1. 1 Class #20 The power of Equivalent 1-D problem and Pseudopotential  Kepler’s 3 rd law Orbits and Energy  The earth-moon flywheel :02

2. 2 Two particles with central forces

3. 3 Reduced two-body problem :15

4. 4 The power of :20

5. 5 The power of - part 2 :25

6. 6 Equivalent 1-D problem :30 Relative Lagrangian Radial equation Total Radial Force

7. 7 Pseudopotential and Energy :35

8. 8 Pseudopotential and Energy :37

9. 9 Potential Wells :25 Mass m Spring constant k K > 0 K < 0

10. 10 Taylor Series Expansion :35 Taylor series -- Generic Taylor series -- Potential Can be ignored or set to zero … “gauge invariance” Is already zero for potential evaluated about a critical point x-0

11. 11 Earth and Moon 1. What is the reduced mass for the earth-moon system (in kg)? 2. How many percent different is it than the lunar mass 3. What is theta-dot? 4. What is the radius of a circular orbit? 5. How would this change if the earth were fixed in space by the hand of God or a Borg tractor beam?

12. 12 Earth and Moon 1. What is the reduced mass for the earth-moon system (in kg)? 2. How many percent different is it than the lunar mass 3. What is theta-dot? 4. What is the radius of a circular orbit? 5. How would this change if the earth were fixed in space by the hand of God or a Borg tractor beam?

13. 13 Potential and Force for solid spheres

14. 14 Orbital Energy :47 1. Last class we derived values for omega, mu and r for the earth- moon system 2. Total energy consumption on Earth is 1000 Terajoules/day 3. If we could power human activites by stealing the angular kinetic energy from the earth-moon system, how much should omega change to give us 100 years of power?

15. 15 Class #20 Windup :60