Fg
G m1 m2
r2
Fe
K Q1 Q2
r2
ATOMIC NATURE OF MATTER
DOE-HDBK-1019/1-93
Atomic and Nuclear Physics
NP-01
Page 8
Rev. 0
Newton stated that the gravitational force between two bodies is directly proportional to the
masses of the two bodies and inversely proportional to the square of the distance between the
bodies. This relationship is shown in the equation below.
where:
F
=
gravitational force (newtons)
g
m
=
mass of first body (kilograms)
1
m
=
mass of second body (kilograms)
2
G
=
gravitational constant (6.67 x 10
N-m /kg )
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2
2
r
=
distance between particles (meters)
The equation illustrates that the larger the masses of the objects or the smaller the distance
between the objects, the greater the gravitational force. So even though the masses of nucleons
are very small, the fact that the distance between nucleons is extremely short may make the
gravitational force significant. It is necessary to calculate the value for the gravitational force and
compare it to the value for other forces to determine the significance of the gravitational force
in the nucleus. The gravitational force between two protons that are separated by a distance of
10
meters is about 10
newtons.
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Coulomb's Law can be used to calculate the force between two protons. The electrostatic force
is directly proportional to the electrical charges of the two particles and inversely proportional
to the square of the distance between the particles. Coulomb's Law is stated as the following
equation.
where:
F
=
electrostatic force (newtons)
e
K
=
electrostatic constant (9.0 x 10 N-m /C )
9
2
2
Q
=
charge of first particle (coulombs)
1
Q
=
charge of second particle (coulombs)
2
r
=
distance between particles (meters)
Using this equation, the electrostatic force between two protons that are separated by a distance
of 10
meters is about 10
newtons. Comparing this result with the calculation of the
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12
gravitational force (10
newtons) shows that the gravitational force is so small that it can be
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neglected.
