Notes

The first man who came up with the idea of gravity was Isaac Newton. It was an evening in 1665 when he was trying to solve the mystery of why planets revolve around the Sun. Suddenly an apple fell from the tree under which he was sitting. The idea of gravity flashed in his mind. He discovered not only the cause of the falling apple but also the cause that makes the planets revolve around the Sun and the moon around the Earth. This unit deals with the concepts related to gravitation.

The force of gravitation:

            There exists a force due to which everybody in the universe attracts every other body. This force is called the force of gravitation.

Law of gravitation:

Everybody in the universe attracts every other body with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Explanation:

Consider two bodies of masses m₁ and m₂. The distance between the centers of masses is d.

According to the law of gravitation, the gravitational force of attraction F with which the two masses m₁ and m₂ separated by a distance d attract each other is given by:

$F \: \alpha \: m_{1}m_{2}$   ……………   (i)

$F \alpha\frac{1}{d^{2}}$……………   (ii)

By combining (i) and (ii) we get

$F \: \alpha \:\frac{m_{1}m_{2}}{d^{2}}$

or

$F=G \: \frac{m_{1}m_{2}}{d^{2}}$

The universal constant of gravitation (G):

Here G is the proportionality constant. It is called the universal constant of gravitation. Its value is the same everywhere.

In SI units the value of G is  $6.673\times10^{-11}\: Nm^2{kg^{-2}}$