Law of Gravitation
In 1687 Isaac Newton published his Law of Gravitation which is stated mathematically in
the following form:
1
2
2
g
Gm m
F
r
=
Law of Gravitation
2
11
2
6.672
10
Nm
G
kg
−
=
×
(Gravitation Constant)
F
g
F
g
m
1
m
2
r
R
1
m
1
R
2
m
2
F
g
F
g
r
Although the Law of Gravity applies to particles (point masses), Newton also showed
that it applies to spherically symmetric bodies because they behave as if their mass was
concentrated at their center.
If the bodies are not symmetrical,
you can still compute
the gravitational force between them by using the distance between the center of mass
of both objects.
Weight
Consider an object at rest on earth’ surface:
R
E
M
E
m
N
F
g
2
E
g
E
GM
m
W
F
R
=
=
Weight of an object near earth’s surface
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Acceleration of Gravity
Consider an object of mass ‘m’ in freefall at a height ‘h’ from earth’s surface:
R
E
M
E
m
F
g
h
+y
a
y
=
g
(
)
2
y
g
y
E
E
F
F
ma
GM
m
mg
R
h
=
=
=
+
∑
(
)
2
E
E
GM
g
R
h
=
+
Acceleration of Gravity
At surface of earth
h
= 0:
(
)
(
)
2
11
24
2
2
2
2
6
6.672
10
5.97
10
9.8
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 Fall '09
 Luna
 Gravity, Mass, Potential Energy, General Relativity, Newton's law of universal gravitation

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