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Chapter 12: Gravitation. Newton’s Law of Gravitation. Gravitational attraction. Note : Two particles of different mass exert equally strong gravitational force on each other. Gravitational Forces (I). M M. M M M E F G = G r 2. - PowerPoint PPT Presentation
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Chapter 12: Gravitation
1 22
-11 2 2
G=gravitational constant = 6.673(10) 10 /
g
Gm mF
r
Nm kg
E
The weight of a body of mass m on the earth's surface with
radius
Note:
R is
2 2 or E E
E E
Gm m Gmmg g
R R
Newton’s Law of Gravitation
Gravitational attraction
Note: Two particles of different mass exert equally strong gravitational force on each other
Gravitational Forces (I)
‘‘Attractive Force”
MM ME
FG = G r 2
ME
MM
Cavendish balance
Cavendish(1798) announced that he has weighted the earth
g = 9.80 m/s2
RE = 6.37 x 106 m
ME = 5.96 x 1024 kg E = 5.50 x 103 kg/m3
= 5.50 g/cm3 ~ 2 x Rock
???
Average Density of the Earth
The gravitational force is conservative
Note:
Work done is
Path independent!
Gravitational potential energy
Note: The gravitational potential is zero at infinity
Projectile
1 1 2 2
21
1
1( ) 0 ( )
2 2
/
E E
E E
E E
K U K U
Gm m Gm mmv
R R
v Gm R
Projectile
Circular orbit
2
2
/
E
E
G m m mv
r r
v Gm r
Kepler’s Laws
1. Each planet moves in an elliptical orbit, with the sun at one focus of the ellipse
2. 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.
Geometry of an ellipse
Elliptical orbit
0d L
r Fdt
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