Gravitation ~ The earth exerts some invisible force on the object, which is known as the Gravitational Force. When the object is thrown up an external force is applied by the person throwing it up. At that time also earth’s gravitational force is working on it and hence its velocity gradually decreases down to zero. Then after it again starts falling down towards the earth surface. This also is an example of earth’s gravitational force. Another example of this force is the movement of water drops from the clouds to the earth surface.

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## ✍️ **Gravitation**

It is said that once Newton was sitting beneath an apple tree and an apple fell on him. Newton was inspired to find the reason underlying this episode. He thought as to why the apple fell towards earth? Why was it not attracted towards the moon. Thus on the daily life observations Newton proposed the theory of Gravitation. In this chapter we will study about the Gravitation and the Universal Laws of Gravitation. We will also consider the movement of object under the influence of the gravitational force, the change in weight of objects and why do objects fly in the space.

**Activity** :

- Tie a small stone to a piece of a thread.
- Move the stone on a circular path by catching hold of the other end of the thread, as shown in fig.
- Observe the direction of the movement of the stone.
- Now leave the thread and observe the direction of movement of the stone.

Before we left the thread the stone was moving in a circular path. At that time it experienced a force towards its center which is known as the Centripetal Force. This force is responsible for the circular motion of the objects. On leaving the thread the stone proceeds in a simple line and then moves in a free manner i.e. the circular motion ends on removing the Centripetal Force.

The movement of moon around the earth is due to the presence of centripetal force. This centripetal force is derived from the earth’s gravitational force. Gravitational Force occurs naturally between all the objects of the world, but we are unable to experience the gravitational force working between the normal objects. Since the mass of celestial bodies is more this force becomes effective and controls their motion.

It was in fifth century that the Bhartiya astronomer Aryabhatt propounded the geocentric model to understand the movement of planets. Nearly 500 years before Newton and Kepler, Bhaskaracharya in the grah-ganit section of his famous work Siddhantsiromani had discussed the gravitational power of earth and the planetary movements, in detail. Bhaskaracharya calculated the radius (R) and circumference (2pr) of the earth.

The western scientist Copernicus (1473-1543) propounded the model of the movement of celestial bodies on the basis of Aryabhatt’s vision. Even Kepler and Galileo also worked out some laws to clarify the understanding about the movement of the planets.

The famous seventeenth century scientist Isaac Newton (1642-1727) gave the Laws of Motion and the Universal Law of Gravitation. These were based on substantial scientific logic and were proved mathematically. The contributions of these scientists in the sphere of physics were very important.

## ✍️ **Universal Law of Gravitation**

Each particle (body) of the universe exerts a force of attraction towards itself on every other particle (body) which is known as the Gravitational Force. According to the Law of Gravitation “the force of attraction between two particles of matter or bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them.

The direction of this force is the same as the direction of the line joining the two particles”. Suppose two bodies of mass M and m are placed at a distance d from each other. Then the gravitational force F working between will be

Here G is the proportional constant known as the Universal Gravitational constant.

The value of G has been worked out to be – 6.67×10^{-11} Newton–meter^{2}–Kilogram^{2}, from various experiments. Its value does not depend on the nature of the particles, medium, time, temperature etc., i.e. it remains the same at every place.

Hence it is known as the Universal Constant. The earth also attracts things towards itself. This, earth’s force of attraction is known as the Force of Gravitation.

Many phenomenon can be easily interpreted by the Law of Gravitation. Some of the important ones includes :

(1) The force that binds us to the earth

(2) Movement of planets around the sun

(3) Movement of the moon around the earth

(4) Occurrence of tides in the sea.

## ✍️ **Gravitational Acceleration**

When the change in an object’s velocity i.e. acceleration, is due to the earth’s force of gravitation, it is known as the Gravitational Acceleration. It is denoted by g and its unit is ms-2.

From the second law of motion

Force = mass × acceleration or F = mg

The gravitational acceleration of any planet depends upon its mass and radius. In other words, heavier a planet comparatively more will be its gravitational acceleration.

## ✍️ **Movement of objects under the influence of the earth’s force of gravitation **

It is clear from the equations 10.4 and 10.5 that the Gravitational Acceleration experienced by various objects does not depend upon the mass and shape of the objects. This means that different objects should fall down with the same rate when dropped from the same height. But is it so? Again we will perform an activity to get an answer.

The initial velocity of the free falling objects is zero.

The value of gravitational acceleration ‘g’ remains constant for a height of some kilometers from the earth’s surface. Therefore to study the motion of objects near the earth’s surface, the equation for uniform acceleration motion described in the last chapter is made use of.

## ✍️ **Mass**

Mass is the measure of the inertia of an object. In other words, greater the mass of a body more will be its inertia. The mass of a body remains the same every where; whether it is on earth or in space.

## ✍️ **Weight**

On earth the weight of an object is a type of a force that takes it towards the earth. As per definition the weight of a substance is the force by which it is attracted towards the earth.

Mathematically F = mg

the weight of the body w = mg.

Since the value of g at a given point is constant, therefore, the weight of an object is proportional to it’s mass. The mass remains the same with the change in the value of g but the weight changes.

## ✍️ **Weight of an object on the Moon **

Weight of a body on Moon is the force with which the moon attracts it towards itself. The mass of moon is less as compared to that of the earth therefore even the force of attraction will be less. We can say that the weight of an object on moon is relatively less than that on earth. Since we have seen that the gravitational acceleration on moon is 1.61 m/s^{2} which is 1/6 of that present on the earth’s surface, whose gravitational acceleration is 9.8 m/s^{2} , therefore the weight of the object on moon will be 1/6 of its weight on earth.