Notes- Gravitation class 9

Gravitation

 Gravitational force

Every object present in the universe attract each other if any object is thrown upward it falls downwards towards the earth with gravitational force. Every object present on Earth is attracted by another object on earth or with the force that force is known as gravitational force.

The universal law of gravitation or Newton's law of gravitation.

Consider two objects of mass M and m are separated by a distance d. According to universal law of gravitation, the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Importance of gravitation or the gravitational force

1. The gravitational force is responsible to bind the atmosphere.

2. It is also responsible for the rainfall and the snowfall.

3. It is also responsible for the solar and lunar eclipse.

4. It is also responsible for falling off all the object towards the earth.

5. It is also responsible for generating Tides in the oceans.

6. It is also responsible for the revolution of the moon around the earth or revolution of the earth around the sun.

Kepler's  Laws of planetary motion

Kepler had given three laws of planetary motion:-

1. Kepler's first law

According to Kepler's first law, All planet move around the sun in an elliptical Orbit, and sun is present at any one of the foci of this ellipse.

                                

2. Kepler's second law

According to Kepler's second law of every planet sweeps equal area in equal interval of time.

 3.Kepler's third law

According to Kepler's third law, the square of the time period of a planet is directly proportional to the cube of the semi-major axis of that planet.

How Newton guesses Inverse Square Law?

 Freefall

 It is defined as when an object come towards Earth under the action of gravity. This condition is called free fall.

Acceleration Due to Gravity

When an object falls towards the earth there is a change in its acceleration due to the gravitational force of the earth. So this acceleration is called acceleration due to gravity.

The acceleration due to gravity is denoted by g.

The unit of g  is same as the unit of acceleration, i.e., ms⁻²

Mathematical Expression for g

From the second law of motion, force is the product of mass and acceleration.    

            F = ma

For free fall, acceleration is replaced by acceleration due to gravity. 

Therefore, force becomes:                      

            F = mg            ….(i)

But from Universal Law of Gravitation,

Difference between mass and weight

Mass	Weight
1.     It is defined as the amount of the matter contained in a body. 2.     It is scalar quantity. 3.     It is constant quantity. 4.     Mass can never be zero. 5.     Unit of mass is kilogram or gram. 6.     Mass can be measured with beam balance.	1.     It is defined as the force with which an object that attracted towards the earth. 2.     It is a vector quantity. 3.     It is a variable quantity. It varies with Gravity. 4.     Weight can be zero at the centre of the earth. 5.     The unit of weight is Newton. 6.     Weight can be measured with spring balance.

Weight of an object on the moon is 1/6 weight of the object on the earth.

Let m→ mass of an object

M_e →  mass of earth                 M_m →  mass of  moon

R_e →  Radius of an earth                R_m →  Radius of the moon

W_e →  weight of an object on  earth

 W_m →  weight of an object on the moon