Question

Write Newton’s gravitation law. Derive it in vector form an explain that it follows action-reaction law.

Answer 1

Gravitational Law in Vector Form

As shown in the figure. the position vectors of particles M₁ and M₂ are \(\overrightarrow{r_{1}}\) and \(\overrightarrow{r_{2}}\) respectively.

Negative sign tells about the attractive nature of force
Similarly, force on M₁ and M₂ 

from the equation (1) and (3) 

\(\vec F_{12} = - \vec F_{21}\)

Hence, it is clear that the applied forces are equal and opposite. Hence, the gravitational force follows Newton’s third law.