Question
How did Newton guess the inverse square rule obeyed by the gravitational force?
Solution
Kepler's third law of planetary motion was used by Newton to guess how the force of gravitation of the earth is weakened by distance.
Suppose a planet revolves around the sun in a circular orbit of radius r with speed v, then the force acting on the planet is given by,
...(1)
If 'T' is the period of revolution of the planet around the sun, then its orbital velocity will be
According to Kepler's third law,
This is inverse-square rule for the force of gravitation.
According to the inverse-square law of gravitaion, the force of gravitation on a planet should decrease as the square of the distance of the planet from the sun.
According to the inverse-square law of gravitaion, the force of gravitation on a planet should decrease as the square of the distance of the planet from the sun.
Newton further showed that the gravitational force is proportional to the product of the masses of the two objects.
Thus, Newton formulated the universal law of gravitation.
Thus, Newton formulated the universal law of gravitation.
