It is well known that if
each planet moved only under the influence of the gravitating
force of the sun its motion would accord rigorously with the laws
of Kepler, and the problems of theoretical astronomy would be
greatly simplified. When, therefore, the results of Kepler's laws
were compared with ancient and modern observations it was found
that they were not exactly represented by the theory. It was
evident that the elliptic orbits of the planets were subject to
change, but it was entirely beyond the power of investigation, at
that time, to assign any cause for such changes. Notwithstanding
the simplicity of the causes which we now know to produce them,
they are in form extremely complex. Without the knowledge of the
theory of gravitation it would be entirely out of the question to
form any tables of the planetary motions which would at all satisfy
our modern astronomers.
When the theory of universal gravitation was propounded by Newton
he showed that a planet subjected only to the gravitation of a
central body, like the sun, would move in exact accordance with
Kepler's laws. But by his theory the planets must attract one
another and these attractions must cause the motions of each to
deviate slightly from the laws in question.
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