11:13 am
I'm working now at my office and get bored.. and I remember about one of the world famous scientist..Isaac Newton. He was born on Christmas day 1642.. He was an English Physicist, mathematician, astronomer, natural philosopher, alchemist and theologian.. I admire him because he dedicated his life for science.. Now,enjoy reading guys.. ;)
Gravity
Newtonian Relationships
by Nathaniel Page Stites, M.A./M.S.
What causes objects to fall toward the earth? Why do the planets orbit the sun? What holds galaxies together? If you traveled to another planet, why would your
weight change? All of these questions relate to one aspect of physics: gravity. For all of its influence on our daily lives, for all of its
control over the cosmos, and for all of our ability to describe and model its effects, we do not understand the actual mechanisms of gravitational
force. Of the four fundamental forces identified by physicists – strong nuclear, electroweak, electrostatic, and gravitational – the gravitational force is the least understood. Physicists today strive toward a "Grand Unified
Theory," wherein all four of these forces are united into one physical model that describes the behavior of everything in the
universe. At this point in time, the gravitational force is the troublesome one, the force that resists unification.
In spite of the mystery behind the mechanisms of gravity, physicists have been able to describe the behavior of objects under the influence of gravity quite thoroughly.
Isaac Newton, a seventeenth into eighteenth century English scientist and mathematician (among other things), was the first person to propose a mathematical model to describe the gravitational attraction between objects.
Albert Einstein built upon this model in the twentieth century and devised a more complete description of gravity in his
theory of general
relativity. In this module, we will explore Newton’s description of gravity and some of the experimental confirmations of his theory that came many years after he proposed his original idea.
The Apple
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©Corel Corporation |
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Whether or not
Isaac Newton actually sat under an apple tree while pondering the nature of gravity, the fact that objects fall toward the surface of the earth was well understood long before Newton’s time. Everyone has experience with gravity and its effects near the surface of the earth, and our intuitive view of the world includes an understanding that what goes up must come down.
Galileo Galilei (1564 – 1642) demonstrated that all objects fall to the surface of the earth with the same acceleration, and that this acceleration was independent of the
mass of the falling object. Isaac Newton was no doubt familiar with this concept, and he would eventually formulate a broad and far-reaching
theory of gravitation. Newton’s theory would encompass not only the behavior of an apple near the surface of the earth, but also the motions of much larger bodies quite far away from the earth.
Leaning Tower of Pisa Experiment
Concept simulation - Reenacts Galileo's experiment of two different objects falling at the same rate.
The Planets
Early conceptions of the
universe were "geocentric" – they placed the earth at the center of the universe and had the planets and stars move around the earth. The Ptolemaic Model of the universe dominated scientific thought for many centuries, until the work of such careful astronomers as
Tycho Brahe,
Nicolaus Copernicus,
Galileo Galilei, and
Johannes Kepler supplanted this view of the cosmos. The “Copernican Revolution” placed the sun at the center of the solar
system and the planets, including earth, in orbit around the sun. This major shift in perception laid the foundation for
Isaac Newton to begin thinking about gravitation as it related to the motions of the planets.
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Figure 1: The Solar System |
An early unification theory
Just as physicists today are searching for ways to unify the fundamental
forces,
Isaac Newton also sought to unify two seemingly disparate phenomena: the motion of objects falling toward the earth and the motion of the planets orbiting the sun. Isaac Newton’s breakthrough was not that apples fall to the earth because of gravity; it was that the planets are constantly falling toward the sun for exactly the same reason: gravity! Newton built upon the work of early astronomers, in particular
Johannes Kepler, who in 1596 and 1619 published his laws of planetary motion. One of Kepler's central observations was that the planets move in elliptical orbits around the sun. Newton expanded Kepler’s description of planetary motion into a
theory of gravitation.
Newton’s Law of Universal Gravitation
The essential feature of Newton’s Law of Universal Gravitation is that the
force of gravity between two objects is inversely proportional to the square of the distance between them. Such a connection is known as an “inverse square” relationship. Newton derived this relationship from Kepler’s assertion that the planets follow elliptical orbits. To understand this, consider the
light radiating from the surface of the sun. The light has some intensity at the surface of the sun. As the light travels away from the sun, its intensity diminishes. The intensity of the light at any distance away from the sun equals the strength of the source divided by the surface area of a sphere surrounding the sun at that radius.
As the distance away from the sun (r) doubles, the area of the sphere surrounding the sun quadruples. Thus, the intensity of the sun’s
light depends inversely on the square of the distance away from the sun. Newton envisioned the gravitational
force as radiating equally in all directions from a central body, just as sunlight in the previous example. Newton recognized that his gravitational model must take the form of an inverse square relationship. Such a model predicts that the orbits of objects around a central body will be
conic sections, and years of astronomical observations have borne this out. Although this idea is most commonly attributed to
Isaac Newton, the English mathematician
Robert Hooke claimed that he originated the idea of the inverse square relationship. Nonetheless, Newton eventually published his
theory of gravitation and became famous as a result.
The relationship that Newton came up with looks like this:
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Figure 2: Newton's Law of Universal Gravitation |
where F is the
force of gravity (in
units now referred to as newtons), m
1 and m
2 are the masses of the two objects (in kilograms), r is the distance separating the centers of
mass of the objects and G is the "gravitational constant." This relationship has come to be known as Newton's Law of Universal Gravitation. It is "universal" because all objects in the
universe are attracted to all other objects in the universe according to this relationship. Two people sitting across a room from each other are actually attracted gravitationally. As we know from everyday experience, human-sized objects don't crash into each other as a result of this force, but it does exist even if it is very small. Although Newton correctly identified this relationship between force, mass, and distance, he was able only to estimate the value of the gravitational constant between these quantities. The world would have to wait more than a century for an experimental measurement of the constant of proportionality: G.
Measuring the Mass of the Earth: The Cavendish Experiment
In 1797 and 1798
Henry Cavendish set out to confirm Newton's
theory and to determine the constant of proportionality in Newton's Law of Universal Gravitation. His ingenious experiment, based on the work of
John Michell, was successful on both fronts. To accomplish this, Cavendish created a "torsion balance," which consisted of two masses at either end of a bar that was suspended from the ceiling by a thin wire (see Figure 3).
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Figure 3: The Torsion Balance, devised by Michell and Cavendish to determine the constant of proportionality in Newton's Law of Universal Gravitation. |
Attached to the wire was a mirror, off of which a beam of
light was reflected. Cavendish brought a third
mass close to one of the masses on the torsion balance. As the third mass attracted one of the ends of the torsion balance, the entire apparatus, including the mirror, rotated slightly and the beam of light was deflected. Through careful measurement of the angular deflection of the beam of light, Cavendish was able to determine the extent to which the known mass was attracted to the introduced mass. Not only did Cavendish confirm Newton's
theory, but also he determined the value of the gravitational constant to an
accuracy of about 1 percent.
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Figure 4: Gravitational Constant |
Cavendish cleverly referred to his research as “Measuring the
Mass of Earth.” Since he had determined the value of G, he could do some simple calculations to determine the mass of the earth. By Newton’s Second Law, the
force between an object and the earth equals the product of the acceleration (g) and the mass of the object (m):
F = ma Galileo had determined the acceleration of all objects near the surface of the earth in the early 1600s as g = 9.8 m/s
2.
Therefore, setting this equation equal to Newton’s Law of Universal Gravitation described above, Cavendish found:
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Figure 5: Newton's Law of Universal Gravitation as used by Cavendish to determine the mass of the Earth. |
where m is the
mass of the object, m
E is the mass of the earth, and r
E is the radius of the earth. Solving for the mass of the earth yields the following result:
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Figure 6: Results of Cavendish's calculation for the mass of the Earth. |
Cavendish had determined the
mass of the earth with great
accuracy.
We can also use this relationship to calculate the
force of attraction between two people across a room. To do this, we simply need to use Newton’s Law of Universal Gravitation with Cavendish’s gravitational constant. Assume the two people have masses of 75 and 100 kilograms, respectively, and that they are 5 meters apart. The force of gravitation between them is:
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Figure 7: Gravitational attraction between two people. |
Although it is small, there is still a force!
Conclusion
Newton’s Law of Universal Gravitation grew in importance as scientists realized its utility in predicting the orbits of the planets and other bodies in space. In 1705, Sir
Edmund Halley, after studying comets in great detail, predicted correctly that the famous comet of 1682 would return 76 years later, in December of 1758. Halley had used Newton’s Law to predict the behavior of the comet orbiting the sun. With the advent of Cavendish’s accurate value for the gravitational constant, scientists were able to use Newton’s law for even more purposes. In 1845,
John Couch Adams and
Urbain Le Verrier predicted the existence of a new, yet unseen, planet based on small discrepancies between predictions for and observations of the position of Uranus. In 1846, the German astronomer Johann Galle confirmed their predictions and officially discovered the new planet, Neptune.
While Newton’s Law of Universal Gravitation remains very useful today,
Albert Einstein demonstrated in 1915 that the law was only approximately correct, and that it fails to work when gravitation becomes extremely strong. Nonetheless, Newton’s gravitational constant plays an important role in Einstein’s alternative to Newton’s Law, the
Theory of General
Relativity. The value of G has been the subject of great debate even in recent years, and scientists are still struggling to determine a very accurate value for this most elusive of fundamental physical constants.
source : http://www.visionlearning.com/library/module_viewer.php?mid=118
