2. PHYSICS 103: Lecture 11 Circular Motion (continued) Gravity and orbital motion Example Problems Agenda for Today:

3. HW (due Tuesday) Read Chapter 6

4. CENTRIPETAL FORCE: EXAMPLE ROTATING SPACE SHIP: MOVIE 2001

5. F ORCE OF G RAVITY Attractive force between all massive objects Increases as the two objects get closer by r -2 Increases with increasing masses G = 6.67  10 -11 N m 2 /kg 2

6. Gravitational Force Between People Calculate the gravitational force between you and your neighbor. Assume your masses are 100 kg and the distance between you is 50 cm. Compare this to the gravitational force between you and the Earth. The radius of the Earth is 6370 km and its mass is 5.98  10 24 kg.

7. ORBITAL SPEEDS

8. Example: What is the speed of the Moon? 1) Newton’s Law of Motion 2) Newton’s Law of Gravitation 3) Circular motion F = m  a F = (G  m  M) / r 2 a = v 2 / r

9. Steps...acceleration of mass is a = v 2 /r therefore force acting on object is f = m  a = If object (m) is circling another massive object (M), then f = G  m  M/r 2 i.e.,m  v 2 /r = G  m  M/r 2 i.e., v 2 = G  M/r m  v 2 /r

10. How fast does the moon orbit? v  1000 m/s How fast does a satellite orbit? v  7800m/s (17,400 miles/hr!) Orbital velocity

11. Problem: Speed of moon? Data: r = 3.84  10 8 m G = 6.67  10 -11 N M e = 5.98  10 24 kg r V = 1020 m/s

12. Problem: Speed of moon? Data: r = 3.84  10 8 m Steps: speed = distance / time period total dist. = 2  r = 2    3.84  10 8 (m) time period= 27.3  24  60  60 (s)  speed= (2.4  10 9 ) / (2.4  10 6 ) = ~ 1  10 3 m/s

13. Main Points from Today’s Lecture Gravity You should understand that gravity is a force that exists between all objects and that it is proportional to the masses of the objects and inversely proportional to the distance squared. Gravity and Orbital Motion You should understand that gravity is a force that exists between all objects. It is the force that is responsible for the moon orbiting the earth, the earth orbiting the sun, etc. The orbital velocity of anything is where M is the mass of the central body being orbited.