§ 17

Origin of the Moon

But there is another aspect of the tides which is of vastly greater interest and importance than the theory we have just been discussing. In the hands of Sir George H. Darwin, the son of Charles Darwin, the tides had been made to throw light on the evolution of our solar system. In particular, they have illustrated the origin and development of the system formed by our earth and moon. It is quite certain that, long ages ago, the earth was rotating immensely faster than it is now, and that the moon was so near as to be actually in contact with the earth. In that remote age the moon was just on the point of separating from the earth, of being thrown off by the earth. Earth and moon were once one body, but the high rate of rotation caused this body to split up into two pieces; one piece became the earth we now know, and the other became the moon. Such is the conclusion to which we are led by an examination of the tides. In the first place let us consider the energy produced by the tides. We see evidences of this energy all round the word's coastlines. Estuaries are scooped out, great rocks are gradually reduced to rubble, innumerable tons of matter are continually being set in movement. Whence is this energy derived? Energy, like matter, cannot be created from nothing; what, then, is the source which makes this colossal expenditure possible.

The Earth Slowing down

The answer is simple, but startling. The source of tidal energy is the rotation of the earth. The massive bulk of the earth, turning every twenty-four hours on its axis, is like a gigantic flywheel. In virtue of its rotation it possesses an enormous store of energy. But even the heaviest and swiftest flywheel, if it is doing work, or even if it is only working against the friction of its bearings, cannot dispense energy for ever. It must, gradually, slow down. There is no escape from this reasoning. It is the rotation of the earth which supplies the energy of the tides, and, as a consequence, the tides must be slowing down the earth. The tides act as a kind of brake on the earth's rotation. These masses of water, held back by the moon, exert a kind of dragging effect on the rotating earth. Doubtless this effect, measured by our ordinary standards, is very small; it is, however, continuous, and in the course of the millions of years dealt with in astronomy, this small but constant effect may produce very considerable results.

But there is another effect which can be shown to be a necessary mathematical consequence of tidal action. It is the moon's action on the earth which produces the tides, but they also react on the moon. The tides are slowing down the earth, and they are also driving the moon farther and farther away. This result, strange as it may seem, does not permit of doubt, for it is the result of an indubitable dynamical principle, which cannot be made clear without a mathematical discussion. Some interesting consequences follow.

Since the earth is slowing down, it follows that it was once rotating faster. There was a period, a long time ago, when the day comprised only twenty hours. Going farther back still we come to a day of ten hours, until, inconceivable ages ago, the earth must have been rotating on its axis in a period of from three to four hours.

At this point let us stop and inquire what was happening to the moon. We have seen that at present the moon is getting farther and farther away. It follows, therefore, that when the day was shorter the moon was nearer. As we go farther back in time we find the moon nearer and nearer to an earth rotating faster and faster. When we reach the period we have already mentioned, the period when the earth completed a revolution in three or four hours, we find that the moon was so near as to be almost grazing the earth. This fact is very remarkable. Everybody knows that there is a critical velocity for a rotating flywheel, a velocity beyond which the flywheel would fly into pieces because the centrifugal force developed is so great as to overcome the cohesion of the molecules of the flywheel. We have already likened our earth to a flywheel, and we have traced its history back to the point where it was rotating with immense velocity. We have also seen that, at that moment, the moon was barely separated from the earth. The conclusion is irresistible. In an age more remote the earth did fly in pieces, and one of those pieces is the moon. Such, in brief outline, is the tidal theory of the origin of the earth-moon system.

The Day Becoming Longer

At the beginning, when the moon split off from the earth, it obviously must have shared the earth's rotation. It flew round the earth in the same time that the earth rotated, that is to say, the month and the day were of equal length. As the moon began to get farther from the earth, the month, because the moon took longer to rotate round the earth, began to get correspondingly longer. The day also became longer, because the earth was slowing down, taking longer to rotate on its axis, but the month increased at a greater rate than the day. Presently the month became equal to two days, then to three, and so on. It has been calculated that this process went on until there were twenty-nine days in the month. After that the number of days in the month began to decrease until it reached its present value or magnitude, and will continue to decrease until once more the month and the day are equal. In that age the earth will be rotating very slowly. The braking action of the tides will cause the earth always to keep the same face to the moon; it will rotate on its axis in the same time that the moon turns round the earth. If nothing but the earth and moon were involved this state of affairs would be final. But there is also the effect of the solar tides to be considered. The moon makes the day equal to the month, but the sun has a tendency, by still further slowing down the earth's rotation on its axis, to make the day equal to the year. It would do this, of course, by making the earth take as long to turn on its axis as to go round the sun. It cannot succeed in this, owing to the action of the moon, but it can succeed in making the day rather longer than the month.

Surprising as it may seem, we already have an illustration of this possibility in the satellites of Mars. The Martian day is about one half-hour longer than ours, but when the two minute satellites of Mars were discovered it was noticed that the inner one of the two revolved round Mars in about seven hours forty minutes. In one Martian day, therefore, one of the moons of Mars makes more than three complete revolutions round that planet, so that, to an inhabitant of Mars, there would be more than three months in a day.

BIBLIOGRAPHY

Arrhenius, Svante, Worlds in the Making.
Clerk-Maxwell, James, Matter and Motion.
Daniell, Alfred, A Text-Book of the Principles of Physics.
Darwin, Sir G. H., The Tides.
Holman, Matter, Energy, Force and Work.
Kapp, Gisbert, Electricity.
Kelvin, Lord, Popular Lectures and Addresses. Vol. i. Constitution of Matter.
Lockyer, Sir Norman, Inorganic Evolution.
Lodge, Sir Oliver, Electrons and The Ether of Space.
Perrin, Jean, Brownian Movement and Molecular Reality.
Soddy, Frederick, Matter and Energy and The Interpretation of Radium.
Thompson, Silvanus P., Light, Visible and Invisible.
Thomson, Sir J. J., The Corpuscular Theory of Matter.