1. Universal Gravitation Chapter 8

2. 8.1 Motion in the Heavens and on Earth Stars - regular path Planets - wanderers, complicated path Comets - more erratic path Galileo, Kepler, & Newton provided insight into how objects move.

3. Tycho Brahe observed eclipse of sun & vowed to become astronomer. Persuaded King Frederick I of Denmark to give him the island of Hven as observatory. Worked for 20 years there.

4. In 1597, became astronomer to Emperor Rudolph of Bohemia where his assistant was Kepler. Brahe - earth centered Kepler - sun centered Analyzed Brahe’s data and formulated three laws of motion.

5. Three Laws 1. Path of planets are ellipses with the sun at the center.Path 2. An imaginary line from the sun to planet sweeps out equal areas in equal time intervals. Move fastest when closest to the sun.equal closest 3. (T a /T b ) 2 = (r a /r b ) 3

6. Table 8-1 Planetary Data p 178 Newton used mathematical properties to prove Kepler’s first law. F  1/d 2 F = G (m 1 m 2 /d 2 ) Because force depends on 1/d 2, its called the inverse square law.

7. Fig 8-3 p 182 Gravitational Forces

8. m p = mass of planet m s = mass of sun r = radius of planet’s orbit T= time for one revolution G = universal gravitation constant F = ma F = m p a c

9. G(m s m p / r 2 ) = m p (4  2 r/T 2 ) T 2 = (4  2 /Gm s )r 3 which is Kepler’s third law Cavendish tested law of universal gravitation between small masses on Earth.tested

10. Able to measure the constant G in Newton’s Law of Universal Gravitation. Me = 5.98E24 kg

11. References http://www.walter-fendt.de/ph11e/keplerlaw1.htm http://www.walter-fendt.de/ph11e/keplerlaw2.htm http://www.physicsclassroom.com/mmedia/circmo t/ksl.htmlhttp://www.physicsclassroom.com/mmedia/circmo t/ksl.html http://www.pbs.org/wgbh/nova/einstein/relativity/ http://www.spaceref.com/tools/vi.html?id=139&c at=blackholes&imgs=moviehttp://www.spaceref.com/tools/vi.html?id=139&c at=blackholes&imgs=movie http://www.physicsclassroom.com/mmedia/specre l/lc.htmlhttp://www.physicsclassroom.com/mmedia/specre l/lc.html