Question

A LASER is a source of a very intense, monochromatic, and a unidirectional beam of light. These properties of laser light can be exploited to measure long distances. The distance of the Moon from the Earth has been already determined very precisely using a laser as a source of light. A laser light beamed at the Moon takes 2.56 s to return after reflection at the Moon's surface. How much is the radius of the lunar orbit around the Earth?

Answer 1

Hint: Time taken by the light beam after reflection from the moon's surface is given. Using that data, find the time taken by a light beam to reach the moon surface. The radius of the lunar orbit is basically the distance between earth and moon. We know the speed of light and we already calculated time. So using these data and the formula for speed, distance, and time, find the distance. This obtained value is the radius of lunar orbit.

Formula used:
$Speed= \dfrac {distance}{time}$

Complete step-by-step solution:
Given: Time taken by the light beam to return on Earth after reflection at earth's surface ${T}_{r}= 2.56s$
Time taken by the light beam to reach moon will be,
$T= \dfrac {{T}_{r}}{2}$ ...(1)
$\therefore T= \dfrac {2.56}{2}$
$\therefore T= 1.28s$
Therefore, the light beam takes 1.28s to reach the moon’s surface.
Now, the radius of the lunar orbit is equal to the distance between the Earth and the Moon
From distance-time relation, we know,
$Speed= \dfrac {distance}{time}$
Rearranging the above equation we get,
$distance= Speed \times time$ ...(2)
We know, speed of light is $3 \times {10}^{8} {m}/{s}$
Substituting values in the equation. (2) we get,
$distance= 3 \times {10}^{8} \times 1.28$
$\therefore distance= 3.84 \times {10}^{8} m$
Thus, the distance between Earth and the Moon is $ 3.84 \times {10}^{8} m$.
Hence, the radius of lunar orbit around earth is $3.84 \times {10}^{5} km$.

Note: A typical red laser of 5 milliwatts can actually hit the moon's surface. But only a few photons will come back and be captured by the telescope. Most of the photos will spread out in the atmosphere itself. It actually takes 2.5 secs for the light to hit the moon and come back.