#### Introduction

- All celestial bodies those found in the universe attract each other and the force of attraction among these bodies is called as the
**gravitational force**.

#### Universal Law of Gravitation

- Every object in the universe has the property to attract every other object with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them (see the image given below).

- The SI unit of G is
**N m2 kg–2**.

G = Fr^{2} M*m |

- G is obtained by substituting the units of force, distance and mass as given in the following equation:

- Henry Cavendish had calculated the value of ‘
**G**’ as**673 × 10–11 N m2 kg–2**. - Henry Cavendish had used a sensitive balance to find the value of ‘G.’

#### Significance of Universal Law of Gravitation

- Following are the salient significance of the Universal Law of Gravitation:
- It explains the force that binds all objects (including human beings) to the earth
- It describes the motion of the moon around the earth
- It explains the motion of planets around the Sun
- It clarifies the tides due to the moon and the Sun

#### Free Fall

- Whenever an object falls towards the earth, it involves an acceleration; this acceleration is produces due to the earth’s gravitational force.

- The acceleration, produces due to the earth’s gravitational force, is known as the acceleration due to the gravitational force of the earth (or acceleration due to gravity).
- The acceleration produces due to the gravitational force is denoted by
**g**. - As the radius of the earth increases towards the equator (from the poles) the value of ‘
**g’**becomes greater at the poles than at the equator.

#### The Value of g

- Value of g is calculated as:

- G = universal gravitational constant, which is =
**7 × 10–11 N m2 kg-2** - M = mass of the earth, which is =
**6 × 1024 kg** - R = radius of the earth, which is
**= 6.4 × 106 m** - So, the value of acceleration due to gravity of the earth (g) is :

**Notes on Gravitation-**

So we will discuss step by step about important topics from this chapter followed by an overview of this chapter.

Then we will understand important formulas from this chapter. Remembering these formulas will increase your speed while question-solving.

**Gravitation Topics**

- The universal law of gravitation.
- Acceleration due to gravity
- Kepler’s laws of planetary motion.
- Gravitational potential energy; gravitational potential.
- Escape velocity. Orbital velocity of a satellite. Geostationary satellites.

**Overview of Gravitation**

**Newton’s Law of Gravitation-**

Gravitational force is an attractive force acting between two masses and separated by a distance r. This force is directly proportional to the and inversely proportional to .

After studying that Gravitation force operates between any two objects on the earth, You may wonder and ask why not all bodies attract each other and stick together due to gravitational force. So answer to this question is that Gravitational Force is the weakest among all the four fundamental forces known to us till now. Let Suppose 2 similar ball of mass 1 kg are placed 1m apart then the gravitational force acting between them is simply G which is equal to ** **As you see this is a very negligible attractive force.

In this chapter, you will learn about various concept regarding acceleration due to gravity (g) with its definitions and suitable example.

Height, Depth, Shape of earth, Rotation of earth are the important factors which affect the value of g.

**Let’s have a look at how g value changes due to the shape of the earth.**

Radius of equator

Radius of pole

Equatorial radius is about 21 km longer than the polar radius.

So** **

In fact

Or we can say that Weight increases as the body are taken from equator to pole.** **

You will also learn about satellites and their motion in space. You will also learn to calculate their orbital velocity, their escape velocity, etc.** **

**Formulas for Gravitation**

**Gravitational force-**

**Acceleration due to gravity (g)**

**Variation in ‘g’ with height**

**Variation in ‘g’ with depth**

**Variation in ‘g’ due to Rotation of earth**

**Gravitational field Intensity**

**Where F=Gravitational force**

**Gravitational Potential**

** or **

**Work done against gravity**

**Escape velocity**

**Escape energy**

**Kepler’s 2nd law**

**Kepler’s 3rd law**

**or **

**Energy of satellite**