Universal Gravitation
The Earth-centered Universe of Aristotle and Ptolemy held sway on Western thinking for almost 2000 years. Then, in the 16th century a new idea was proposed by the Polish astronomer Nicholas Copernicus
(Mikotaj Kopérnik) Polish astronomer. Studied astronomy at the Univ. of Kraków, he spent a number of years in Italy studying various subjects, including medicine and canon law. He lectured in Rome on mathematics and astronomy. In 1512 he settled in Frauenburg, East Prussia, where he had been nominated canon of the cathedral. There he performed his canonical duties and also practiced medicine. But the work that immortalized him is De revolutionibus orbium coelestium, in which he set forth his beliefs concerning the universe, known as the Copernican system. Probably completed by 1530 but was not published until 1543, when Copernicus was on his deathbed. Modern astronomy was built upon the foundation of the Copernican system.
Nicholas Copernicus (1473-1543)
In his book On the Revolutions of the Heavenly Bodies, Copernicus proposed that the Sun, not the Earth, was the center of the Solar System. Such a model is called a heliocentric system. The ordering of the planets known to Copernicus in this new system are recognized as the modern ordering of those planets.
In this new ordering the Earth is just another planet (the third outward from the Sun), and the Moon is in orbit around the Earth, not the Sun. The stars are distant objects that do not revolve around the Sun. Instead, the Earth is assumed to rotate once in 24 hours, causing the stars to appear to revolve around the Earth in the opposite direction.
Tycho Brahe (1546-1601)
Published his observationswhich were used by following generations of scientists.
Geocentrist – Earth as the center of the solar system. The sun, all planets and the stars revolve about the Earth.
Given the Island of Hven by the king of Denmark to create an observatory. Tremendously large instruments made accurate observations of the planets and stars for 20 years.
Johannes Kepler (1571-1630) Johannes Kepler, the German
assistant and successor to Tycho Brahe, was a Copernican from his twenties on, and was destined to bring about acceptance of the heliocentric concept. That is, he believed the sun rather than the earth was the center of the planetary system.The life-long question that concerned Kepler was the nature of the timing and motion of the celestial machinery, for he was convinced that simple mathematical relations existed that could make sense of the planetary system. He saw the planetary system operating according to its own set of mathematical laws which was quite a radical idea for those times.
"By the study of the orbit of Mars,we must either arrive at the secrets of astronomyor forever remain in ignorance of them."Johannes Kepler
Kepler was a mathematician rather than an observer. Kepler was supplied with years of impeccable data by the elder Tache Brahe who had carefully marked the position of Mars in relationship to the rest of the celestial map. Kepler rejected many ideas, such as circular orbits, because they did not fit Brahe's observations. In 1609, Johannes Kepler finally published his first two laws of planetary motion in a book entitled New Astronomy. A decade later (1619), his third law was published in The Harmonies of the World.
LAW 1: The orbit of a planet/comet about the Sun is an ellipse with the Sun's center of mass at one focus
Kepler’s Laws of Planetary MotionLAW 3: The squares of the periods of the planets are proportional to the cubes of their average distances from the sun
LAW 2: A line joining a planet/comet and the Sun sweeps out equal areas in equal intervals of time
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Sir Issac Newton (1642-1727)
Newton used Keplers Planetary laws to show that the net force on a planet must vary inversely with the square of the distance between the planet and the sun.
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Newton wrote that the sight of a falling apple made him think of the problem of the motion of the planets. The apple fell because the Earth attracted it. This force might be extended beyond the earths surface to the heavens. He recognized that the force on the apple must be proportional to the mass of both the apple and the earth. F mm 1 2
Sir Isaac Newton (1642-1727)
Law of Universal Gravitation
Combining both proportional statements you obtain the:
Where:Where:r is the distance between the centers of the spherical massesm1 and m2 are the masses of the objectsG is the universal constant, one that is the same everywhere
F G mmr
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Henry Cavendish (1731-1810)Cavendish attended Cambridge University
from 1749 to 1753, but left without a degree. After touring Europe with his brother, he lived frugally in London, even after an inheritance made him one of the wealthiest men in England. He immersed himself in scientific studies but did not bother to publish a number of his important discoveries. Exceedingly shy and retiring, Cavendish was sociable only with his scientific friends.
His last major work was the first measurement of Sir Isaac Newton's gravitational constant, together with the mass and density of the Earth. The accuracy of this experiment was not improved on for nearly a century.
Cavendish's apparatus for experimentally determining the value of G involved a light, rigid rod which was 6-feet long. Two small metal spheres were attached to the ends of the rod and the rod was suspended by a wire. When the long rod becomes twisted, the torsion of the wire begins to exert a torsional force which is proportional to the angle of rotation of the rod. Cavendish had calibrated his instrument to determine the relationship between the angle of rotation and the amount of torsional force.
Cavendish then brought two large lead spheres near the smaller spheres attached to the rod. Since all masses attract, the large spheres exerted a gravitational force upon the smaller spheres and twisted the rod a measurable amount. Once the torsional force balanced the gravitational force, the rod and spheres came to rest and Cavendish was able to determine the gravitational force of attraction between the masses. By measuring m1, m2, d and Fgrav, the value of G could be determined. Cavendish's measurements resulted in an experimentally determined value of 6.75 x 10-11 N m2/kg2. Today, the currently accepted value is 6.67259 x 10-11 N m2/kg2.
G x Nmkg
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Henry Cavendish (1731-1810)
So what is the mass of the Earth?
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