Question

Why is Newton's law of gravitation called inverse square law?

Answer 1

1. Newton’s Law of Universal Gravitation states that every particle attracts every other particle in the universe with force directly proportional to the product of the masses and inversely proportional to the square of the distance between them.
   
2. Mathematically
   $$\begin{gathered} F\alpha \frac{m_1{m}_2}{r^2} \\ \Rightarrow F=G\frac{m_1{m}_2}{r^2} \\ where, \\ F\to Gravitationalforce \\ {m}_1\to Massofthefirstbody \\ {m}_2\to Massofthesecondbody \\ r\to dis\tan cebetweenthecentresoftwobodies \end{gathered}$$
   
3. The constant proportionality $\left(G\right)$ in the above equation is known as the universal gravitation constant.
4. The value of $G$ is found to be $G=6.673\times {10}^{-11}N{m}^2/k{g}^2$.
5. Here the value of gravitational force varies inversely as a square of $r$.
6. Hence, it is known as inverse square law.

Thus, Newton's law of gravitation is called inverse square law since the value of gravitational force varies inversely as a square of $r$.