1. PH 201 Dr. Cecilia Vogel Lecture 23

2. REVIEW  equilibrium  stable vs. unstable  static OUTLINE  eqlb  universal gravitation

3. Universal Gravity  Newton’s Universal Law of Gravity:  applies universally  Applies to surface of planet  Applies to orbiting satellites  Applies to projectiles  etc…

4. Satellites  A satellite is  planet around Sun  moon around planet  artificial satellite around planet  Keppler’s Laws were stated in terms of planets around Sun  but apply to others, too

5. Keppler’s Laws  Keppler’s 1 st Law  planets travel in elliptical orbit,  link to image link to image  with Sun at one focus  ellipse has 2 foci  nothing at other focus  larger orbit  larger semi-major axis  more circular  smaller eccentricity  perfect circle  e=0, a=r

6. Keppler’s Laws  Keppler’s 2 nd Law  planet sweeps out equal areas in equal times,  when closer  PE is ________, so KE is ___  so goes faster when close  when farther  PE is ________, so KE is ___  so goes slower when far  The same planet goes slower when it is far from the sun than when it is close to the sun

7. Satellite Energy  Generally  within one planet’s orbit:  larger r, slower speed  Circular Orbit  uniform circ motion, with F g =F c

8. Keppler’s Laws  Keppler’s 3 rd Law=“Law of Periods”  T 2 is proportional to a 3,  perfect circle:  F=ma  closer planets go

9. How to Weigh the Sun  Observe planet  the period  and  or  Calculate the mass of the Sun

10. Geosynchronous Orbits  Artificial satellite  if it is to keep over same point,  T =  also M =  so  All circular geosynchronous orbits are at  r = 42000 km  h = 36,000 km

11. Planet’s Gravity  What is the gravitational pull of a planet on something on its surface ?  let M = planet’s mass, m = object’s mass  R = radius of planet

12. Planet’s Gravity  What is the gravitational acceleration on a planet’s surface?  let a g = free-fall acceleration on planet  free-fall —>  F = ma  on Earth:  M = 5.98X10 24 kg, R = 6.37X10 6 m

13. Earth’s Gravity  What is the gravitational acceleration on a Earth’s surface?  a g = 9.83 m/s 2  g = 9.80 m/s 2  ????  Force of gravity provides force for  centripetal  and  a g = g + h