1. Physics 218 Challenge Exam will take place on December 3. Please come and participate! DATE: Monday, December 3, 2007 TIME: 6:00 p.m. LOCATION: 202T ENPH

3. Platform rotates with a constant angular velocity  0. At t = 0 it starts rotating with angular acceleration  (t)=  t. At the same time a man starts a distance L from the center and walks in along a straight line painted on the platform towards the center. He decreases his distance from the center at a constant rate, V 0. What force does the platform exert on the man, as a function of his distance from the center?

4. Johannes Kepler (1571 – 1630)

5. Kepler hypothesized that a physical force moved the planets, and that the force diminished with distance. Planets closer to the sun feel a stronger force and move faster. Elliptical orbits – key to the problem of the planetary motion

6. A platform rotates with a constant angular velocity  0. At t = 0 it starts rotating with angular acceleration  (t)=  t. At the same time a man starts a distance L from the center and walks in along a straight line painted on the platform towards the center. He decreases his distance from the center at a constant rate, V 0. What force does the platform exert on the man, as a function of his distance from the center?

8. 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

9. Eccentricities of Ellipses e = 0.02 e = 0.1e = 0.2 e = 0.4e = 0.6 1)2)3) 4) 5)

10. Eccentricities of Planetary Orbits Orbits of planets are virtually indistinguishable from circles: Earth: e = 0.0167 Most extreme example: Pluto: e = 0.248

11. LAW 2: A line joining a planet/comet and the Sun sweeps out equal areas in equal intervals of time The closer to the sun, the larger the orbital velocity

12. Planetary Orbits (2) A planet’s orbital period (P) squared is proportional to its average distance from the sun (a) cubed: P y 2 = a AU 3 A line from a planet to the sun sweeps over equal areas in equal intervals of time. (P y = period in years; a AU = distance in AU)