Lecture06

# Lecture06 - Tycho Brahe (1546-1601 C.E.) Built instruments...

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1 ©2010 W.W. Norton & Company, Inc. Tycho Brahe (1546-1601 C.E.) Built instruments to measure the positions of planets very accurately (~1 arc minute) Found that comets moved outside of the Earth’s atmosphere Witnessed a supernova and concluded that it was much farther away than any celestial sphere As he could detect no parallax motion in the stars, he held that the planets go around the Sun, but the Sun, in turn, orbits around the Earth ©2010 W.W. Norton & Company, Inc. Tycho Brahe measured distances using parallax that disproved ancient ideas about the heavens He observed a supernova in 1572 and with this showed that the heavens were both changing and had a dimension of distance; this troubled scholars who previously thought the heavens were unchanging. He showed that comets were objects that occurred in the region of the planets, not in Earth’s atmosphere. ©2010 W.W. Norton & Company, Inc. Kepler Kepler came up with empirical rules to describe the orbits. Empirical science describes how something works, not why. ©2010 W.W. Norton & Company, Inc. Johannes Kepler (1571 – 1630) • Used the precise observational tables of Tycho Brahe to study planetary motion mathematically. 1. Circular motion • Planets move around the sun on elliptical paths, with non-uniform velocities. • Found a consistent description by abandoning both 2. Uniform motion

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2 ©2010 W.W. Norton & Company, Inc. Kepler’s Laws of Planetary Motion 1.The orbits of the planets are ellipses with the sun at one focus. Eccentricity e = c/a c ©2010 W.W. Norton & Company, Inc. Eccentricities of Ellipses e = 0.02 e = 0.1 e = 0.2 e = 0.4 e = 0.6 1) 2) 3) 4) 5) ©2010 W.W. Norton & Company, Inc. Eccentricities of Planetary Orbits Orbits of planets are virtually indistinguishable from circles: Earth: e = 0.0167 Most extreme example: Pluto: e = 0.248 ©2010 W.W. Norton & Company, Inc. Kepler’s Second Law Often called the Law of Equal Areas. The line between the Sun and the planet “sweeps” out equal areas in equal times.
3 ©2010 W.W. Norton & Company, Inc. Kepler’s Second Law Consequences: A planet will go fastest when closest to the Sun.

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## Lecture06 - Tycho Brahe (1546-1601 C.E.) Built instruments...

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