grav - Physics 53 Gravity Nature and Nature's law lay hid...

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Physics 53 Gravity Nature and Nature's law lay hid in night: God said, "Let Newton be!" and all was light. — Alexander Pope Kepler’s laws Explanations of the motion of the celestial bodies — sun, moon, planets and stars — are among the oldest scientiFc theories. The apparent rotation of these bodies around the earth every day was attributed by the ancients to their place in "celestial spheres" which revolved daily around the stationary earth, assumed to be at the center of the universe. The wandering of the planets against the background of stars presented a challenge to this earth-centered (“geocentric”) model. Their peculiar motions were explained in terms of smaller spheres rolling on larger ones. As observations became more accurate these explanations became more intricately complicated. The sun-centered (“heliocentric”) model of Copernicus (about 1540) was simpler, but it made the earth merely one of the planets orbiting the sun. This provoked outrage, since it challenged the central importance of homo sapiens in the universe. In the late 1500’s the Danish astronomer Tycho Brahe carried out a careful and systematic set of observations of the night sky, especially of the motions of the planets. His assistant Johannes Kepler inherited the voluminous data he had accumulated; Kepler subjected them to careful numerical analysis, and in the early years of the next century he was able to discern in the data three regularities: Kepler’s laws of planetary motion 1. The orbits of planets are ellipses, with the sun at one focus. 2. As the planet moves, the line from the sun to a planet sweeps out equal areas in equal times. 3. The ratio T 2 / a 3 is the same for all planets, where T is the period and a is the semi-major axis of the orbit. PHY 53 1 Gravity

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How to explain these three laws (the "Kepler problem") was a major concern of the scientists of the 17th century, among whom was Isaac Newton. Universal gravitation Newton's analysis of gravity was partly motivated by the Kepler problem, but more by the idea that the moon in its orbit is continually “falling” toward the earth, much as objects near the surface of the earth — including the famous apple? — fall to the ground. He proposed that the solution to both problems lay in a universal law: Law of universal gravitation Every pair of point masses m 1 and m 2 attract with a force given by F = G m 1 m 2 r 2 , where r is the distance between the masses and G is a universal constant. Because of its simplicity, elegance and its universality — note that it applies to every pair of point masses in the universe — this has served over the centuries as a model for what a general law of nature ought to be like. The value of
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This note was uploaded on 10/19/2011 for the course PHYSICS 53L taught by Professor Mueller during the Spring '07 term at Duke.

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grav - Physics 53 Gravity Nature and Nature's law lay hid...

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