At the same time, we might, without any inexactness, agree that
the mass of a heavenly body should be fixed by the weight it would
have in New York. As we could not even imagine a planet at New
York, because it may be larger than the earth itself, what we are
to imagine is this: Suppose the planet could be divided into a
million million million equal parts, and one of these parts
brought to New York and weighed. We could easily find its weight
in pounds or tons. Then multiply this weight by a million million
million, and we shall have a weight of the planet. This would be
what the astronomers might take as the mass of the planet.
With these explanations, let us see how the weight of the earth is
found. The principle we apply is that round bodies of the same
specific gravity attract small objects on their surface with a
force proportional to the diameter of the attracting body. For
example, a body two feet in diameter attracts twice as strongly as
one of a foot, one of three feet three times as strongly, and so
on. Now, our earth is about 40,000,000 feet in diameter; that is
10,000,000 times four feet. It follows that if we made a little
model of the earth four feet in diameter, having the average
specific gravity of the earth, it would attract a particle with
one ten-millionth part of the attraction of the earth.
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