Letters on Astronomy: in which the Elements of the Science are Familiarly Explained in Connection with Biographical Sketches of the Most Eminent AstronomersOlmsted, Denison
Science
Letters on Astronomy: in which the Elements of the Science are Familiarly Explained in Connection with Biographical Sketches of the Most Eminent Astronomers
Olmsted, Denison
Astronomy
The sun is one million four hundred thousand times as large as the
earth; but its matter is not more than about one fourth as dense as that
of the earth, being only a little heavier than water, while the average
density of the earth is more than five times that of water. Still, on
account of the immense magnitude of the sun, its entire quantity of
matter is three hundred and fifty thousand times as great as that of the
earth. Now, the force of gravity in a body is greater, in proportion as
its quantity of matter is greater. Consequently, we might suppose, that
the weight of a body (weight being nothing else than the measure of the
force of gravity) would be increased in the same proportion; or, that a
body, which weighs only one pound at the surface of the earth, would
weigh three hundred and fifty thousand pounds at the sun. But we must
consider, that the attraction exerted by any body is the same as though
all the matter were concentrated in the centre. Thus, the attraction
exerted by the earth and by the sun is the same as though the entire
matter of each body were in its centre. Hence, on account of the vast
dimensions of the sun, its surface is one hundred and twelve times
further from its centre than the surface of the earth is from its
centre; and, since the force of gravity diminishes as the square of the
distance increases, that of the sun, exerted on bodies at its surface,
is (so far as this cause operates) the square of one hundred and twelve,
or twelve thousand five hundred and forty-four times less than that of
the earth. If, therefore, we increase the weight of a body three hundred
and fifty-four thousand times, in consequence of the greater amount of
matter in the sun, and diminish it twelve thousand five hundred and
forty-four times, in consequence of the force acting at a greater
distance from the body, we shall find that the body would weigh about
twenty-eight times more on the sun than on the earth. Hence, a man
weighing three hundred pounds would, if conveyed to the surface of the
sun, weigh eight thousand four hundred pounds, or nearly three tons and
three quarters. A limb of our bodies, weighing forty pounds, would
require to lift it a force of one thousand one hundred and twenty
pounds, which would be beyond the ordinary power of the muscles. At the
surface of the earth, a body falls from rest by the force of gravity, in
one second, sixteen and one twelfth feet; but at the surface of the sun,
a body would, in the same time, fall through four hundred and
forty-eight and seven tenths feet.
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