# Gravitation

## Contents

### About the lesson

Previous Knowledge required: Kinematical equations and Newton's laws of motionTime duration: 45 minutesLevel: IX Std.

**Reference**: IX Std NCERT textbook

**After the lesson the students will be able to:**

- use Newton's law of gravitation to explain various phenomena and apply in various situations
- explain the concepts of gravitational acceleration and weight

### Introduction

People have always wondered why doesn't the Moon fall to the Earth? Let us explore this question using a simulation given by Michael Fowler of Department of Physics, University of Virginia . You may change the speed with which the object is thrown from a mountain and see whether it will always hit the ground. Click on the image below to interact use the simulation.

Now that you have seen how an object can revolve around earth , let us know the history of this interesting exploration of gravity.

There have been numerous theories of gravitation since ancient times. Greek philosopher **Aristotle** (f. 4th century BC) believed that objects tend toward a point **due to their inner gravitas** (heaviness). **Vitruvius** (f. 1st century BC) understood that objects fall based on their **specific gravity.** In the 7th century, **Brahmagupta** spoke of gravity as **an attractive force.**

In the early 17th century, **Galileo Galilei** found that all objects tend to **accelerate equally in free fall.** In 1632, he put forth the basic principle of relativity. The existence of the gravitational constant was explored by various researchers from the mid-17th century, helping Isaac Newton formulate his law of universal gravitation. Newton's classical mechanics were superseded in the early 20th century, when **Albert Einstein** developed the special and **general theory of relativity**. Let us watch a youtube video by John Bernad Moylan, which explains **Galileo's ideas**on gravitation. Click on the image below to watch the video.

### Newton's law of Gravitation

Sir Isaac Newton was able to prove that the there is a force of attraction between the objects and this force called gravitational force depends on the masses and the distance between them. This law is also called as universal law of gravitation and can be stated as under.

*Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is along the line joining the centres of two objects.*

**where:**

**F** is the force between the masses;
**G** is the gravitational constant **(6.674×10 ^{−11} N · (m/kg)^{2});**

**m**is the first mass;

_{1}**m**is the second mass;

_{2}**r**is the distance between the centers of the masses.

Saying that F is inversely proportional to the square of distance means, for example, that if d gets bigger by a factor of 6, F becomes 1/36 times smaller.

The universal law of gravitation successfully explained several phenomena which were believed to be unconnected:

- the force that binds us to the earth;
- the motion of the moon around the earth;
- the motion of planets around the Sun; and
- the tides due to the moon and the Sun.

You may have some questions like the ones given below:

##### Questions to Ponder

- How did Newton guess the inverse-square rule?
- Do I weigh less on the equator than at the North Pole?

## Isaac Newton and gravitational law : |
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There has always been a great interest in the motion of planets. By the 16th century, a lot of data on the motion of planets had been collected by many astronomers. Based on these data Johannes Kepler derived three laws, which govern the motion of planets. These are called Kepler’s laws.

These are: 1. The orbit of a planet is an ellipse with the Sun at one of the foci, as shown in the figure given below.

In this figure O is the position of the Sun.

2. The line joining the planet and the Sun sweep equal areas in equal intervals of time. Thus, if the time of travel from A to B is the same as that from C to D, then the areas OAB and OCD are equal.

3. The cube of the mean distance of a planet from the Sun is proportional to the square of its orbital period T. Or, r^{3}/T^{2}= constant.

It is important to note that Kepler could not give a theory to explain the motion of planets. It was Newton who showed that the cause of the planetary motion is the gravitational force that the Sun exerts on them. Newton used the third law of Kepler to calculate the gravitational force of attraction. The gravitational force of the earth is weakened by distance.

Let us now understand how Newton discovered law of gravitation. Click on the image below to watch the video.

#### Further Reading

1) Lecture Notes: Michael Fowler, UVa. : http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/GravityIndex.htm 2) NASA Archives : https://www-spof.gsfc.nasa.gov/stargaze/Sgravity.htm