Gravitation Reasonings

Earth is continuosly pulling moon towards its centre. Why does not moon fall on to earth?

OR: The moon is accelerating towards the earth, why isn’t it getting closer to us?

The earth is continuously pulling the moon towards its centre due to its gravitational force. At the same time, the moon is also trying to move straight ahead because of its speed and inertia of direction. Being in a circular orbit means that the path of the moon is balanced by equal inward moving tendency as well as the outward moving tendency. So, the moon does not fall on to earth and also does not get farther from the earth.

Mathematically, the moon is accelerating towards the earth such that the force of gravity exerted on moon by the earth is completely balanced by the centripetal force of the moon.

\[\text{i.e.}\;\;\frac{GMm}{d^2}=\frac{Mv^2}{d}\] where $d$ is the radius of the circular orbit of the moon.