These two laws Kepler published as early as 1609. Many years more
of patient investigation were required before he found out the
secret of the relation between planetary distances and times of
revolution which his third law expresses. In 1618, however, he
was able to formulate this relation also, as follows:

3. The squares of the distance of the various planets from the
sun are proportional to the cubes of their periods of revolution
about the sun.


All these laws, it will be observed, take for granted the fact
that the sun is the centre of the planetary orbits. It must be
understood, too, that the earth is constantly regarded, in
accordance with the Copernican system, as being itself a member
of the planetary system, subject to precisely the same laws as
the other planets. Long familiarity has made these wonderful laws
of Kepler seem such a matter of course that it is difficult now
to appreciate them at their full value. Yet, as has been already
pointed out, it was the knowledge of these marvellously simple
relations between the planetary orbits that laid the foundation
for the Newtonian law of universal gravitation. Contemporary
judgment could not, of course, anticipate this culmination of a
later generation. What it could understand was that the first law
of Kepler attacked one of the most time-honored of metaphysical
conceptions--namely, the Aristotelian idea that the circle is the
perfect figure, and hence that the planetary orbits must be
circular. Not even Copernicus had doubted the validity of this
assumption. That Kepler dared dispute so firmly fixed a belief,