University of Virginia Library

THE EARTH-MOON SYSTEM

Our Earth and Moon form a unique combination in that they are more nearly of the same size than are any other planet and its satellites in our system. It required a 26-inch telescope on the Earth to discover the tiny moons of Mars; but an astronomer on Mars does not need any telescope to see the Earth and Moon as a double planet—the only double planet in the solar system.

According to the Kantian school of hypotheses the Earth and Moon owe their unique character to the accident that two centers of condensation—two nuclei—not very unequal in mass, were formed close to each other and were endowed with or acquired motions such that they revolved around each other. They drew in the surrounding materials; one of the two bodies got somewhat the advantage of the other in gravitational attraction; it succeeded in building itself up more than the other nucleus did; and the Earth and the Moon were the result.

According to the Laplacean hypothesis, on the contrary, the Earth and Moon were originally one body, gaseous and in rotation. This ball of gas radiated heat, diminished in size, rotated more and more rapidly, and finally abandoned a ring of nebulosity, which later broke up and eventually condensed into one mass called the Moon. The central mass composed the Earth. It is a curious fact that Venus, which is only a shade smaller than the Earth, should not have divided into two bodies comparable with the Earth and Moon. Have the tides on Venus produced by the Sun always been strong enough to keep the rotation and revolution periods equal, as they are thought to be now, and thus to have given no opportunity for a rapidly rotating Venus to divide into two masses?

A third hypothesis of the Moon's origin is due principally to Darwin. He and Poincaré have shown that a great rotating mass of fluid matter, such as the Earth-Moon could be assumed to have been, by cooling, contracting and increasing rotation speed, would, under certain conditions thought to be reasonable, become unstable and eventually divide into two bodies revolving around their common center of mass, at first with their surfaces nearly in contact. Here would begin to act a tide-raising force which must have played, according to Darwin's deductions, a most important part in the further history of the Earth and Moon. The Earth would produce enormous tides in the Moon, and the Moon much smaller tides in the Earth. Both bodies would contract in size, through loss of heat, and would try to rotate more and more rapidly. The two rotating bodies would try to carry the matter in the tidal waves around with the rest of the materials

in the bodies, but the pull of each body upon the wave materials in the other would tend to slow down the speed of rotation. The tidal resistance to rotation would be slight if the bodies at any time were attenuated gaseous masses, for the friction within the surface strata would be slight. Nevertheless, there would eventually be a gradual slowing down of the Moon's rotation, a gradual slowing down of the Earth's rotation, and a slow increase in the distance between the two bodies. In other words, the Moon's day, the Earth's day and our month would gradually increase in length. Carried to its logical conclusion, the Moon would eventually turn the same face to the Earth, the Earth would eventually turn the same face to the Moon, and the Earth's day and the Moon's day would equal the month in length. The central idea in this logic is as old as Kant: in 1754 he published an important paper in which he said that tidal interactions between Earth and Moon had caused the Moon to keep the same face turned toward us, that the Earth's day was being very slowly lengthened, and that our planet would eventually turn the same face to the Moon. Laplace, a half-century later, proposed the action of such a force in connection with the explanation of lunar phenomena, and Helmholtz, just 100 years after Kant's paper was published, lent his support to this principle; but Sir George Darwin has been the great contributor to the subject. His popular volume, "The Tides,'' devotes several chapters to the effects of tidal friction upon the motions of two bodies in mutual revolution. We must pass over the difficult and complicated intermediate steps to Darwin's conclusions concerning the Earth and Moon, which are substantially as follows: the Earth and Moon were originally much closer together than they now are: after a very long period of time, amounting to hundreds of millions of years, the Moon will revolve around the Earth in 55 days instead of in 27 days as at present; and the Moon and Earth will then present the same faces constantly to each other. The estimated period of time required, and the final length of day and month, 55 days, are of course not insisted upon as accurate by Darwin.

These tidal forces were unavoidably active, it matters not if the Earth and Moon were originally one body, as Laplace and Darwin have postulated, or originally two bodies, growing up from two nuclei, in accordance with the Kantian school. Whether these forces have been sufficiently strong to have brought the Earth and Moon to their present relation, or will eventually equalize the Moon's day, the Earth's day, and the month, is a vastly more difficult question. Moulton's researches have cast serious doubt upon this conclusion. All such investigations are enormously difficult, and many questionable assumptions must be made if we seek to go back to the Moon's origin, or forward to its ultimate destiny.

Tidal waves, in order to be effective in reducing the rotational speed of a planet, must be accompanied by internal friction; and this requires that the planet be to some extent inelastic. It was the view of Darwin and others that the viscous state of the Earth and Moon permitted wave friction to come into play. Michelson has recently proved that the Earth has a high degree of elasticity. It deforms in response to tidal forces, but quickly recovers from the action of these forces. It therefore seems that the rate of tidal evolution of the Earth-Moon system at present and in the future must be extremely slow, and possibly almost negligible. What the conditions within the Earth and Moon were in the distant past is uncertain, but these bodies probably passed through viscous stages which endured through enormously long periods of time. No one seriously doubts that Jupiter, Saturn, Uranus and Neptune are now largely gaseous, and that they will evolve, through various degrees of viscosity, into the solid and comparatively elastic state. It is natural to assume that the Earth has already passed through an analogous experience.

The Moon turns always the same hemisphere toward the Earth. Observations of Venus and Mercury are prevailingly to the effect that those planets always turn the same hemispheres toward the Sun. Many, and perhaps all, of the satellites of Jupiter and Saturn seem to turn the same hemispheres always toward their respective planets. This widely prevailing phenomenon is no doubt due to a widely prevailing cause, which astronomers have all but unanimously attributed to tidal action.