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# 222222222 - PY211 Lecture 19(10 Nov 2016 Gravitation[Ch 13...

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PY211 Lecture 19 (10 Nov 2016) Gravitation [Ch. 13 Young and Freedman] Fluids [Ch. 12 Young and Freedman]

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Class info Midterm 2: scores posted on Blackboard – Please submit regrade requests by next week Problem Set 8: due next Friday, Nov. 18 by 5pm. – To be posted. Problems from Chapters 12, 13. – Ten problems online. Half also submitted on paper Discussion this week: on topics from Chs. 12, 13. • Lab: next week in SCI-B9 – Lab6: Fluids Help: SCI-121 More help: [email protected]
0 5 10 15 20 25 30 95 85 75 65 55 45 35 25 15 5 PY211 Midterm 2 (Fall 16) Out of: 100 High: 99 Mean: 73.5 N: 177 Low: 27 Stdev: 15.8

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Quick Quiz The elliptical shapes of planetary orbits can be defined by parameter e , called the eccentricity. The eccentricity of the earth's orbit is 1. 0 2. close to 0 3. close to 1 4. 1 5. infinity
Kepler's Laws From careful astronomical observations, Johannes Kepler was able to formulate three empirical laws of planetary motion. Kepler's 1 st Law: The path of each planet about the Sun is an ellipse (not a circle) with the Sun at one focus. In practice à

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Kepler's Laws Kepler's 2 nd Law: A line drawn between the sun and a planet sweeps out equal areas in equal amounts of time. For a circular orbit, that is easy to see. For an elliptical orbit, it means that a satellite speeds up closer to the sun.
Quick Quiz Two planets orbit a star. Planet 1 has orbital radius r 1 and planet 2 has r 2 = 4 r 1 . Planet 1 orbits with period T 1 . Planet 2 orbits with period A. T 2 = T 1 . B. T 2 = T 1 /2. C. T 2 = 8 T 1 . D. T 2 = 4 T 1 . E. T 2 = 2 T 1 . T 2 r 3 T r 3/2 T 2 T 1 = r 2 r 1 3/2

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Kepler's Laws Kepler's 3 rd Law: The square of the period of one full orbit is proportional to the cube of the radius. For circular orbits: T 2 = 4 π 2 GM r 3 This applies to the motion of planets around the sun, as well as to satellites around planets. One interesting case is a geosynchronous orbit , in which a satellite orbits the earth in 24 hours.
Satellite Orbits For satellites in circular orbits, Newton's 2 nd law gives: F = GMm r 2 = ma r = mv 2 r For circular orbits only: v = GM r What is the total energy of a satellite in a circular orbit?

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