Newton’s Law of Gravitation
Gm1m2
Fg 
r2
G  6.67  10 11 N  m 2 / kg 2  gravitational const
r
F g (2 on 1)
m2
F g (1 on 2)
Gravity is one of the fundamental forces of nature.
Gravitation force always is attractive.
Gravitation force exist between any two objects and always act
along the line joining the two objects.
Determining the Value of G
For determining of G, Henry Cavendish in 1798 used an instrument
called a torsion balance. A modern version of the Cavendish torsion
balance is shown below.
2
G
Fg r
m1m2
Galaxy
Gravitational force is one
of the fundamental forces
acting in our galaxy
Planets of the Solar System
Gravitational force is the
main force of interaction
between the sun and
planets including Earth
Weight
The weight of a body is the total gravitational force acting on that body
Consider an object near
the surface of the earth:
Mm
w  G 2  mg
r


Mm
w  G 2  rˆ   mg
r
What happened if
the object will move
far from the earth?
Weight:
Mm
w  G 2  mg
r
M
g G 2
r
Example: If man’s weight is 1000 N
when stand on Earth, what would his
weight be if he stood on a scale model
of Earth made of the same materials
but scaled to half the size?
1. 125 N
2. 150 N
3. 250 N
 4r 3 

M  V   
 3 
Earth
4. 500 N
5. 1000 N
6 400 km
12 800 km
Model of Earth
 4r 3  m  4 
Mm
 2   Gmr
w  G 2  G 
r
 3 
 3 r
w~ r
w2 r2

w1 r1
w2  w1
r2
 500 N
r1
Gravitational potential energy
r2
 
U  U 2  U 1  W    Fdr    Fdr
r2
r1
r1
r2
Mm
GMm GMm
U   G 2 dr  

r2
r1
r
r1
Mm
U (r )  G
r
Near the Earth’s surface: r = R + h; h/R <<1
U (h)  G
Mm
Mm
1
Mm
1  h / R   G Mm  G Mmh
 G
 G
Rh
R 1 h / R
R
R
R2
M
U (h)  G 2 mh  const  mgh  const
R
Escape speed
vi
Ki  Ui  K f  U f
R
2
mvi2
Mm mv f
Mm
G

G
2
ri
2
rf
ri  R
rf  
vf  0
vi  ?
mvi2
Mm
G
0
2
R
vi 

vi 

2 6.67  10 11 N  m 2 / kg 2 5.79  10 24 kg
6.38  10 6 m
2GM
R

vi  1.12  10 4 m / s  11.2 km / s