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Unformatted text preview: 3.3 Copernican Revolution Copernicus Adopted Aristarchuss Sun-centered idea Discovered simple geometric relationships that allowed him to calculate each planets orbital period around the Sun and its relative distance from the Sun in terms of Earth-Sun distance Hesitant to publish his book for fear of being considered absurd. Did not make substantially better predictions than Ptolemys model, because Copernicus still believed that heavenly motion must occur in perfect circles. Found it necessary to add circles upon circles to his system just as Ptolemy had done Tycho Observed a widely anticipated alignment of Jupiter and Saturn but the alignment had occurred two days later than Copernicus had predicted. Sought to improve the state of astronomical prediction: compiled careful observations of stellar and planetary positions in the sky. Fame grew after he observed a new star = supernova By measuring its parallax and comparing it to the parallax to the Moon, he proved that the supernova was much farther away than the Moon. Over a period of 3 decades compiled naked eye observations accurate to better than 1 arc minute Failed to explain the motion of the planets Kepler Believed Earth and other planets traveled around the sun in circular orbits Tried to match circular motions to Tychos data but his predictions differed from Tychos Abandoned the idea of circular orbits to find the correct solution Key discovery: planetary orbits are not circles but ellipses Three laws of planetary motion: Keplers first law: the orbit of each planet around the Sun is an ellipse with the Sun at one focus Tells us that a planets distance from Sun caries during its orbit. Closest at point called perihelion Farthest at aphelion Average of a planets perihelion and aphelion is the length of its semi major axis (planets average distance from the sun) Second Law: As a planet moves around its orbit it sweeps out equal areas in equal times The planet moves a greater distance when its near perihelion than it does in the same amount of time near aphelion The planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun. Third Law: more distant planets orbit the Sun at slower average speeds, obeying a precise mathematical relationship p = a p = planets orbital period in years a = average distance from the Sun in astronomical units....
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- Spring '08