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Every object and all matter attracts
other matter to it through the force of gravity. The
Universal Gravity Equation defines how much this force
is as a function of the masses of the objects and the
distance between them. This equation can be used to
verify the acceleration of gravity on Earth. It also has
other applications in Astronomy and Nuclear Science.
Questions you may have are:
-
What is the Universal Gravity
Equation?
-
What are the gravity equations on
Earth?
-
How are these equations used?
Universal Equation
Two objects will attract each other
proportional to their masses and inversely proportional
to the square of distance between them. If the mass of
one body is designated as M, the mass of the other as m,
and the distance between them is r, then the force of
attraction F between the two bodies is:
F =
G*M*m/r2
where G is the universal gravitational
constant.
G = 6.67*10-11 N-m2/kg2. The units of G
can be stated as Newton meter-squared per
kilogram-squared or Newton square meter per square
kilogram.
Since force = mass times acceleration,
the universal gravity equation implies that as objects
are attracted and get closer together, the force
increases and the acceleration between them also
increases.
Gravity acceleration on Earth
The acceleration of gravity on the Earth
has be determined by experiments and measurement. But by
applying the Universal Gravity Equation, we can verify
that the acceleration of gravity of objects near the
Earth is g = 9.8 m/s2 (meters per seconds-squared).
The following material is the derivation
of the simple gravity equation near the Earth from the
Universal Gravity Equation.
Let M equal the mass of the Earth. The
approximate value for M = 6*1024 kilograms (6 followed
by 24 zeros). Also, let m be the mass of some object
near the surface of the Earth. As you will see later, we
don't need to know the mass of the object.
This takes a little stretch of the
imagination, but let's assume that an object near the
surface of the Earth is attracted toward the center of
the Earth, as if all of the Earth's matter was
compressed at that point. If r was the radius of the
Earth, then the object near the surface would be a
distance of r from the center of gravity.
The approximate radius of the Earth is
6.376*106 meters, and the distance between M and m is r
= 6.376*106 m. Also, r2 = 4*1012 m2 (meters-squared or
square meters).
Since a Newton is a kg-m/s2, we change
the units of G from N-m2/kg2 to m3/s2kg (meter-cubed per
second-squared-kilograms). This is done so that the
units are all the same.
Now let's put the values into the
Universal Gravity Equation:
F = G*M*m/r2 = 6.67*10-11 m3/s2kg *
6*1024 kg * m / 4*1012 m2
F = m*10 m/s2
(Note how the various units will cancel
out in the multiplication and division. This is
important to verify that your units and the equation are
correct.)
Now we know that the force of gravity
near the Earth is:
F = m*g
Thus, from the Universal Gravity
Equation calculations above, g = 10 m/s2. Since we used
approximate values for r and M, that value is
approximately g = 9.8 m/s2 and the holds for
measurements on Earth.
Other applications
There are other applications of the
Universal Gravity Equation.
The equation can be use to measure the
force of attraction between the Earth and the Moon and
predict the speed of the Moon around the Earth by
applying the principle of centrifugal inertia force. It
can also be used to measure the forces and motion of
other astronomical bodies in space.
The Universal Gravity Equation is also
sometimes used to calculate the gravitational attraction
between molecules or atoms.
In conclusion
All matter has gravity, which is a force
that attracts other matter. The Universal Gravity
Equation states that the force of gravity depends on the
masses of the objects and the square of the distance
between them. This equation can be used to determine the
acceleration of gravity on Earth and other applications. |
