**INTRODUCTION**

Our current ideas of motion and rest were developed by *Galileo Galilei* and *Sir Isaac Newton* in the seventeenth and early eighteenth century.

These ideas developed by Galileo and Newton are the parts of *Classical Physics* or *Newtonian Physics* in which Newton had a very huge contribution including his *laws of motion* and his *universal law of gravitation *which will be discussed in this article.

Classical Physics is more complete in itself.

Modern Physics includes two major theories – *Einstein’s theory of Relativity (or Relativistic Mechanics)* and theory of *quantum physics *(including quantum mechanics and quantum field theory).

**1. GEOCENTRIC AND HELIOCENTRIC THEORIES**

Before Galileo and Newton, people believed Ptolemy and Aristotle who said that Earth is the center of universe. It is not very surprising because when you look at the sky, the Sun, the Moon and stars seem to be orbiting the Earth. In that time, telescopes weren’t developed to see what is actually happening.

So, Ptolemy and Aristotle thought that Earth is center of universe and every other object in the sky, orbits the Earth.

And, there was another reason for thinking of Earth as the center of universe. When an object is dropped from a certain height, it is attracted towards the center of Earth. So, they thought that the center of Earth is the center of universe. This theory was called the *Geocentric Theory* (‘Geo’ means Earth and ‘centric’ is used for centre).

Aristotle was the person who found that Earth is not flat (as was previously assumed), but is a sphere. He presented this idea of spherical earth in 330 BC.

Thirty years after this, in 300 BC, a Greek astronomer, *Aristarchus*, found that not everything is revolving around Earth, but, is revolving around the Sun also, that is, Earth and other five planets (at that time five planets other than Earth were discovered, including Mars, Venus, Jupiter and Saturn), are revolving around the Sun, but only the Moon is revolving around the Earth.

But, as Aristotle and Ptolemy were thought superior at that time, Aristarchus wasn’t believed by people at that time.

It was not until sixteenth century (around 1543), when a Polish astronomer and Mathematician, Nicolas Copernicus, put forward a same theory as Aristarchus, which he called the *Heliocentric Theory*.

In his theory, Sun was placed at the center of universe and the planets orbited (or revolved) the Sun and the Moon orbited the Earth.

In seventeenth century, an Italian astronomer Galileo Galilei developed his telescope, and observed the *moons of Jupiter*, he found that the moons were orbiting Jupiter rather than Earth (as was described in the geocentric theory), so, his observations put an end to the geocentric theory and confirmed heliocentric theory.

He, actually not only confirmed heliocentric theory but also modified this theory. He excluded Sun as the center of the universe and suggested that the pinpoints in the sky, which twinkled, were also like our Sun.

**1.1 KEPLER’S LAWS OF PLANETARY MOTION**

At the same time Galileo proved heliocentric theory (with modifications), a German Astronomer, *Johannes* Kepler presented his laws of planetary motion which are as follows:

**1.** The planets orbits the Sun in elliptical (oval) orbits and Sun is located at one of its two focus [the mid-point of semi major axis is called focus and there are two foci, plural of focus – foci].

**2.** A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.

**3.** The square of the time period of one revolution of a planet is directly proportional to cube of semi major axis [it means that greater the length of semi major axis , greater the time period of one revolution].

Square of time period means that the time taken to complete one revolution is multiplied two times with itself and cube of semi major axis means the length of semi major axis is multiplied three times with itself.

For example, if, the time period is **3 seconds**, then the square of time period will be **3 × 3** that is** 9**, and if length of semi major axis is **4**, the cube of semi major axis will be **4 × 4 × 4** that is **64**.

The laws of Kepler were later used and confirmed by Sir Isaac Newton.

**2. NEWTON’S LAWS OF MOTION**

Sir Isaac Newton provided three laws of motion in which the second law is one of the most fundamental laws of physics.

To, understand Newton’s Laws, we should firstly discuss ‘*Inertia*’.

**2.1 Inertia and Galileo’s Experiment**

Galileo discovered a property that every body possesses called ‘inertia’.

He did a simple experiment (illustrated below).

He placed two slopes opposite to each other. The slopes were friction-less (friction is a force which opposes motion of an object on a surface).

He placed the ball on one slope and the ball came down because of gravitation (or gravity).

Now, the ball went up on the second slope and it reached the same height from which it was left (or, say dropped).

Then he decreased the angle of second slope and repeated this experiment, the result was same, the ball reached the same height from which it was dropped.

Then he reduced the angle of second slope to zero.

Now, the ball didn’t stopped and continued to move.

He concluded from this observations that every object resist the change in its state of motion or rest and this property of a body is called inertia and greater the mass of body, greater its inertia.

There are also some examples of inertia, like, when a car is at rest, it needs more force to accelerate it because it will resist the change in its state of rest.

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Aristotle also believed that an object having large mass would fall faster than an object having a comparatively smaller mass. The reason behind this (that he believed) was that an object having a large mass would have a greater pull towards Earth than an object of small mass.

An object having large mass do fall faster than an object having smaller mass when it is dropped from a certain height on Earth, because the object having smaller mass is resisted by air (or air friction) and the object having large mass would experience smaller air friction (most of the times).

But Galileo also proved that Earth accelerated everything at a constant rate.

We will see the Newton’s mathematical reason of this very soon in this article.

**2.2 Newton’s First Law – The Law of Inertia**

On the basis of Galileo’s calculations, Newton formulated his first law of motion (also referred to as law of inertia).

This law states that a body will continue its state of uniform motion or rest until a force acts on it.

You might have seen some examples of this law in your daily life. When you make a ball roll on the ground and leave it, it continue its state of motion and doesn’t stops.

But, it stops after sometimes because of frictional force.

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**2.3 Newton’s Second Law – The Law of Action**

Physically, force can be defined as a push or pull which changes or tends to change position or state of an object.

Newton’s Second Law of Motion provides a mathematical definition of force.

It states that the force applied on any object is equal to the *rate of change of momentum. *

*Momentum* is simply the product of an object’s mass and its velocity.

If we define momentum ‘physically’, momentum is the physical quantity which tells us that how much force it will apply on another object or experience a force by another object when it will collide with another object or simply it can also be defined as ‘*combined effect or impact of mass and velocity*’.

It can be understood by an example.

Suppose light is coming towards you from an electric bulb.

Light’s speed (or velocity) is very high that it can cover a distance if **300,000 kilometers** in only a **single second**.

Light is composed of very small particles called *photons*.

Now, when light will reach you, that is, when photons will collide with you, will you feel any force? The answer is certainly no.

This is because photons have almost zero mass, so their momentum will also be almost zero and ultimately the force will also be negligible.

But now suppose a car of about 100 kilograms moving with a speed near (but smaller) than light, and it collides with you.

You can think what will happen with you if such thing happens.

This is because the mass and velocity both the quantities are very large, so momentum will be larger than both the quantities and force will also be huge.

Rate of change of momentum means the difference in the *final momentum* (momentum after the application of force) and *initial momentum* (momentum before the application of force) and dividing this difference by the *time in which the momentum has changed* gives us the value of rate of change of momentum, and, rate of change of momentum is equal to the force.

As described above momentum is mass of an object multiplied by its speed (or velocity).

So, initial momentum will be the mass multiplied by initial velocity and final momentum will be mass multiplied by final velocity.

Rate of change of momentum is change in momentum divided by the time in which it has changed.

Change in momentum is obtained by subtracting initial momentum from final momentum, that is, final momentum minus initial momentum, so, it will simply become mass multiplied by final velocity minus initial velocity, that is —

* Mass × (final velocity ₋ initial momentum)*,

and final velocity minus initial velocity means change in velocity, so it means change in momentum is equal to mass multiplied by change in velocity, that is —

* Change in Momentum = Mass × (Change in Velocity)*,

and as described above, rate of change of momentum is equal to change in momentum divided by the time in which it has changed, so,

* Rate of Change of Momentum = (Mass) × [ (Change in Velocity) ÷ (Time) ]*,

and we are familiar with the fact that acceleration is the rate of change of velocity, that is, acceleration is equal to change in velocity divided by time in which it has changed, so, above equation can be written as —

* Rate of Change of Momentum = Mass × Acceleration*,

And, according to Newton’s second law, rate of change of momentum of any object after application of force on it is equal to the force applied on it so, we can conclude —

**Force = ***Mass × Acceleration*,

So, force applied on any body is simply equal to the mass of the body multiplied by the acceleration produced in it after application of force on it.

This is a fundamental law of physics.

We can also prove the first law of motion with the second law.

If force applied on an object is zero (that is, no force is working on it), this means that whether mass is zero or acceleration is zero.

And, force can be applied on an object which have some mass, so, mass can’t be zero.

So, acceleration will be zero, which means that the velocity hasn’t change, so, the object will continue its state of rest (that is, if velocity is zero), or uniform motion (that is, velocity will remain constant without any acceleration) if force is not applied on the object.

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**2.4 Newton’s Third Law – The Law of Reaction**

The third law of motion states that a force applied on any object have an opposite and equal reaction force.

The action and reaction forces always act on two different objects.

For example, when you walk you push the ground backwards (but it doesn’t move), and, in turn, the ground pushes you forward.

So, the action and reactions acts on two different bodies and the directions of both are opposite.

So it can be concluded that —

* (Action Force) = ₋ (Reaction Force)*,

And —

**(Reaction Force) = ₋ (Action Force)**

There is a ‘**₋**’ (minus) sign to represent the opposite direction, because negative (**₋)** is opposite of positive (+).

3. NEWTON’S THEORY OF GRAVITY

3. NEWTON’S THEORY OF GRAVITY

Newton is best known for his *law of universal gravitation*.

This concept of gravity, started by Newton, unified the terrestrial with celestial because Newton said that the reason of an apple falling on Earth and the Moon orbiting the Earth is same.

This reason was ‘*Gravitation*’ or simply ‘*Gravity*’.

Newton’s theory of gravity states that every single object in the universe attracts every other object in the universe with a force which vary directly to the product of masses of the two bodies and this force vary inversely to the square of distance between them.

This means that larger the masses of the two objects (or single), larger the force of gravity and larger the distance between the two objects, smaller the force.

For example, if the gravitational mass of any single body is doubled, the force between the two bodies will be doubled and if the distance between them is doubled, the force between them will reduce to one-fourth of the original force.

The strength of gravity according to Newton’s theory is given by:

**F**is force of gravitation,

**G**is universal gravitational constant whose value is about

**0.00000000006**,

**M**and

**m**are gravitational masses of the two bodies and

**R**is the distance between them.

In simple words it can be said that the force of gravity between any two objects ‘**A**’ and ‘**B**’ will be simple equal to the mass of ‘**B**‘ multiplied by intensity of gravitational field of ‘**A**’.

Every object having mass possess a gravitational field, which is infinite in Newton’s theory but the strength of the field goes on decreasing as distance from the source of gravitational field increases.

So, it can be concluded, for any two objects ‘**A**’ and ‘**B**‘ —

**Force of Gravity between ‘A’ and ‘B’ = Strength of gravitational field of object ‘A’ × Mass of object ‘B’**

In simple language, the above equation can be written as,

**Force of Gravity = Mass × Strength of Gravitational Field**

And also according to Newton’s second law of motion,

*Force = Mass × Acceleration*,

In case of force of gravity, the acceleration is ‘*acceleration due to gravity*’, because any gravitational field accelerates any object uniformly, for example, earth accelerates everything which falls from a certain height at a particular acceleration of about **9.8 m/s ^{2}.**

It means that when an object falls from a certain height towards the earth, after every single second, its velocity increases by **9.8 m/s**. (**m/s** is standard unit of measuring velocity and **m/s**^{2 }is standard unit of measuring acceleration.)

We can conclude —

* Force of Gravity = Mass × Acceleration due to gravity*,

And, also,

**Force of Gravity = Mass × Strength of Gravitational Field**

So, to satisfy above two relations, acceleration due to gravity must be equal to strength of gravitational field, that is —

**Acceleration due to gravity** = ** Strength of Gravitational Field**

And this is the reason why every object on earth would fall at the same time, if there were no air friction or air resistance, because acceleration due to gravity only depends upon strength of gravitational field and not the mass of falling object, in fact, acceleration due to gravity is equal to strength of gravitational field.

**About the Author – Madhur Sorout**

Sorout is currently a last third year high school student, living in India. His main fascination lies in Physics mainly in the field of general theory of relativity and topics related to it like Big Bang, Black Holes and Evolution of Universe. He likes to make out the meaning of what he see in this universe. He loves to read books by Stephen Hawking, Neil deGrasse Tyson and other authors (and Physicists). He is an atheist and believes that Physics completely rejects the idea of a god. He likes to play cricket also and he wants to continue down the route of research in Theoretical Astrophysics.

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