1. Kepler’s Laws

2. 2.5 The Laws of Planetary Motion Law 2. Imaginary line connecting Sun and planet sweeps out equal areas in equal times

3. 2.5 The Laws of Planetary Motion Law 3. Square of period of planet’s orbital motion is proportional to cube of semimajor axis

4. More Precisely 2-1: Some Properties of Planetary Orbits Semimajor axis and eccentricity of orbit completely describe it Perihelion: closest approach to Sun Aphelion: farthest distance from Sun

6. Another way to say them The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses) An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas) http://www.physicsclassroom.com/mmedia/circmot/ksl.cfm http://www.physicsclassroom.com/mmedia/circmot/ksl.cfm The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (The Law of Harmonies)

7. Easy math If planet A is 4 units from the sun then what is its orbital period. (a 3 = p 2)

8. Keplar’s laws http://www.youtube.com/watch?v=GcKiG- CuvtA

9. Let’s watch different planets in action http://astro.unl.edu/classaction/animations/r enaissance/kepler.html http://astro.unl.edu/classaction/animations/r enaissance/kepler.html

10. 2.7 Newton’s Laws Gravity For two massive objects, gravitational force is proportional to the product of their masses divided by the square of the distance between them

11. 2.7 Newton’s Laws Gravity The constant G is called the gravitational constant; it is measured experimentally and found to be G = 6.67 x 10 -11 N m 2 /kg 2

12. But let’s look at an easier way F g  m 1 m 2 / d 2 The force of gravity is proportional to the product of the mass of the two objects divided by the distance squared

13. White board problem If Marvin is 36 lbs how much is his weight if he is at 2r (distance from Earth) Weight = 36/2 2 36/4=9lbs

14. So if this is true and astronauts at the space station are still within the earth’s gravity, why do they experience weightlessness??? http://www.youtube.com/watch?v= 2V9h42yspbo

15. Vomit Comet http://www.youtube.com/watch?v=2 V9h42yspbo

16. 2.8 Newtonian Mechanics Escape speed: the speed necessary for a projectile to completely escape a planet’s gravitational field. With a lesser speed, the projectile either returns to the planet or stays in orbit.

17. So what did Einstein have to say about gravity? But what is gravity, what is it that attracts to objects to one another? http://www.youtube.com/watch?v=O- p8yZYxNGc http://www.youtube.com/watch?v=O- p8yZYxNGc http://www.youtube.com/watch?v=DbhuRcmSk Mg&feature=related