Problem 11

1
(No Transcript)
2
(No Transcript)
3
(No Transcript)
4
(No Transcript)
5
Chapter 12 Gravitation
Newtons Law of Gravitation
6
Gravitational attraction
Note Two particles of different mass exert
equally strong gravitational force on each other
7
(No Transcript)
8
Gravitational Forces (I)
MM
MM ME FG G
r 2

• Attractive Force

ME
9
(No Transcript)
10
Cavendish balance
Cavendish(1798) announced that he has weighted
the earth
11
(No Transcript)
12
(No Transcript)
13
Average Density of the Earth

• g 9.80 m/s2
• RE 6.37 x 106 m
• ME 5.96 x 1024 kg
• rE 5.50 x 103 kg/m3
• 5.50 g/cm3 2 x rRock
• ? ???

14
The gravitational force is conservative
Note Work done is Path independent!
15
(No Transcript)
16
Gravitational potential energy
Note The gravitational potential is zero at
infinity
17
(No Transcript)
18
(No Transcript)
19
Projectile
20
Projectile
21
Circular orbit
22
(No Transcript)
23
Keplers Laws

• Each planet moves in an elliptical orbit, with
  the sun at one focus of the ellipse
• A line from the sun to a given planet sweeps out
  equal areas in equal times.
• 3. The periods of the planets are proportional
  to the 3/2 powers of the major axis lengths of
  their orbits.

24
Geometry of an ellipse
25
Elliptical orbit
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
(No Transcript)
30
(No Transcript)