Gravitation
Another example of circular motion is that of the planets around the sun.
Here the only force that acts on the planets is that of gravity.
When Newton first
published his theory of motion, he also included a theory of gravity.
Newton had
concluded that the gravitational force between two bodies was proportional to the
product of the masses of the two bodies and inversely proportional to the square
of the distance between them.
Thus
F
G
m m
r
=
1
2
2
(7.1)
The constant
G
is called the gravitational constant, and it has been determined
by experiment to have a value of
G
= 6.672 x 10
11
Nm
2
/kg
2
The force acts along a line from one object to another.
It can be shown that for
uniform spheres (which the planets can be approximated to be), the sphere can
be replaced by a point source at the center of the sphere with the same mass as
the original sphere.
Interestingly enough, this same effect causes the force that
gravity exerts on us to get weaker as we go deeper into the Earth's interior.
In
fact, at the center of the Earth, the force of gravity on a person would be zero!
Example
:
Although gravity is the force that holds the universe together, it is by far
the weakest of the four known forces.
To see this, consider two protons, each
with a mass of 1.673 x 10
27
kg.
It turns out that the force that one electric charge
exerts on another is given by a relation similar to that of gravitation, namely
F
k
q q
r
em
=
1
2
2
where
k
is Coulomb's constant, with a value of
k
= 8.9876 x 10
9
Nm
2
/C
2
.
However, unlike the gravitational force, this force is pointing outward along the
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 Spring '09
 Knott
 Physics, Circular Motion, Force, Gravity, General Relativity, Fundamental interaction

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