of each planet is
connected with its average distance by this law; but there is another
application of Kepler's law which gives us information of the distance
and the period of the moon in former stages of the earth-moon history.
Although the actual path of the moon is of course an ellipse, yet that
ellipse is troubled, as is well known, by many disturbing forces, and
from this cause alone the actual path of the moon is far from being
any of those simple curves with which we are so well acquainted. Even
were the earth and the moon absolutely rigid particles, perturbations
would work all sorts of small changes in the pliant curve. The
phenomena of tidal evolution impart an additional element of
complexity into the actual shape of the moon's path. We now see that
the ellipse is not merely subject to incessant deflections of a
periodic nature, it also undergoes a gradual contraction as we look
back through time past; but we may, with all needful accuracy for our
present purpose, think of the path of the moon as a circle, only we
must attribute to that circle a continuous contraction of its radius
the further and the further we look back. The alteration in the
radius will be even so slow, that the moon will accomplish thousands
of revolutions around the earth without any appreciable alteration in
the average distance of the two bodies. We can therefore think of the
moon as revolving at every epoch in a circle of special radius, and as
accomplishing that revolution in a special time. With this
understanding we can now apply Kepler's law to the several stages of
the moon's past history. The periodic time of each revolution, and the
mean distance at which that revolution was performed, will be always
connected together by the formula of Kepler. Thus to take an instance
in the very remote past. Let us suppose that the moon was at one
hundred and twenty thousand miles instead of two hundred and forty
thousand, that is, at half its present distance. Applying the law of
Kepler, we see that the time of revolution must then have been only
about ten days instead of the twenty-seven it is now. Still further,
let us suppose that the moon revolves in an orbit with one-tenth of
the diameter it has at present, then the cube of 10 being 1000, and
the square root of 1000 being 31.6, it follows that the month must
have been less than the thirty-first part of what it is at present,
that is, it must have been considerably less than one of our p