Question

Assuming that the planets are moving in circular orbits, apply Kepler's laws to show that the acceleration of a planet is inversely proportional to the square of its distance from the sun.

Answer 1

Answer

Let us suppose

the planets are moving in circular orbits.

So gravitational force can be written as

$F=\frac{GMm}{r^2}$ ...... 1

Force is given as

$F=ma$ ...... 2

Using both equation

$F=ma=\frac{GMm}{r^2}$

$a=\frac{GM}{r^2}$

So acceleration

$a\propto\frac{1}{r^2}$