them to suggest hypotheses to his mind; at last, by good luck, one of these worked.
Kepler's great achievement was the discovery of his three laws of Planetary motion. Two of these
he published in 1609, and the third in 1619. His first law states: The planets describe elliptic
orbits, of which the sun occupies one focus. His second law states: The line joining a planet to the
sun sweeps out equal areas in equal times. His third law states: The square of the period of
revolution of a planet is proportioned to the cube of its average distance from the sun.
Something must be said in explanation of the importance of these laws.
The first two laws, in Kepler's time, could only be proved in the case of Mars; as regards the other
planets, the observations were compatible with them, but not such as to establish them definitely.
It was not long, however, before decisive confirmation was found.
The discovery of the first law, that the planets move in ellipses, required a greater effort of
emancipation from tradition than a modern man can easily realize. The one thing upon which all
astronomers, without exception, had been agreed, was that all celestial motions are circular, or
compounded of circular motions. Where circles were found inadequate to explain planetary
motions, epicycles were used. An epicycle is the curve traced by a point on a circle which rolls on
another circle. For example: take a big wheel and fasten it flat on the ground; take a smaller wheel
which has a nail through it, and roll the smaller wheel (also flat on the ground) round the big
wheel, with the point of the nail touching the ground. Then the mark of the nail in the ground will
trace out an epicycle. The orbit of the moon, in relation to the sun, is roughly of this kind:
approximately, the earth describes a circle round the sun, and the moon meanwhile describes a
circle round the earth. But this is only an approximation. As observation grew more exact, it was
found that no system of epicycles would exactly fit the facts. Kepler's hypothesis, he found, was
far more closely in accord with the recorded positions of Mars than was that of Ptolemy, or even
that of Copernicus.
The substitution of ellipses for circles involved the abandonment of the æsthetic bias which had
governed astronomy ever since Pythagoras. The circle was a perfect figure, and the celestial orbs
were perfect bodies--originally gods, and even in Plato and Aristotle closely