Question 4.

Answer the following question.

Write the three laws given by Kepler. How did they help Newton to arrive at the inverse square law of gravity?

Answer:

Johannes Kepler studied about the planets motion and their positions and. He noticed that motion of the planets follows a certain law. He gave three laws describing the planetary motion. These are known as Kepler’s laws which are as follows:

__Kepler’s First law__: The orbit of planet is an ellipse with sun at one of the foci. The figure below illustrates the elliptical orbit of earth with sun at its focus.

__Kepler’s Second law__: The line joining the planet and the Sun sweeps equal areas in equal intervals of time.

In the above figure A1 = A2 according to law.

__Kepler’s Third law__: The Square of its period of revolution around the Sun is directly proportional to the cube of the mean distance of a planet from the Sun.

If ‘r’ is the average distance of the planet from the sun and ‘T’ is the period of revolution then according to third law;

__Inverse Square law of gravity__: We know that centripetal force F is given by ;

F =

Where v = velocity of the planet =

Distance travelled in one revolution=2Ï€r

Where r = radius of the orbit.

V =

F =

According to Kepler’s third law;

Hence

F = (Multiplying and dividing by r2)

F =

F = (By Kepler’s third law).

But is constant

Therefore

And this is __the newton’s inverse square law which states that the centripetal force acting on planet is inversely proportional to the square of the distance (‘r’) between the sun and the planet__