Question

The Moon is about 3.8 ✕ 108 m from Earth. Traveling at the speed of light, 3.0 ✕ 108 m/s, how long does it take a laser beam to go from Earth to the Moon and back again (in s)? The same physics was responsible for the noticeable delay in communications signals between lunar astronauts and controllers at the Houston Space Flight Center

Answer 1

Hello

1) The total distance the light has to cover to go from Earth to the Moon and back is twice the distance between the Earth and the Moon:
$S=2d=2\cdot 3.8 \cdot 10^8~m =7.6 \cdot 10^8~m$

2) Given the relationship
$v= \frac{S}{t}$
where $v=3\cdot10^8~m/s$ is the speed of light, S the total distance covered calculate at point 1), and t the time, we can find the time the light needs to go from Earth to the Moon and back again:
$t= \frac{S}{v}= \frac{7.6\cdot10^8 m}{3\cdot10^8~m/s}=2.53~s$