Maharashtra Board Class 10 Science Part 1 Chapter 1 Gravitation PDF Download

Gravitation

We have seen in the previous standard that the gravitational force is a universal force and it acts not only between two objects on the earth but also between any two objects in the universe. Let us now learn how this force was discovered.

Gravitation

As we have learnt, the phenomenon of gravitation was discovered by Sir Isaac Newton. As the story goes, he discovered the force by seeing an apple fall from a tree on the ground. He wondered why all apples fall vertically downward and not at an angle to the vertical. Why do they not fly off in a horizontal direction?

After much thought, he came to the conclusion that the earth must be attracting the apple towards itself and this attractive force must be directed towards the center of the earth. The direction from the apple on the tree to the center of the earth is the vertical direction at the position of the apple and thus, the apple falls vertically downwards.

Figure 1.1 on the left shows an apple tree on the earth. The force on an apple on the tree is towards the center of the earth i.e. along the perpendicular from the position of the apple to the surface of the earth. The Figure also shows the gravitational force between the earth and the moon. The distances in the figure are not according to scale.

Newton thought that if the force of gravitation acts on apples on the tree at different heights from the surface of the earth, can it also act on objects at even greater heights, much farther away from the earth, like for example, the moon? Can it act on even farther objects like the other planets and the Sun?

Teacher's Note

Gravity pulls everything down towards the earth. This is why a ball thrown in the air always comes back down. Even in India, when you jump, you always fall back to the ground because of gravity.

Exam Trick

Remember: Newton saw an apple fall and thought about gravity. Apple falling = gravity pulling towards earth's center. Just remember the apple story to never forget this.

Points to Remember

Gravitational force pulls all objects towards the earth's center.
The force acts on all objects - apples, the moon, planets, everything.
This force was discovered by Sir Isaac Newton.
The direction of this force is always towards the center of the earth.

Force and Motion

We have seen that a force is necessary to change the speed as well as the direction of motion of an object.

1.1 Concept of the gravitational force and the gravitational force between the earth and the moon

Teacher's Note

When you kick a ball, you use force to change its speed and direction. Gravity also uses force to pull things down. Force always changes motion.

Exam Trick

Remember: Force = Change in motion. No force = No change. If nothing pushes you, you keep moving the same way.

Points to Remember

A force is needed to change how fast something moves.
A force is also needed to change the direction of motion.
Without force, objects keep moving the same way.
Gravity is a type of force that pulls things down.

Great Scientists: Sir Isaac Newton (1642-1727)

Sir Isaac Newton was one of the greatest scientists of recent times. He was born in England. He gave his laws of motion, equations of motion and theory of gravity in his book Principia. Before this book was written, Kepler had given three laws describing planetary motions. However, the reason why planets move in the way described by Kepler's laws was not known. Newton, with his theory of gravity, mathematically derived Kepler's laws.

In addition to this, Newton did ground breaking work in several areas including light, heat, sound and mathematics. He invented a new branch of mathematics. This is called calculus and has wide ranging applications in physics and mathematics. He was the first scientist to construct a reflecting telescope.

Teacher's Note

Newton was a very smart Indian scientist who discovered gravity. He wrote important books about how things move and why things fall down. His ideas are still used today in India.

Exam Trick

Remember: Newton = Gravity + Motion + Mathematics. He did all three big things. Newton = Newtons (the unit of force). The unit is named after him!

Points to Remember

Newton discovered gravity and the laws of motion.
He wrote a famous book called Principia.
He invented a new type of mathematics called calculus.
He made the first reflecting telescope.
He explained why planets move the way Kepler said they do.

Circular Motion and Centripetal Force

Tie a stone to one end of a string. Take the other end in your hand and rotate the string so that the stone moves along a circle. Are you applying any force on the stone? In which direction is this force acting? How will you stop this force from acting? What will be the effect on the stone?

As long as we are holding the string, we are pulling the stone towards us i.e. towards the centre of the circle and are applying a force towards it. The force stops acting if we release the string. In this case, the stone will fly off along a straight line which is the tangent to the circle at the position of the stone when the string is released, because that is the direction of its velocity at that instant of time. You may recall that we have performed a similar activity previously in which a 5 rupee coin kept on a rotating circular disk flies off the disk along the tangent to the disk. Thus, a force acts on any object moving along a circle and it is directed towards the centre of the circle. This is called the Centripetal force. 'Centripetal' means centre seeking, i.e. the object tries to go towards the centre of the circle because of this force.

You know that the moon, which is the natural satellite of the earth, goes round it in a definite orbit. The direction of motion of the moon as well as its speed constantly changes during this motion. Do you think some force is constantly acting on the moon? What must be the direction of this force? How would its motion have been if no such force acted on it? Do the other planets in the solar system revolve around the Sun in a similar fashion? Is similar force acting on them? What must be its direction?

From the above activity, example and questions it is clear that for the moon to go around the earth, there must be a force which is exerted on the moon and this force must be exerted by the earth which attracts the moon towards itself. Similarly, the Sun must be attracting the planets, including the earth, towards itself.

Teacher's Note

When you spin a bucket of water above your head, the water does not fall. The string or bucket pulls the water towards the center. This pulling force is called centripetal force. It keeps things moving in circles.

Exam Trick

Remember: Centripetal = Center-seeking. The force always pulls towards the center of the circle. Like a rope pulling a stone - pull the rope, stone comes to center.

Points to Remember

A centripetal force is needed to move something in a circle.
This force always points towards the center of the circle.
If the force stops, the object flies off in a straight line.
The moon moves in a circle around the earth because of centripetal force.
The earth's gravity provides this centripetal force to the moon.

Kepler's Laws

Planetary motion had been observed by astronomers since ancient times. Before Galileo, all observations of the planet's positions were made with naked eyes. By the 16th century a lot of data were available about planetary positions and motion. Johannes Kepler, studied these data. He noticed that the motion of planets follows certain laws. He stated three laws describing planetary motion. These are known as Kepler's laws which are given below.

An ellipse is the curve obtained when a cone is cut by an inclined plane. It has two focal points. The sum of the distances to the two focal points from every point on the curve is constant. F1 and F2 are two focal points of the ellipse. If A, B and C are three points on the ellipse then, AF1 + AF2 = BF1 + BF2 = CF1 + CF2

Kepler's First Law

The orbit of a planet is an ellipse with the Sun at one of the foci. Figure 1.4 shows the elliptical orbit of a planet revolving around the sun. The position of the Sun is indicated by S.

Kepler's Second Law

The line joining the planet and the Sun sweeps equal areas in equal intervals of time. AB and CD are distances covered by the planet in equal time i.e. after equal intervals of time, the positions of the planet starting from A and C are shown by B and D respectively. The straight lines AS and CS sweep equal area in equal interval of time i.e. area ASB and CSD are equal.

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.

Thus, if r is the average distance of the planet from the Sun and T is its period of revolution then,

\[T^2 \propto r^3 \text{ i.e. } \frac{T^2}{r^3} = \text{constant} = K\]

Kepler obtained these laws simply from the study of the positions of planets obtained by regular observations. He had no explanation as to why planets obey these laws. We will see below how these laws helped Newton in the formulation of his theory of gravitation.

Teacher's Note

Kepler found that planets move in oval shapes, not circles. The sun is at one end of the oval. This oval shape is called an ellipse. Like the shape of an egg.

Exam Trick

Remember: Kepler's three laws - (1) Ellipse shape, (2) Equal areas, (3) T squared = r cubed. These three laws explain how planets move around the sun.

Points to Remember

Planets move in ellipse shapes, not perfect circles.
The sun is at one point of the ellipse, not the center.
Planets sweep equal areas in equal time as they orbit.
The time to orbit depends on how far from the sun the planet is.
Kepler found these laws by watching planets over many years.

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