Universal Law of Gravitation
So because of Newton’s 3rd law every body
in the universe exerts a force of attraction on
every other body.
• This is Newton’s Universal Law of Gravitation
The force between two
objects, due to their masses,
is called the gravitational force
(Fg)- in this case it’s
not Earth specific and is not
9.81 m/s2).
GmM
Fg 
2
r
Masses of the 2 objects
Universal
Gravitational
2
Constantm
6.67 x 10-11 N  2
kg
GmM
Fg 
2
r
Distance between
the objects
What is the gravitational force
between the Earth and the Moon?
mEarth = M = 6.0 x 1024 kg
mMoon = m = 7.4 x 1022 kg
r = 3.8 x 108 m
2
m
G = 6.67 x 10-11 N  kg 2
What if the distance between the
Earth and the Moon was doubled?
What if the distance between the Earth and
the Moon was tripled?
What if the distance between the Earth and
the Moon was quadrupled?
What is the gravitational force
between the Earth and Venus?
mEarth = M = 6.0 x 1024 kg
mVenus = m = 5.0 x 1024 kg
r = 3.8 x 1010 m
2
m
G = 6.67 x 10-11 N  kg 2
Solving the ULG equation using
variables:
GmM
Fg 
r2
= 100 N
Fg’ = ? If M’ = 3M, and r’ = 2r
F’g = GmM’ = Gm3M
(2r)2
r’2
= Gm3M = 3 GmM = 3 (100 N)
4r2
4 r2
4
75 N
There is also a way to determine the
gravitational field around one object:
GmM
Fg 
2
r
For one object this is weight, so this becomes…
This is now
the gravitational
Field Strength
GmM
w
2
r
GmM
mg 
r2
=
GmM

mg
 
r2
=
GM
g 2
r
For the Earth the gravitational
field strength should be 9.81
m/s2…find it.
• Radius of the Earth – 6.37 x 106 m
For the Moon the gravitational
field strength should be
2
1.6 m/s …find it.
• Radius of the Moon – 1.7 x 106 m
Both the ULG and the GFS
follow the Inverse square law:
• ULG-If the distance between two objects is
doubled the gravitational attraction is (1/4)
of the original.
OR
• GFS-If we travel beyond the Earth by a
distance that is double it’s radius than we
will only feel a quarter of Earth’s
gravitational pull (9.81 m/s2/4 = 2.45 m/s2).
r = 6.4 x 106 m
1x
9.81 m/s2
2x
3x
1/4 =
2.24
1/9 =
1.09
4x
1/16 =
.61
Gravitational Field Strength
Inverse Square Law
Gravitational
Field Strength
12
10
8
6
4
2
0
0
10000000
20000000
Distance(m)
30000000
HW:
• The gravitational attraction between the Earth
and Mars is 8.7 x 1016 N. The distance between
the two planets is 5.5 x 1010m. Earth has a
mass of 6.0 x 1024 kg. What’s the mass of
Mars?