Download - Gravity origin & evolution
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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