1. Isaac Newton’s 3rd Law and the Universal Law of Gravitation

2. = a push or pull acting on an object.
Force
= a push or pull acting on an object.
Examples:
gravity = pull
electrostatic attraction = pull
electrostatic repulsion = push

3. Newton’s Second Law of Motion:
The acceleration of an object is directly proportional to the force acting on it, and inversely proportional to its mass.
In mathematical form:
Or alternatively:

4. Example of Newton’s Second Law:
A package of cookies has mass m = kilograms,
And experiences gravitational acceleration g = 9.8 meters/second2
How large is the force acting on the cookies?

11. Newton’s Third Law of Motion:
For every action, there is an equal and opposite reaction.
Whenever A exerts a force on B, B exerts a force on A that’s equal in size and opposite in direction.
All forces come in pairs.

14. Example of Newton’s Third Law:
Cookies push on hand: F = 1 pound, downward.
Hand pushes on cookies: F = 1 pound, upward.
Remove hand!
Earth pulls on cookies: F = 1 pound, downward.
Cookies pull on earth: F = 1 pound, upward.

15. THIRD Law states: force on Earth = force on cookies
SECOND Law states: acceleration = force divided by mass
Mass of Earth = 1025 x mass of cookies
Therefore, acceleration of cookies = x acceleration of Earth.
(Cookies reach a high speed while the Earth hardly budges.)

16. But…why do the cookies and the Earth exert a force on each other?
Newton’s Law of Gravity states that gravity is an attractive force acting between ALL pairs of massive objects.
Gravity depends on:
(1) MASSES of the two objects,
(2) DISTANCES between the objects.

18. Newton’s question: can GRAVITY be the force keeping the Moon in its orbit?
Newton’s approximation: Moon is on a circular orbit.
Even if its orbit were perfectly circular, the Moon would still be accelerated.

19. The Moon’s orbital speed:
radius of orbit: r = 3.8 x 108 m
circumference of orbit: 2pr = ???? m
orbital period: T = 27.3 days = ???? sec
orbital speed:
v = (2pr)/T = ??? m/sec = ? km/sec!

20. The Moon’s orbital speed:
radius of orbit: r = 3.8 x 108 m
circumference of orbit: 2pr = 2.4 x 109 m
orbital period: T = 27.3 days = 2.4 x 106 sec
orbital speed:
v = (2pr)/T = 103 m/sec = 1 km/sec!

21. Acceleration required to keep Moon on a circular orbit

22. Ratio of Accelerations to Distances

23. Bottom Line Triumph for Newton!!
If gravity goes as one over the square of the distance,
Then it provides the right acceleration to keep the Moon on its orbit (“to keep it falling”).
Triumph for Newton!!

24. Figure 5-2 The force on a 0.1-kilogram mass at various distances from Earth. Notice that the force decreases as the square of the distance.
Fig. 5-2, p.81

25. Figure 5-3 The sum of all the forces on the apple exerted by all portions of Earth acts as if all the mass were located at Earth’s center.
Fig. 5-3, p.82

26. Figure 5-1 If the sphere’s radius is doubled, the sphere’s surface increases by a factor of 4.
Fig. 5-1, p.80

27. Earth's surface 6.38 x 106 m 9.8 1000 km above surface 7.38 x 106 m
Location
Distance from
Earth's center (m)
Value of g
m/s2
Earth's surface
6.38 x 106 m
9.8
1000 km above surface
7.38 x 106 m
7.33
2000 km above surface
8.38 x 106 m
5.68
3000 km above surface
9.38 x 106 m
4.53
4000 km above surface
1.04 x 107 m
3.70
5000 km above surface
1.14 x 107 m
3.08
6000 km above surface
1.24 x 107 m
2.60
7000 km above surface
1.34 x 107 m
2.23
8000 km above surface
1.44 x 107 m
1.93
9000 km above surface
1.54 x 107 m
1.69
10000 km above surface
1.64 x 107 m
1.49
50000 km above surface
5.64 x 107 m
0.13

29. p. 83: The attraction between these spheroidal friends depends on the distance between their centers.
p.83

31. (4) Newton’s Law of Gravity:
The gravitational force between two objects
F = gravitational force
M = mass of one object
m = mass of the second object
r = distance between centers of objects
G = “universal constant of gravitation”

33. Example: What is gravitational force between Earth and cookies?

34. Example: What is gravitational force between Earth and cookies?

35. Table p.85

36. p. 85: The lunar rover would collapse under its own weight if used on Earth. (NASA)

37. p. 89 (bottom): Star clusters provide evidence of gravity at work between stars. (NASA)

38. p. 90: The Andromeda Galaxy is similar to our own Milky Way Galaxy
p.90: The Andromeda Galaxy is similar to our own Milky Way Galaxy. (California Institute of Technology/Palomar Observatory)
p.90

39. Q5- 3: (NASA)
Fig. Q5-3, p.92

40. Fig. Q5-19, p.93

41. Q5-25: (NASA)
Fig. Q5-25, p.93

43. Isaac Newton (1643-1727): English
Discovered:
three laws of motion,
one law of universal gravitation.