1. © Simon Porter 2007
Orbital Motion

2. How far could you kick a dog?
From a table, medium kick.

3. How far can you kick a dog?
Gravity

4. Harder kick?

5. Harder kick
Gravity

6. Small cannon?
Woof! (help)

7. Small cannon
Woof! (help)
Gravity

8. Bigger cannon?

9. Bigger cannon
Gravity
Gravity

10. Even bigger cannon?

11. Even bigger cannon
Gravity
Gravity
Gravity

12. VERY big cannon?

13. VERY big cannon
Gravity

14. Humungous cannon?

15. Dog in orbit!
The dog is now in orbit! (assuming no air resistance of course)

16. Dog in orbit!
The dog is falling towards the earth, but never gets there!

17. Dogs in orbit!
The force that keeps an object moving in a circle is called the centripetal force (here provided by gravity)
Gravity

18. Uniform Circular Motion
© Simon Porter 2007
Uniform Circular Motion
Remember we have already looked at circular motion
Centripetal acceleration = v2/r
Centripetal force = mv2/r
velocity

19. Uniform Circular Motion
© Simon Porter 2007
Uniform Circular Motion
For orbital motion, the centripetal force is provided by gravity
Earth’s gravitational attraction on moon

20. Uniform Circular Motion
© Simon Porter 2007
Uniform Circular Motion
centripetal force = force of gravity
Mmv2/r = GMeMm/r2
v2 = GMe/r
Earth’s gravitational attraction on moon

21. Period of orbit v2 = GMe/r Distance travelled in one orbit = 2πr
© Simon Porter 2007
Period of orbit
v2 = GMe/r
Distance travelled in one orbit = 2πr
Speed = distance/time = 2πr/T
Earth’s gravitational attraction on moon
(T = period of orbit)

22. This is known as Kepler’s third law of planetary motion.
© Simon Porter 2007
Period of orbit
v2 = GMe/r
(2πr/T)2 = GM/r
T2 = 4π2r3/GM
T2 α r3
This is known as Kepler’s third law of planetary motion.

23. Total energy = GMm/2r – GMm/r = -GMm/2r
© Simon Porter 2007
Energy of a satellite
A satellite has kinetic energy and gravitational potential energy.
Total energy = ½mv2 - GMm/r
v2 = GM/r so Ek = GMm/2r
Total energy = GMm/2r – GMm/r = -GMm/2r
Total energy = -½mv2
from slide 4

24. Energy of a satellite Total energy of satellite = -GMm/2r
© Simon Porter 2007
Energy of a satellite
Total energy of satellite = -GMm/2r
Kinetic energy = GMm/2r
Potential energy = - GMm/r

25. © Simon Porter 2007
Energy of a satellite
energy Ek
distance ET Ep

26. © Simon Porter 2007
Weightlessness
Consider an astronaut in a space ship orbiting the earth

27. © Simon Porter 2007
Weightlessness
Remember both the ship and astronaut are falling towards the earth (centripetal acceleration) v
mv2/r

28. © Simon Porter 2007
Weightlessness
Because they are both falling together, the astronaut feels no reaction force from the floor of the space craft so she feels “weightless” (you get a small feeling of this as a lift (elevator) starts to descend).
acceleration = v2/r

29. Weightlessness There is a mathematical way to look at this.
© Simon Porter 2007
Weightlessness
There is a mathematical way to look at this.

30. © Simon Porter 2007
Weightlessness
The forces on the astronaut are gravity from the earth (GMm/r2) and the normal reaction force (N) of the floor of the spacecraft.
The net force must be equal to mv2/r if he is in orbit.
GMm/r2 – N = mv2/r

31. Weightlessness GMm/r2 – N = mv2/r N = GMm/r2 – mv2/r
© Simon Porter 2007
Weightlessness
GMm/r2 – N = mv2/r
N = GMm/r2 – mv2/r
N = (m/r)(GM/r – v2)
since v2 = GM/r, N = zero

32. © Simon Porter 2007
Weightlessness
So there is a force of gravity on the astronaut, but no reaction force from the floor so the astronaut feels weightless.
YouTube - Zero G Puke Bag
YouTube - Greg Olsen - Drinking water on the ISS
YouTube - Joe Francis with hot chicks floating in space!
YouTube - flying dog

33. More questions! Page 152 Questions 1, 3, 4, 15, 24. Page 153 Q7, 13
© Simon Porter 2007
Page 152 Questions 1, 3, 4, 15, 24.
Page 153 Q7, 13
Pages 307 Questions
2, 4, 5, 6, 11, 12.
You can have some time to finish them in this lesson, and then you can finish the rest for homework, due in Wednesday 30th September
TEST on 6th October
More questions!
I hate physics.