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Universal Gravitation
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Brief Astronomical History 85-165 A.D Ptolemy Greek Astronomer 85-165 A.D. Believed in Geo- centrism First to latitude and longitude Nicholas Copernicus 1473-1543 Galileo Galilei 1564- 1642 Polish Astronomer Changed societal belief to helio- centric model, though orbits were circular in his model. Tycho Brahe 1546-1601 Danish astronomer Built first astronomical observatory Made accurate observations of night sky Catalogued 1000 stars Italian Physicist Continued to promote helio- Centrism Discovered Moons of Jupiter and phases of Venus
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Johannes Kepler Johan Kepler, a student of Tyco Brahe, was a German astronomer who lived between 1571-1630. He introduced three important laws of planetary motion and helped the Copernican model of the solar system gain general acceptance, but Kepler accurately modeled the path of planets as ellipses.
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Kepler’s Laws 1) The paths of planets are ellipses with the sun at a focus. 2) An imaginary line from the sun to a planet sweeps out equal areas in equal times. 3) The square of the ratio of the periods of two orbiting bodies is equal to the cube of their radii ratio.
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Ellipse Explanation Major Axis Minor Axis focus dd a b a+b=constant a b a b
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Kepler’s First Law
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Kepler’s Second Law (Also called the Law of Equal Areas) Equal areas in equal times. t1t1 t2t2 A1A1 A2A2 If t 1 =t 2, then A 1 =A 2 Orbiting bodies move faster near the central mass and slower farther away.
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Kepler’s Third Law rArA rBrB r A =orbital radius of Object A (distance from central mass). r B =orbital radius of object B (distance of object B from central mass)
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Kepler’s Third Law T A =period of body A T B = period of body B The square of the ratio of the period of two bodies orbiting the same central mass is equal to the cube of their orbital radii ratio.
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Kepler’s 3 rd Law Example Saturn’s period of revolution is 29 years. What is the distance of Saturn from the Sun as a multiple of Earth’s distance? T S = 29 years T E = 1.0 years r S = ? r E = ?
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Example Continued Saturn is located 9.4 times farther from the Sun than Earth.
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