Time and Tide: A Romance of the MoonBall, Robert S. (Robert Stawell)
History
Time and Tide: A Romance of the Moon
Ball, Robert S. (Robert Stawell)
Moon; Satellites; Tides
I have already shown that the fact of the ebbing and the flowing of
the tide necessitates an expenditure of energy, and we saw that this
energy must come either from that stored up in the earth by its
rotation, or from that possessed by the moon in virtue of its distance
and revolution. The law of the conservation of spin will enable us to
decide at once as to whence the tides get their energy. Suppose they
took it from the moon, the moon would then lose in energy, and
consequently come nearer the earth. The quantity of spin contributed
by the moon would therefore be lessened, and accordingly the spin to
be made up by the earth would be increased. That means, of course,
that the velocity of the earth rotating on its axis must be increased,
and this again would necessitate an increase in the earth's rotational
energy. It can be shown, too, that to keep the total spin right, the
energy of the earth would have to gain more than the moon would have
lost by revolving in a smaller orbit. Thus we find that the total
quantity of energy in the system would be increased. This would lead
to the absurd result that the action of the tides manufactured energy
in our system. Of course, such a doctrine cannot be true; it would
amount to a perpetual motion! We might as well try to get a
steam-engine which would produce enough heat by friction not only to
supply its own boilers, but to satisfy all the thermal wants of the
whole parish. We must therefore adopt the other alternative. The tides
do not draw their energy from the moon; they draw it from the store
possessed by the earth in virtue of its rotation.
We can now state the end of this rather long discussion in a very
simple and brief manner. Energy can only be yielded by the earth at
the expense of some of the speed of its rotation. The tides must
therefore cause the earth to revolve more slowly; in other words, _the
tides are increasing the length of the day_.
The earth therefore loses some of its velocity of rotation;
consequently it does less than its due share of the total quantity of
spin, and an increased quantity of spin must therefore be accomplished
by the moon; but this can only be done by an enlargement of its orbit.
Thus there are two great consequences of the tides in the earth-moon
system--the days are getting longer, the moon is receding further.
Public-domain text, read in full here on John Shaqi.
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