A glance at the accompanying figure will help to answer this
question. We must remember that the moon is not stationary, but
travelling at tremendous speed--so much so, that it circles the entire
earth every month. Now if the earth were absent the path of the moon
would be a straight line, say MB. If, however, the earth exerts
attraction, the moon would be pulled inward. Instead of following
the line MB it would follow the curved path MB'. And again, the moon
having arrived at B', is prevented from following the line B'C, but
rather B'C'. So that the path instead of being a straight line tends
to become curved. From Kepler's researches the probabilities were that
this curve would assume the shape of an ellipse rather than a circle.
The only reason, then, why the moon does not fall to the earth is on
account of its motion. Were it to stop moving even for the fraction
of a second it would come straight down to us, and probably few would
live to tell the tale.
Newton reasoned that what keeps the moon revolving around the earth is
the gravitational pull of the latter. The next important step was to
discover the law regulating this motion. Here Kepler's observations of
the movements of the planets around the sun was of inestimable value;
for from these Newton deduced the hypothesis that attraction varies
inversely as the square of the distance. Making use of this hypothesis,
Newton calculated what the attractive power possessed by the earth must
be in order that the moon may continue in its path. He next compared
this force with the force exerted by the earth in pulling the apple
to the ground, and found the forces to be identical! "I compared,"
he writes, "the force necessary to keep the moon in her orb with the
force of gravity at the surface of the earth, and found them answer
pretty nearly." One and the same force pulls the moon and pulls the
apple--the force of gravity. Further, the hypothesis that the force
of gravity varies inversely as the square of the distance had now
received experimental confirmation.
The next step was perfectly clear. If the moon's motion is controlled
by the earth's gravitational pull, why is it not possible that the
earth's motion, in turn, is controlled by the sun's gravitational
pull? that, in fact, not only the earth's motion, but the motion of
all the planets is regulated by the same means?
Here again Kepler's pioneer work was a foundation comparable to
reinforced concrete. Kepler, as we have seen, had shown that the earth
revolves around the sun in the form of an ellipse, one of the foci of
this ellipse being occupied by the sun. Newton now proved that such
an elliptic path was possible only if the intensity of the attractive
force between sun and planet varied inversely as the square of the
distance--the very same relationship that had been applied with such
success in explaining the motion of the moon around the earth!
Public-domain text, read in full here on John Shaqi.
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