Gravity origin & evolution

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Theory of Gravitation Origin and Evolution

Transcript of Gravity origin & evolution

Page 1: Gravity origin & evolution

Theory of GravitationOrigin and Evolution

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The universe is full of such ‘falling downs’

GRAVITY

Why do we fall down?

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Isaac Newton

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

1642-1727

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Two Giants!

Galileo Galilei

1564-1642

Johannes Kepler

1571-1630

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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

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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.

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Law of areas

The farther it goes, the slower it becomes

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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

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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

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The legendary Apple!

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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

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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

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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

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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.

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This was proved inNewton’s Principia.

This is his own copy.

Possibly the first proof.

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Idea 2The Moon is in orbit around the Earth because

gravity supplies this centripetal force.

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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

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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

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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).

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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

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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

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Now we can substitute this into our expression for ge

ge = Rmo2 x gm

Re2

where Rmo2 / Re

2 = 602

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and so, finally,

ge = 602 x 0.00271m/s2

ge = 9.8m/s2

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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’

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

F = Gm1m2/r2

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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’

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Firing Cannon Balls

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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?

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What makes gravity so prominent?

Long rangeAlways attractive

Fundamental Interactions

Strong Interaction 1038

Electromagnetic Interaction 1036

Weak Interaction 1025

Gravitational Interaction 1

Strength

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Action at a distance

But Why Gravity?

A force

field

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

-Major William Anders (Apollo 8, 1968)

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Einstein’s Startling Discovery

Nothing can travel faster than light!

It hit to the face of Newton’s theory!

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What if Sun suddenly disappears?

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

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Theory of Relativity

Time and Space are the Same!

A four Dimensional World

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

Curved Spacetime!

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Gravitational Waves

Accelerating mass spreads gravitational disturbances to the surroundings

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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

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Thank

you

“Gravity is not responsible for people falling in love”

Vaisakhan Thampi D S