1. Gravitation

2. Gravitational Force the mutual force of attraction between particles of matter Newton’s Law of Universal Gravitation F g =G(m 1* m 2 /r 2 ) G= 6.67x10 -11 Nm/kg2

3. Force Force is proportional to the mass times mass Force is inversely proportional to the distance squared or the radius squared

4. Elliptical Orbits http://spaceweather.com/swpod2007/23oct07/orbit.gif

5. Elliptical orbits Perigee greatest force greatest velocity smallest distance

6. Elliptical orbits Apogee least force least velocity greatest distance

7. Circular orbits distance is constant velocity is constant F c is constant

8. Kepler’s Laws First Law Each planet travels in an elliptical orbit around the sun with the sun as one focal point Second Law- An imaginary line drawn from the sun to any planet sweeps out equal areas in equal time intervals. Third Law- The square of an orbital’s period is proportional to the cube of the average distance between the planet and the sun T 2 is proportional to t 3

9. Equations T=2π√(r 3 /Gm) v=√(Gm/r)

10. Circular Motion = the movement of an object at constant speed around a circle with fixed radius Axis – straight line around which rotation takes place Rotation – object turns around an internal axis Ex. Ice skater Revolution – object turns around an external axis Ex. Earth around the sun

11. Rotational Speed Linear speed – distance/time Tangential speed – speed along a circular path Rotational speed – number of rotations per unit of time Example: Carousel horses travel at same rotational speed but different tangential speed

12. Centripetal Force Force that causes an object to follow a circular path Ex. Force holding occupants safely in a rotating carnival ride F net = mv 2 r

13. Centripetal Acceleration Always points toward the center of the circular motion. Period (T) = time needed for an object to make one complete revolution Distance traveled = circumference Circumference = 2πr = πd

14. Other formulas Centripetal Acceleration equals the velocity squared divided by the radius A c = v 2 /r The number of revolutions equals the distance traveled divided by the circumference Revolutions = distance/circumference