / 1.255 m

r ? 2.996 x 10^8 m/s (This is our measured speed of light.)

Do the actual calculation on a calculator. This is the exact figure down to the third decimal place. That seems pretty close to 3 x 10^8 m/s to me. The % error is only 0.133 %, which is extremely close to the given value, considering we may not be using the exact figures your teacher has for the radius of the earth and moon.