Newton

1
Newton

• 1st Law of Motion
• Gravity
• Mass/Weight
• Centripetal Force
• Keplers Third Law
• Calculating Mass
• Solving for G
• Orbits
• Earth Moves

2
Newtons 1st

• An object at rest remains at rest, and an object
  in motion continues in a straight line unless
  acted on by an outside force.

3
Newtons 1st

• An object at rest remains at rest unless acted on
  by an outside force.

4
Newtons 1st

• An object in motion continues in a straight line
  unless acted on by an outside force.

5
Newtons 1st

6
Newton

• 1st Law of Motion
• Gravity
• Mass/Weight
• Centripetal Force
• Keplers Third Law
• Calculating Mass
• Solving for G
• Orbits
• Earth Moves

7
Gravity
-G M m r2
Fg
8
Gravity
-G M m r2
Fg
Attractive Force
9
Gravity
-G M m r2
Fg
Universal Gravitational Constant
10
Gravity
-G M m r2
Fg
Masses of Two Objects
11
Gravity
-G M m r2
Fg
Distance Between Centers
12
Gravity
8 X

64 X
13
Newton

• 1st Law of Motion
• Gravity
• Mass/Weight
• Centripetal Force
• Keplers Third Law
• Calculating Mass
• Solving for G
• Orbits
• Earth Moves

14
Mass / Weight

• Mass Quantity of Matter
• Which has more matter, a pound of lead or a pound
  of feathers?
• The pound of feathers is bigger, but thats a
  different question.
• The pound of lead is denser, but thats a
  different question.
• If they are both on Earth, they have the same
  mass.
• A pound of feathers on the moon has more mass
  than a pound of lead on Earth.
• If I take a pound of lead to the moon, it will
  weigh less, but the mass will still be the same.
• Weight Force of Gravity Holding it to Surface
• kilogram measure of mass
• pound measure of force

15
Mass / Weight

• With a mass of 68 kg, I weigh 150 lbs on Earth.
• The moons gravity is weaker.
• I would only weigh 31.5 lbs there.
• On Mars, I would weigh 67.5 lbs.

16
Newton

• 1st Law of Motion
• Gravity
• Mass/Weight
• Centripetal Force
• Keplers Third Law
• Calculating Mass
• Solving for G
• Orbits
• Earth Moves

17
Gravity is a Centripetal Force.

• Any force that is directed toward the center of
  motion.
• A Ball on a String
• A Car on a Curved Road

18
"

19
(No Transcript)
20
Centripetal Force
-m v2 r

21
Centripetal Force
-m v2 r
-G M m r2

22
Centripetal Force
-m v2 r
-G M m r2

23
Centripetal Force
v2 r
G M r2

24
Centripetal Force
22p2r2 P2
Circular Orbit
v2
v2 r
G M r2

25
Centripetal Force
4p2r2 P2 r
G M r2

26
Centripetal Force
4p2r P2
G M r2

27
Centripetal Force
G M r2
4p2r

P2
28
Centripetal Force
4p2r3
G M

P2
29
Centripetal Force
Circular Orbit r a
4p2 G M
r3

P2
30
Centripetal Force
Circular Orbit r a
4p2 G M
a3

P2
31
Keplers Third Law
P2 k a3
4p2 G M
a3

P2

32
Newton

• 1st Law of Motion
• Gravity
• Mass/Weight
• Centripetal Force
• Keplers Third Law
• Calculating Mass
• Solving for G
• Orbits
• Earth Moves

33
Finding Mass
4p2 G M
a3

P2
34
Finding Mass
4p2 G
a3

P2
M
35
Finding Mass
One problem remains.
a3 P2
4p2 G

M
36
Finding Mass
One problem remains.
a3 P2
4p2 G

M
37
Mass of Earth
Phillip von Jolly
M
38
Mass of Earth
Phillip von Jolly
M
-GMÅm RÅ2
-GMÅm RÅ2
-GMm D2
F

39
Mass of Earth
Phillip von Jolly
m
m n
M
-GMÅn RÅ2

40
Mass of Earth
-GMÅm RÅ2
-GMÅm RÅ2
-GMm D2
-GMÅn RÅ2
F


41
Mass of Earth
42
Finding Mass
One problem remains.
a3 P2
4p2 G

MÅ
( (
43
Newton

• 1st Law of Motion
• Gravity
• Mass/Weight
• Centripetal Force
• Keplers Third Law
• Calculating Mass
• Solving for G
• Orbits
• Earth Moves

44
Orbits

• Å

Apogee
Perigee
Circular
45
Orbits

• Å

Apogee
Perigee
46
Transfer Orbits

• Å

47
Newton

• 1st Law of Motion
• Gravity
• Mass/Weight
• Centripetal Force
• Keplers Third Law
• Calculating Mass
• Solving for G
• Orbits
• Earth Moves

48
Proof of Earths Motion
Rotation Revolution
49
Proof of Earths Revolution
What would satisfy Aristotle? Parallax
50
Parallax
Å

Å
51
Parallax
52
Parallax
shift in the position of one nearby star,
compared to the background of more distant stars
53
Parallax
Å

Quadrature
Å
54
Proof of Earths Revolution
Stellar Aberration Aberration of Starlight
55
Aberration of Starlight
56
Aberration of Starlight
57
Aberration of Starlight
Tilt it at an angle.
What angle?
How does this compare with light entering a
telescope?
It depends on what? Speed of Dripping
Water Speed of Tube
58
Aberration of Starlight
zero aberration for stars at quadrature
Å

Å
59
Aberration of Starlight

Å
60
Aberration of Starlight
Å

61
Aberration of Starlight
Å

62
Aberration of Starlight
Å

It depends on what? Speed of Light Speed of
Earth Direction of Earth
63
Aberration of Starlight
Å
Å

64
Proof of Earths Revolution Around Sun

• Parallax
• one nearby star
• two photos
• max at quadratures
• Earth moved

• Aberration
• all stars in same direction
• zero at quadrature
• max at opposition
• Earth moving

65
Proof of Earths Motion
Rotation Revolution
66
Proof of Earths Rotation
Coriolis Effect Important When You Cant See
Target
67
Proof of Earths Rotation
Oblate Earth