1. Lecture 19 Satellites

2. Quick Review • Newton’s Law of gravity

3. Circular Orbits • M is mass of parent and m the mass of the satellite. M>>m • Kepler’s Law

4. Geostationary Satellite • At the equator, how far above the earth’s surface should a satellite orbit so it stays overhead? • Rearth = 6.37 x 106 m • G=6.67 x 1011 N•m2/kg2 Mearth = 5.98 x 1024 kg

5. A cyclist goes around a level, circular track at constant speed. Since the cyclist’s speed is constant, her acceleration is constant • True • False

6. QUIZ • A motor cycle is in a loop-the-loop. At the top of the loop… • A) Draw a free body diagram • B) What is the minimum speed the motor cycle must have if the radius of the loop is 15. m?

7. Homework due Friday • Problems: 6: 24, 25, 27, 29, 33, 44, 45, 51, 58, 59

8. Problem 6:27 • What is the ratio between the sun’s gravitational force on you and the earth’s gravitational force on you? • Rearth = 6.37 x 106 m • G=6.67 x 1011 N•m2/kg2 Mearth = 5.98 x 1024 kg Rearth-sun =1.5 x 1011 m Msun = 1.99x1030 kg

9. Problem 6:27 cont • Take ratio

10. 6:33 • The space shuttle is in an orbit 250 miles high. What are its orbital period (in minutes) and orbital speed? • Rearth = 6.37 x 106 m • G=6.67 x 10-11 N•m2/kg2 Mearth = 5.98 x 1024 kg 1 mi = 1.609 km

11. 6:33 • 250 mi *1.609km/mi=326.5 km • r= 6.37 x 106 m+3.265 x 105 m =6.70 x 106 • T=5.46 x 103 s = 90.9 minutes

12. 6:44 • A 5g coin is placed 15cm from the center of a turntable. µs = 0.80, µk = 0.50. As turntable starts from rest and speeds up to 60 rpm, does coin slide off?

13. So coin does not slip

14. 6:45 Conical Pendulum Find T, ω 1.0m T θ r=0.20m W=mg

15. 6:51 Ultracentrifuge R=0.10 m 70,000 rpm Δm= 10 mg = 0.000010 kg What is net force? r a

16. 6:58 Martian geostationary satellite What are its speed and altitude? dayMars:=24.8 hours

17. 6:59 g on Mars, Maximum walking speed?