f10_sep14 - Keplers First Law of Planetary Motion Tues.,...

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Tues., Sep. 14, 2010 Gravity Rules the Universe Kepler’s Three Laws of Orbital Motion Galileo: Astronomical uses of Telescopes Newton’s Laws of Motion and Gravity The orbit of each planet around the Sun is an ellipse with the Sun at one focus. Kepler’s First Law of Planetary Motion perihelion = closest approach; r peri = (a – ae) = a (1 – e) aphelion = farthest distance; r ap = (a + ae) = a (1 + e) (What’s at the other one?) Elements of an Ellipse a = semi-major axis b = semi-minor axis ae = center to focus distance a (1 – e) = distance from the focus to the point where the major axis hits the ellipse (e.g. equivalent to the dashed horizontal segment). This is called perihelion , and it is the point of closest approach. = a " e 2 Some Properties of Ellipses Derivation 1: a = average of the perihelion and aphelion distances Derivation 2: r + r ! = 2a Derivation 3: b = a " e 2
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As a planet moves around its orbit, it “sweeps out” slices of equal areas in equal times. ! a planet travels faster when it is nearer to the Sun (perihelion), and more slowly when it is farther from the Sun (i.e. at aphelion). Kepler’s Second Law v " r = const # vel $ 1 r ( ) Mathematically, There is a mathematical relationship between the period of a planet’s orbit and its “size” - actually, its semi-major axis, the average of the perihelion and aphelion distances. Kepler’s Third Law P 2 = a 3 P = orbital period in years a = semi-major axis in AU Kepler’s Third Law: Two Representations Galileo: First Astronomical Observations Made Using a Telescope Galileo (1564-1642) Using his telescope, Galileo saw: Sunspots on Sun (“imperfections”) Mountains and valleys on the Moon
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Four “moons” orbiting Jupiter - therefore not orbiting the Earth! The four moons that Galileo saw orbiting Jupiter (Io, Europa, Ganymede, and Callisto) are still called the “Galilean satellites.” Galileo’s Observations Venus showed “phases” like the Moon - including a “full Venus,”
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f10_sep14 - Keplers First Law of Planetary Motion Tues.,...

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