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 Poincare 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.
BINARY STAR SYSTEMS
That an original mass actually divided to form the Earth and Moon, according to the Laplacian or the Darwin-Poincare principle, seems to be extremely doubtful, especially on account of their diminutive sizes, and I greatly prefer to think that the Earth and Moon were built up from two nuclei; but that very much greater masses, masses larger on the average than our Sun, composing highly attenuated stars, have divided each into two masses to form many or most of our double stars, I firmly believe. The two component stars would in such a case at first revolve around each other with their surfaces almost or quite in contact. Tidal forces would very gradually cause the bodies to move in orbits of larger and larger size, with correspondingly longer periods of revolutions, and the orbits would become constantly more eccentric. While these processes were under way the component bodies would be radiating heat and growing smaller, and their spectra would be changing into the more advanced types. We can not hope to watch such changes as they occur, but we can, I think, find abundant illustrations of these processes in the double stars. I have given reasons for believing that one star in every two and one half, as a minimum proportion, is not the single star which it appears to be to the eye or in the telescope, but is a system of two or more suns in mutual revolution. The formation of double stars, therefore, is not a sporadic process: it is one of the straightforward results of the evolutionary process.
Some of the variable stars offer strong evidence as to the early life of the double stars. The so-called beta Lyrae variables vary continuously in brightness, as if they consist in each case of two stars so close together that their surfaces are actually in contact in some pairs and nearly in contact in others, so that from our point of view the two stars mutually eclipse each other. When the two stars are in line with us we have minimum brightness. When they have moved a quarter-revolution farther, and the line joining them is at right angles to our line of sight, so to speak, we have maximum brightness. In every known case the beta Lyrae pairs of stars have spectra of the very early types. Some of them even contain bright lines in their spectra. The densities of these great stars are known to be exceedingly low, in some cases much lower on the average than that of the atmosphere which we breathe.
About 80 Algol variable stars are known. These are double stars whose light is constant except during the short time when one of the components in each system passes between us and the other component. All double stars would be Algol variables if we were exactly in the planes of their orbits. That so few Algols have been observed amongst the tens of thousands of double stars, is easily explained. The two component stars in the few known Algol systems are so great in diameter, in proportion to the size of their orbits, that eclipses are observable throughout a wide volume of space, and the eclipses are of long duration relatively to the revolution period. Their densities are, so far as we have been able to determine them, on an average less than 1/10th of the Sun's density. Let us note well that their spectra, so far as we have been able to determine them, are of the early types; mostly helium and hydrogen stars, and a very few of the Class F, intermediate between the hydrogen and solar stars. There are no known Algols of the Classes G, K, and M: these stars are very condensed and therefore small in size, as compared with stars of Classes B and A; and the components of double stars of these classes are on the average much denser and therefore smaller in size than the components in Classes B and A double stars; the components are much farther apart in Classes G to M doubles than in Classes B and A doubles; and for these reasons eclipses in Classes G to M doubles occur but rarely for observers scattered throughout space. It is difficult to avoid the conclusion that the components of double stars separate more and more widely with the progress of time. The conclusions which we have earlier drawn from visual double stars are in full harmony with the argument.