Newton’s law of gravitation

STATEMENT:

In 1666, Newton’s proposed the universal law of gravitation. It states that,

“Every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.”

EXPLANATION:

Consider two bodies $A$ and $B$ of masses ‘$m_1$’ and ‘$m_2$’ respectively. Let ‘$r$’ be the distance and ‘$F$’ is the gravitation force of attraction between the two bodies. Therefore, by Newton’s law of gravitation

$F \propto m_1m_2$ …………. (i)

$F \propto \frac{1}{r^2}$ …………….. (ii)

By combining equation (i) and (ii):

$F \propto \frac{m_1m_2}{r^2}$

$\boxed{F =G \frac{m_1m_2}{r^2}}$

Here, $G$ is constant of proportionality, known as “Universal Gravitational Constant”. It’s value in S.I unit is $6.674 \text{x} 10^{-11} \thinspace Nm^2Kg^{-2}$ and remains constant everywhere.

Characteristics of gravitational force:

1. It is always present between every two objects because of their masses.

2. It exists everywhere in the universe.

3. It forms an action-reaction pair.

4. It is independent of the medium between the objects.

5. It is directly proportional to the product of the masses of objects.

6. It is inversely proportional to the squre of the distance between the centres of objects.

7. Hence, it foollows the “Inverse square law”.