5. • 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
6. 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.
8. On the shoulder of Galileo
• 1st Law
A body at rest, or in uniform motion, will remain so
until and unless acted upon by an unbalanced force.
• 2nd Law
The change in motion (acceleration) is proportional to
the unbalanced force
• 3rd Law
For every action there is an equal and opposite
reaction
9. 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
11. Idea 1
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.
12. Idea 2
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
13. Idea 3
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.
Idea 4
Acceleration of falling objects on Earth = 9.8m/s2
Estimated by Galileo
14. 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.
15. This was proved in
Newton’s Principia.
This is his own copy.
Possibly the first proof.
16. Idea 2
The Moon is in orbit around the Earth because
gravity supplies this centripetal force.
17. 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
18. Idea 3
The force is inversely proportional to the square
of the distance from source and force is
proportional to acceleration
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 / Re2
19. 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).
20. 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
21. 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
22. Now we can substitute this into our
expression for ge
ge = Rmo2 x gm
Re2
where Rmo2 / Re2 = 602
24. 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’
26. 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’
28. Gravity is too weak a force that the entire
mass of earth is required to pluck a
ripened apple from the tree!
29. Fundamental Interactions
Strength Strong Interaction 1038
Electromagnetic Interaction 1036
Weak Interaction 1025
Gravitational Interaction 1
What makes gravity so prominent?
Long range
Always attractive
37. 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
38. “Gravity is not responsible for
people falling in love”
Vaisakhan Thampi D S
Editor's Notes
The Greek philosopher Aristotle (384–322 B.C.) posed, following earlier traditions, that the material world consisted of four elements: earth, water, air, and fire. For example, a rock was mostly earth with a little water, air, and fire, a cloud was mostly air and water with a little earth and fire. Each element had a natural or proper place in the Universe to which it spontaneously inclined; earth belonged at the very center, water in a layer covering the earth, air above the water, and fire above the air. Each element had a natural tendency to return to its proper place, so that, for example, rocks fell toward the center and fire rose above the air. This was one of the earliest explanations of gravity: that it was the natural tendency for the heavier elements, earth and water, to return to their proper positions near the center of the Universe. Aristotle's theory was for centuries taken as implying that objects with different weights should fall at different speeds; that is, a heavier object should fall faster because it contains more of the centertrending elements, earth and water. However, this is not correct. Objects with different weights fall, in fact, at the same rate. (This statement still only an approximation, however, for it assumes that the Earth is perfectly stationary, which it is not. When an object is dropped the Earth accelerates "upward" under the influence of their mutual gravitation, just as the object "falls," and they meet somewhere in the middle. For a heavier object, this meeting does take place slightly sooner than for a light object, and thus, heavier objects actually do fall slightly faster than light ones. In practice, however, the Earth's movement is not measurable for "dropped" objects of less than planetary size, and so it is accurate to state that all small objects fall at the same rate, regardless of their mass.)Aristotle's model of the Universe also included the Moon, Sun, the visible planets, and the fixed stars. Aristotle assumed that these were outside the layer of fire and were made of a fifth element, the ether or quintessence (the term is derived from the Latin expression quintaessentia, or fifth essence, used by Aristotle's medieval translators). The celestial bodies circled the Earth attached to nested ethereal spheres centered on Earth. No forces were required to maintain these motions, since everything was considered perfect and unchanging, having been set in motion by a Prime Mover—God.Aristotle's ideas were accepted in Europe and the Near East for centuries, until the Polish astronomer NicolausCopernicus (1473–1543) developed a heliocentric (Sun-centered) model to replace the geocentric (Earth-centered) one that had been the dominant cosmological concept ever since Aristotle's time. (Non-European astronomers unfamiliar with Aristotle, such as the Chinese and Aztecs, had developed geocentric models of their own; no heliocentric model existed prior to Copernicus.) Copernicus's model placed the Sun in the center of the Universe, with all of the planets orbiting the Sun in perfect circles. This development was such a dramatic change from the previous model that it is now called the Copernican Revolution. It was an ingenious intellectual construct, but it still did not explain why the planets circled the Sun, in the sense of what caused them to do so.Ads by GoogleStylish Gravity BinGreat Display & Dispenser for CandyCoffee, Cereal, Natural Foods, etcwww.BestBins.netYour Zodiac HoroscopeInsert Your Birthdate & Get Answersabout Past-Present and Future. FreeAboutAstro.com/horoscopeNew Astronomy and PhysicsAstronomy Pictures in Breaking NewsHave a passion for science? Me too!astronasty.blogspot.comwww.flipkart.com/MobilesHuge Selection at Amazing Prices.Latest Prices. Reviews & Comparisonwww.flipkart.com/MobilesWhile many scientists were trying to explain these celestial motions, others were trying to understand terrestrial mechanics. It seemed to be the common-sense fact that heavier objects fall faster than light ones of the same mass: drop a feather and a pebble of equal mass and see which hits the ground first. The fault in this experiment is that air resistance affects the rate at which objects fall. What about another experiment, one in which air resistance plays a smaller role: observing the difference between dropping a large rock and a medium rock? This is an easy experiment to perform, and the results have profound implications. As early as the sixth century A.D. Johannes Philiponos (c. 490–566) claimed that the difference in landing times was small for objects of different weight but similar shape. Galileo's friend, Italian physicist Giambattista Benedetti (1530–1590), in 1553, and Dutch physicist Simon Stevin (1548–1620), in 1586, also considered the falling-rock problem and concluded that rate of fall was independent of weight. However, the individual most closely associated with the falling-body problem is Italian physicist Galileo Galilei (1564–1642), who systematically observed the motions of falling bodies. (It is unlikely that he actually dropped weights off the Leaning Tower of Pisa, but he did write that such an experiment might be performed.)Because objects speed up (accelerate) quickly while falling, and Galileo was restricted to naked-eye observation by the technology of his day, he studied the slower motions of pendulums and of bodies rolling and sliding down incline. From his results, Galileo formulated his Law of Falling Bodies. This states that, disregarding air resistance, bodies in free fall speed up with a constant acceleration (rate of change of velocity) that is independent of their weight or composition. The acceleration due to gravity near Earth's surface is given the symbol g and has a value of about 32 feet per second per second (9.8 m/s2) This means that 1 second after a release a falling object is moving at about 10 m/s; after 2 seconds, 20 m/s; after 10 seconds, 100 m/s. That is, after falling for 10 seconds, it is dropping fast enough to cross the length of a football field in less than one second. Writing v for the velocity of the falling body and t for the time since commencement of free fall, we have v = gt.Galileo also determined a formula to describe the distance d that a body falls in a given time: That is, if one drops an object, after 1 second it has fallen approximately 5m; after 2 seconds, 20m; and after 10 seconds, 500 meters.Galileo did an excellent job of describing the effect of gravity on objects on Earth, but it wasn't until English physicist Isaac Newton (1642–1727) studied the problem that it was understood just how universal gravity is. An old story says that Newton suddenly understood gravity when an apple fell out of a tree and hit him on the head; this story may not be exactly true, but Newton did say that a falling apple helped him develop his theory of gravity.Read more: Gravity and Gravitation - The History Of Gravity - Earth, Objects, Fall, Air, Falling, and Aristotlehttp://science.jrank.org/pages/3129/Gravity-Gravitation-history-gravity.html#ixzz1FAe2xa2f
Neptune was mathematically predicted before it was directly observed. With a prediction by Urbain Le Verrier, telescopic observation confirming the existence of a major planet were made on the night of September 23, 1846, and into the early morning of the 24th,[1] at the Berlin Observatory, by astronomer Johann Gottfried Galle (assisted by Heinrich D'Arrest), working from Le Verrier's calculations
