1. Chapter 4 – Gravity, Projectiles, Satellites
PHS 116
Chapter 4 – Gravity, Projectiles, Satellites

2. Activity 1
[Gravity and reaction time]

3. Sir Isaac Newton Did not “discover” gravity
First to realize that gravity is not confined to Earth
Forces must act on the planets
Netwonian synthesis

4. 4.1 Universal Law of Gravity
Newton: The moon “falls” away from straight line motion

5. Law of Universal Gravitation
After observing Halley’s comet
Came up with this relationship
F ~ mass1 x mass2
(distance)2

6. The Universal Gravitational Constant (G)
F ~ mass1 x mass2
(distance)2
F = G mass1 x mass2
G = 6.67 x N m2/kg2
That’s

7. Henry Cavendish First to calculate “G” independently G = __F___
(m1m2/d2)

8. Sample Problem: Use “G” to calculate the mass of the Earth!
Assume you have a 1 kg mass.
F = 9.8 N (we round to 10 usually)
G = 6.67 x N m2/kg2
m2 = 1 kg
d = Earth’s radius = 6.4 x 106 m
[on board]

9. 4.2 Effect of Distance on Gravity
Gravity is weak to begin with
weakest of the four fundamental forces
gravity, electromagnetic, weak & strong nuclear forces
As distance increases, gravity falls off by 1/d2
Similar example: spray paint

10. 9
1/9 16
1/16

11. Worksheet
page 27

12. Distance
Refers to the distance between the “center of mass” for the two objects
The greater an object’s distance from the Earth, the less it __________
The force of attraction approaches zero at very large distances, but can never reach zero
weighs

14. Question
You climb up a tree 4 m high and measure the force of gravity on your body.
You then climb up a tree 8 m high and measure the force of gravity on your body.
Do you weigh 4 times less (1/d2) when you’re up the 8 m tree?

15. 4.3 Weight and Weightlessness
Weight has no meaning without the concept of “support force”
When you take away the support force you are “weightless” or in “freefall”

16. Weight
You only weigh as much as the amount of support force you feel

17. Weightlessness

18. Artificial Gravity

19. 4.4 Universal Gravitation
Why are the planets round?
mass contained in the planet exerts gravity on other mass within the planet
a sphere is the best way to distribute gravity equally
[draw on board]

20. Planetary Perturbations
Planets influence other planet’s orbits

21. F = G mass1 x mass2
(distance)2
J. Locke

22. Worksheet
page 28

23. 4.5 Projectile Motion
Gravity causes the path of projectiles thrown horizontally to curve
To analyze properly, look at horizontal and vertical components of motion separately

24. The horizontal component
Object moves at constant velocity, no acceleration, due to its own inertia
if we ignore air resistance
dhorizontal = velocity x time

25. The vertical component
acceleration due to gravity
dvertical = ½ g t2

26. Combined

27. Projectiles Launched Horizontally
The curved path is called a parabola
Follows parabolic motion
Object will hit the ground at the same time an object dropped straight down will hit

28. Projectiles Launched at an Angle Up
Still follows parabolic motion
Object will hit the ground after object dropped straight down

29. Projectiles Launched at an Angle Down
Still follows parabolic motion
Object will hit the ground ______
the same object dropped straight down?

30. Worksheet
page 29, 30

31. dideal - dparabola = ½ g t2 = 5 t2

32. Launching Projectiles
What trends do you notice?
What’s the ideal launch angle?

33. What other effects? air resistance (lower angle = less air resistance)
Spin for golf balls (lower angle = less spin)

35. Time of Flight deceleration of g = acceleration of g
time up = time down

36. Worksheet
pages 31, 32

37. 4.6 Satellites The earth is not flat
If an object is projected fast enough, it can “fall” all the way around the earth
satellites
18,000 mph for a baseball

38. The Moon a projectile that circles the Earth
definitely influenced by Earth’s gravity, as are other satellites
Has enough velocity not to fall into the Earth (or it would’ve done so long ago)

39. 4.7 Circular Orbits
A satellite in orbit always moves in a direction perpendicular to the force of gravity acting on it
A very special form of free fall (no support force)
The higher the orbit, the less the speed, the longer the path, and the longer the period (time it takes to make one orbit)
8 km/s ensures a perfect circular orbit

40. above atmosphere

41. 4.8 Elliptical Orbits If a projectile exceeds 8 km/s
orbit will be an ellipse
speed is not constant around the ellipse
faster nearer massive object
highest P.E. farthest from massive object

44. PE = mgh
KE = ½ mv2

45. W =F x d

46. Worksheets
pages 33-35

47. 4.9 Escape Velocity
Fire an object vertically
What normally happens?

48. Escape Speed The “initial burst” speed required to escape orbit
11.2 km/s for Earth (~25,000 mph)
Leaves Earth, traveling slower and slower
From any planet (or body):
v = (2 G M / d)1/2

49. Escape Speeds Sun 333,000 Earth 620 km/s Jupiter 318 Earth 60.2 km/s
Earth 1 Earth km/s
Mars Earth 5.0 km/s
Moon Earth 2.4 km/s

50. Escape Speed Only pertains to the initial thrust needed
Rockets could burn out if initially 11.2 km/s
You can actually escape at any speed if you’re willing to take enough time to do it

51. Chapter 4 Homework
Exercises: 1, 2, 5, 6, 9, 12, 13, 20, 22, 27, 30, 32, 36, 37, 40, 49
Problems: 1, 2, 3, 8