- Gravity is the force that keeps us held to the ground, drives the planets around the sun and the same force that pulls us down a slide.
- It is the force of attraction between any two bodies in this universe.
- Although everything attracts everything else in the universe with some amount of force, but this force is too weak to be observed in most of the cases.
- By definition, the force with which the earth pulls objects towards itself is called the gravitational force of earth.
- Examples:
- A stone dropped from a height falls towards the earth because the earth exerts a force of attraction called gravity on the stone and pulls it down.
- The gravitational force of earth or gravity of earth is responsible for holding the atmosphere above the earth; for the rain falling to the earth; and for the flow of water in the rivers.

__Universal Law of Gravitation:__

- Sir Isaac Newton proposed the universal law of gravitation in the year 1680.
- It is believed that an apple fell on Newton’s head and he realized that gravity exists. Although, Newton already knew about the existence of gravity, he wanted to find out if it extended far enough to influence the moon as well.
- In other words, he wanted to determine if the gravitational pull of the earth held the moon in its orbit.
- Based on the falling apple, he knew that the force exerted between bodies is dependent on the masses and that they influence each other.
- This was the basis of Newton’s second and third law of motion.
- He had to find out how the distance came into play.

__Newton’s law of Universal gravitation:__

- It states that everybody 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 them.
- The direction of the force is along the line joining the centers of two bodies.

__Calculation of force of gravitation:__

According to the universal law of gravitation:

- The force between two bodies is directly proportional to the product of their masses.

That is,

$\mathrm{F}\propto {\mathrm{m}}_{1}\times {\mathrm{m}}_{2}\dots \left(1\right)$- The force between two bodies is inversely proportional to the square of the between them.

That is,

$\mathrm{F}\propto \frac{1}{{\mathrm{r}}^{2}}\dots \left(2\right)$ $\mathrm{F}\propto \frac{{\mathrm{m}}_{1}\times {\mathrm{m}}_{2}}{{\mathrm{r}}^{2}}$ $\mathrm{Gravitational}\mathrm{force},\mathrm{F}=\mathrm{G}\times \frac{{\mathrm{m}}_{1}\times {\mathrm{m}}_{2}}{{\mathrm{r}}^{2}}$Where, G is a constant known as “universal gravitational constant”.

This is why gravity is so weak between distant bodies and strong on the surface of the earth, because the force of gravity reduces as per square law with increase in the distance between the bodies.

__Units of Gravitational Constant, G:__

The unit of gravitational constant becomes:

$\frac{\mathrm{newton}(\mathrm{metre}{)}^{2}}{(\mathrm{kilogram}{)}^{2}}\mathrm{or}\frac{{\mathrm{Nm}}^{2}}{{\mathrm{kg}}^{2}}\mathrm{or}{\mathrm{Nm}}^{2}/{\mathrm{kg}}^{2}$__Value of Gravitational Constant, :__

- The value of is determined experimentally to be

$6.67\times {10}^{\u201311}{\mathrm{Nm}}^{2}/{\mathrm{kg}}^{2}$by Henry Cavendish.

- This value is constant throughout the universe.

__Importance of the Universal Law of Gravitation:__

The universal law of gravitation successfully proves several phenomena.

- Gravitational force holds the Solar System together.
- Gravitational force between the sun and earth keeps the earth in uniform circular motion around the sun.
- Gravitational force of attraction which the moon and the sun exert on the water surface in the sea results in tides formed by the rising and falling of water level in the sea.
- Gravitational force binds us to the earth.

__Applications of the Universal Law of Gravitation:__

- Most of our deep space missions and other interplanetary missions like the mars orbiter mission are applications of gravity.
- Mangalyaan made use of interplanetary slingshot which means using gravity of other celestial bodies like planets and moons to propel a spacecraft. This is the most efficient mode of transport.
- Gravity is also used to power hydroelectric power plants where the flowing of water downstream due to gravity rotates a turbine to generate electricity.

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