1. 1 Class #20 of 30 Celestial engineering Clarification on scattering angles Rotating reference frames Vector angular velocity Newton’s laws on rotating frame Two “fictitious forces” :02

2. 2 Class #19 Windup Epsilon is function of L and E and GMm :60 KEPLER 1 st Law – Planets move in ellipses 2 nd law dA/dt=const 3 rd law Period goes as semi-minor radius to 3/2 power

3. 3 Class #20 Windup No class or office hours on 11/5 and 11/6 Office hours Thurs 11/7. HW 11 due 11/12 in class. HW 12 due 11/14 as usual. :60

4. 4 Planetary Scattering Angle – New … improved!! :37  Sketch for epsilon=2

5. 5 Vector angular velocity :60 Theta=90-Latitude = “CoLatitude” Earth obeys right-hand rule Omega points North  Earth spins clockwise  Sun rises in east

6. 6 Vector velocity – 1 minute problem :60 Latitudes – Socorro – 34 N Nome, Alaska – 64 N Hilo, Hawaii – 19 N Hobart, Tazmania – 43 S What is circumferential velocity of each of these four cities?

7. 7 Vector velocity – 1 minute problem :60 Latitudes – Socorro – (.38 km/s=880 mph) Nome (.20 km/s=473 mph) Hilo – (.44 km/s=1021 mph) Hobart (.34 km/s=790 mph)

8. 8 Vectors expressed in rotating frames :60 Imagine same axes (x,y,z) expressed in two frames S 0 stationary) and S (fixed to earth).

9. 9 :60 Derive Newton in rotating frame

10. 10 Newton in a rotating frame :60 Coriolis Term Centrifugal Term Newtonian Term

11. 11 :60 Alternate form of Left-Hand Rule

12. 12 Class #20 Windup No class or office hours on 11/5 and 11/6 Office hours Thurs 11/7. HW 11 due 11/12 in class. HW 12 due 11/14 as usual. :60