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 2.505 s, what is the measured speed of light? Take the center-to-center distance from Earth to Moon to be 3.84 ? 108 m. Assume that the Moon is directly overhead and do not neglect the sizes of the Earth and Moon.

Answer 1

We first need to correct a typo you've made: the distance from the Earth to the Moon is d = 3.84 x 10^8 meters (*NOT* 3.84 x 108 m).

The speed of light (denoted by the letter "c") is found by dividing the distance the light travels (D) by the time is takes to travel that distance (t). In equation form:

c = D / t

What is D? Well, the TOTAL distance is TWICE the distance from the Earth to the Moon (because the light has to travel TO the Moon, bounce off the reflector, then travel BACK to the Earth). So....

D = 2 x 3.84 x 10^8m = 7.68 x 10^8 meters

The time it takes to the light to travel is given in the problem:

t = 2.503 seconds.

And so now we're ready to solve the problem for the speed of light:

c = D / t = 7.86 x 10^8 m / 2.503 seconds

or

c = 306,831,801 m/s

That's the speed of light!


(NOTE: the REAL speed of light is c = 299792458 m/s - slightly different from the result above. Why? Because we're using an APPROXIMATE distance to the Moon for simplicity. Most textbooks use the "rounded" value of the speed of light as 3 x 10^8 m/s for ease of calculation)