1. Day 50, Thursday, 5 November, 2015 Circular Motion, Kepler’s Laws, and Gravity Quick Review of Circular Motion Conic Sections Kepler’s Laws Universal Law of Gravitation “Weighing” the Earth

2. Quick Review of Circular Motion Pick axis along radius Centripetal (radial), tangential Centripetal Force Centrifugal Force A reaction force caused by Newton’s 3 rd law of motion

3. A walk through 9 equations 1.  r/r =  v/v similar triangles 2.  r/r  t =  v/v  t 3. v/r = a/v 4. a c = v 2 /r 5. V = (2  r)/t circumference/period

4. A walk through 9 equations 6. a c = (2  r/t) 2 /r 7. a c = (4  2 r)/t 2 from equation 5 8. F c = mv 2 /r from F = ma 9. F c = m4  2 r/t 2

5. The Centrifuge aboard the space ship Discovery

6. The classical Space Station

7. Conic Sections are generated by slicing a cone Conic sections are comprised of the circle the ellipse the parabola the hyperbola

8. Kepler’s 3 Laws of Planetary Motion 1 & 2 published in 1609, 3 in 1619 1.The orbit of every planet is an ellipse with the sun at a focus. 2.A line joining a planet and the sun sweeps out equal areas during equal intervals of time. 3.The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

10. Kepler’s 1 st Law Planets orbit Sun in Ellipses

11. Kepler’s 2 nd Law Planets sweep = areas in = times

12. Kepler’s 3 rd Law Periods of Planets Motion

13. Kepler’s 3 rd Law Periods of Planets, slide 2

14. Kepler’s laws are Empirical Laws, They tell us what happens but not why it happens. Why?

15. Newton and the falling apple 1666 It’s tough, but someone has to do it

16. How high does gravity go? It pulls our feet to the ground. It pulls an apple from high up in a tree. Does it go all the way up to the moon? Why doesn’t the moon fall down if gravity is pulling it?

17. Gravity The force holding the Planets in their orbits is inversely proportional to the square of the distance F is proportional to 1/d 2 The force of gravity (mg) depends on the mass of the objects involved

18. Law of Universal Gravitation* F = G (m a m b )/d 2 F = G (m 1 m 2 )/r 2 * AKA the “Law of Gravity”

21. Value of G Universal Gravitational Constant G = 6.67 x 10 -11 N m 2 / kg 2 Henry Cavendish measured it on a torsion balance.

22. In the last 300 years we think differently than all humans who went before us The heavens were different. Different materials Different laws We didn’t belong there. Now the heavens are the same. Same materials Same laws We belong there.

23. Heavenly Motion Fifth element Plato's Timaeus posits the existence of a fifth element (corresponding to the fifth remaining Platonic solid, the dodecahedron) called quintessence, of which the cosmos and all celestial bodies are made. Aristotle included aether in the system of the classical elements of Ionic philosophy as the "fifth element" (the quintessence), on the principle that the four terrestrial elements were subject to change and moved naturally in straight lines while no change had been observed in the celestial regions and the heavenly bodies moved in circles. In Aristotle's system aether had no qualities (was neither hot, cold, wet, or dry), was incapable of change (with the exception of change of place), and by its nature moved in circles

24. Local Motion and Celestial Motion are Unified One set of laws to rule the entire cosmos. Gone: Celestial Motion Quintessence (the perfect, unchanging material) Endless perfectly circular motion Gone: Local Motion Linear motion that grinds to a stop on its own Introduced: Universal Motion One motion that goes in a straight line forever unless some force (like gravity) pulls it out of a line, or some force (like friction) decelerates it to a stop.

25. The heavens are now a place we can go

26. Torsion Balance

27. The torsion balance apparatus

28. Cavendish and the Torsion Balance

29. Cavendish “Weighs” the Earth* F = mg = G (M E m)/r 2 Divide out the little mass g = GM E /r 2 Solve for M E * 1798

30. The Mass of the Earth Mass of Earth is 5.98 x 10 24 kg

31. Credits 2001 Space Station www.imdb.com 2001 Centrifuge treehugger.com/files/ferris-thumb.jpg

32. Credits II Newton Contemplates the apple http://www.theintrovertzcoach.com/newto n3.jpg http://www.theintrovertzcoach.com/newto n3.jpg Kepler’s Laws http://hyperphysics.phy- astr.gsu.edu/hbase/imgmec/kep.gif

33. Credits III Torsion balance Wikipedia Torsion Balance Apparatus www.geocities.com Idealized Torsion balance www.newscientist.com

34. Credits IV Conic sections mathworld.wolfram.com Wikipedia Kepler’s 3 Laws of Planetary Motion (verbal) Wikipedia

35. Credits V The fifth Element Wikipedia Moon Walk picture nottscience.wordpress.com/2009/07/07/moon-walk/ Space Station Astronauts news.xinhuanet.com/.../26/content_11073926.htm