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What is the mass of the Earth?
The Earth was first weighed by Henry Cavendish. He was a chemist as well as a
physicist and he also found hydrogen. (By the way hydrogen means "able to generate water")
Cavendish weighted the Earth by measuring the constant in Newton's Law of Universal
Gravitation which is .
Then what is the Newton's Law of Universal Gravitation?
Every particle in the universe exerts an attractive force on every other particle.
A particle is a piece of matter, small enough in size to be regarded as a mathematical
point. For two particles, which have masses
and which are separated by a distance
, the force that each exerts on the other is directed along the line joining
the particles and has a magnitude given by
Force is mass times acceleration expressed in
or (Newton). In summary, and thus,
. From the acceleration
of a falling body and Newton's Law of Universal Gravitation, Cavendish already knew
the mass of the Earth times :
In the following equations:
=force,
=mass,
=gravity,
=Universal Gravitational constant,
=mass of Earth,
=radius of Earth.
To isolate mass from gravity, he had to
measure the value of . This could be done by finding the force between
two known masses unknown distance apart. It had to be done very carefully because
the gravitational force between normal size mass is so very small. A bar suspended
by a delicate fiber holds a mass at each end. Two larger masses are added. The
gravitational force between these masses causes the bar to twist. By timing the
sway of the bar he could deduce the stiffness of the fiber and thus the force.
Switching the masses around makes the bar twist in the opposite direction to correct
for asymmetries in the experiment. With this delicate experiment and a lot of care,
Cavendish measured the gravitational constant and indirectly weighed the Earth.
And here it is, the mass of the Earth.
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