Theory of GravitationOrigin and Evolution

The universe is full of such ‘falling downs’

GRAVITY

Why do we fall down?

Isaac Newton

“If I have seen farther, it is by standing on the shoulders of giants”

1642-1727

Two Giants!

Galileo Galilei

1564-1642

Johannes Kepler

1571-1630

Galileo Galilei-The First True Physicist

• Mathematical approach to physical problems• Presence of downward force on a projectile• Measured the constant acceleration of falling

bodies and derived a formula to calculate the distance travelled

• Law of Inertia

Kepler’s Laws

1. The orbit of every planet is an ellipse with the Sun at one of the two foci.

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

3. The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

Law of areas

The farther it goes, the slower it becomes

On the shoulder of Galileo

• 1st LawA body at rest, or in uniform motion, will remain so

until and unless acted upon by an unbalanced force.

• 2nd LawThe change in motion (acceleration) is proportional to

the unbalanced force• 3rd Law

For every action there is an equal and opposite reaction

On the shoulder of Kepler

• Law of areas is a consequence of force acting towards sun

• Third law is a consequence of the fact that farther the object, weaker the force

• When two planets at different distances are compared, the force is inversely proportional to the square of its distance

The legendary Apple!

Borrowed Ideas

Earth’s circumference, originally estimated by Eratosthenes (about 200BC), and improved by French surveyors during Newton’s lifetime.

Their best value, in today’s units, 69.2miles/degree = 69.2 x 360 miles

= 24900miles = 40 100km.

This implies a radius (Re) of 6380km.

Idea 1

The Moon’s distance from Earth(radius of Moon’s orbit, Rmo) Estimated by Aristarchus and Hipparchus

Using the size of the shadows during a lunar eclipse, they found the Moon’s distance, Rmo to be about 60 x Earth’s

radius, 60Re.

i.e., about 60 x 6380 = 383000km = 3.83 x 108m

Idea 2

Length of a lunar month (time taken for Moon to make one complete orbit)

=27.32 days = 27.32 x 24 x 3600 sec

= 2.36 x 106seconds.

This is easily measured by counting the number of days taken for several lunar months.

Acceleration of falling objects on Earth =

9.8m/s2 Estimated by Galileo

Idea 3

Idea 4

Own Ideas

Idea 1

The force used to keep an object rotating in a circle depends on the object’s speed and the circle’s radius in this way:-

F = m v2 / r

This implies that the centripetal acceleration (directed towards the centre on the circle)

is equal to v2 / r.

This was proved inNewton’s Principia.

This is his own copy.

Possibly the first proof.

Idea 2The Moon is in orbit around the Earth because

gravity supplies this centripetal force.

There are two places where we can compare the Earth’s gravitational field:

One at the Earth’s surface and the other at the orbit of the Moon.

This uses Idea 3

ge = 1 / (radius of Earth)2

gm 1/ (radius of Moon’s orbit) 2

= (radius of Moon’s orbit) 2 (radius of Earth) 2

= Rmo2 / Re

2

Idea 3

The force is inversely proportional to the square of the distance from source and force is proportional to acceleration

Rearranging slightly

ge = Rmo2 x centripetal accn of Moon(gm)

Re2

To get a numerical value for ge, all we need to do is to insert the centripetal acceleration from Idea 1 and the known value of the ratio of the orbital sizes (60/1).

Idea 1 Centripetal accn of Moon = v2 / Rmo

First - the Moon’s velocity, v,

= circumference of Moon’s orbit

time for one revolution

= 2πRmo / 2.36 x 106 = 1019m/s

and, second, the accn of Moon,

gm = v2 = 10192 = 1.038x106

Rmo Rmo Rmo

= 1.038x106 / (60 x Re)

= 1.038x106/(60 x 6.38 x 106)

gm = 0.00271m/s2

Now we can substitute this into our expression for ge

ge = Rmo2 x gm

Re2

where Rmo2 / Re

2 = 602

and so, finally,

ge = 602 x 0.00271m/s2

ge = 9.8m/s2

The Great Generalization

Newton realized that the motion of a falling apple and the motion of the Moon were both actually the same motion, caused by the same force - the gravitational force.

He coined the word ‘gravity’ from ‘gravitas’ , the Latin word for ‘heaviness’

Universal GravitationNewton realized that gravity was a universal force of attraction acting between any two objects.

F = Gm1m2/r2

Why doesn’t moon fall to earth?• Of course it does!• But the surface of earth falls down as the

moon falls down• So it never reaches the ‘ground’

Firing Cannon Balls

Weakest of all forces!

Gravity is too weak a force that the entire mass of earth is required to pluck a

ripened apple from the tree!

How strong?

What makes gravity so prominent?

Long rangeAlways attractive

Fundamental Interactions

Strong Interaction 1038

Electromagnetic Interaction 1036

Weak Interaction 1025

Gravitational Interaction 1

Strength

Action at a distance

But Why Gravity?

A force

field

“I think, Isaac Newton is doing most of the driving right now”

-Major William Anders (Apollo 8, 1968)

Einstein’s Startling Discovery

Nothing can travel faster than light!

It hit to the face of Newton’s theory!

What if Sun suddenly disappears?

Will we go off our orbit before the darkness caused by the sun’s disappearance reach us?

Theory of Relativity

Time and Space are the Same!

A four Dimensional World

Gravity is no longer a force! Instead, it arises from the curvature of spacetime by the presence of mass.

Curved Spacetime!

Gravitational Waves

Accelerating mass spreads gravitational disturbances to the surroundings

Gravity: The present face

• Quantum gravity- General Relativity and Quantum mechanics

• Gravitons- The hypothetical particle supposed to carry out gravity

• String theory, Quantum loop theory- Examples of Quantum gravity theory

Thank

you

“Gravity is not responsible for people falling in love”

Vaisakhan Thampi D S