Question

What is the distance between the moon’s surface and the Earth’s surface?

Answer 1

The distance between the Earth and the moon is calculated experimentally. But we know that the speed of light and the time taken for the light to travel from the moon to the Earth’s surface. Hence using the expression for the speed of light, we can determine the distance between the Earth and the moon’s surface.

Formula used:
$d=s\times t$

Complete step-by-step solution:
There is no medium i.e. vacuum between the Earth and the moon. The speed ‘s’ of light in vacuum is $3\times {{10}^{8}}m{{s}^{-1}}$. Light takes approximately t = 1.28 sec to travel from the moon’s surface and Earth’s surface. If we treat light as a chain of photons, the distance ‘d’ covered by the light is given by,
$\begin{aligned} & d=s\times t \\\ & \Rightarrow d=3\times {{10}^{8}}m{{s}^{-1}}\times 1.28s \\\ & \therefore d=3.84\times {{10}^{8}}m \\\ \end{aligned}$
Therefore the distance between the Earth’s and moon’s surface is $3.84\times {{10}^{8}}m$.

Additional information:
The distance between the Earth and the moon cannot be determined theoretically. In the above solution we knew the time taken by the light which is obtained practically. Usually the astronomical measurements are made using the parallax method. In this method we use the angle subtended by the distant object to our eye level and knowing the dimensions, we can determine the distance between the object with respect to us. There are other methods as well which gives absolute results without any prerequisite.

Note: It is to be noted that the distance between the Earth and the moon is measured in astronomical units i.e. in light years. One light year is the distance covered by the light in one year. This is done as it is more convenient than such huge distances expressed in meters.