It must have been at least 50,000,000 years ago.
It may have been very much earlier. This crisis was the interesting
occasion when the moon was born. The length of the day was only a very
few hours. If we call it three hours we shall not be far from the truth.
Purhaps you may think that if we looked back to a still earlier epoch,
the day would become still less, and finally disappear altogether. This
is, however, not the case. The day can never have been much less than
three hours in the present order of things. Everybody knows that the
earth is not a sphere, but there is a protuberance at the equator, so
that, as our school books tell us, the earth is shaped like an orange.
It is well known that this protuberance is due to the rotation of
the earth on its axis, by which the equatorial parts bulge out by
centrifugal force. The quicker the earth rotates the greater is the
protuberance. If, however, the rate of rotation exceeds a certain limit,
the equatorial portion of the earth could no longer cling together. The
attraction which unites them would be overcome by centrifugal force, and
a general break up would occur. It can be shown that the rotation of the
earth, when on the point of rupture, corresponds to a length of the day
somewhere about the critical value of three hours, which we have already
adopted.
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