Question

Newton's inverse square law is deduced from Kepler's ____ of planetary motion.

Answer 1

Newton's inverse square law states that gravitational attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The Newton's inverse square law is deduced from Kepler's 'Third law' of planetary motion. Kepler saw that planets move around in an elliptical orbit.

Centripetal force on planet is calculated as :

F = $\frac{m{v}^2}{r}$ = $\frac{m}{r}$($\frac{2\pi R}{T}{)}^2$ = $\frac{4{\pi }^{2}m{r}^2}{r{T}^2}$

F = $\frac{4{\pi }^{2}m}{r^2}$$\frac{r^3}{T^2}$

But from Kepler's law, $\frac{r^3}{T^2}$ is constant for planets

Therefore F = $\frac{4{\pi }^{2}m}{r^2}$ i.e K = $\frac{G}{r^2}$

From this the square inverse nature of gravitational force was derived by Newton.