A Popular History of Astronomy During the Nineteenth Century / Fourth Edition

by Agnes M. Clerke

To recapitulate. Analysis tracks backward the two bodies until it leaves them in very close contiguity, one rotating and the other revolving in approximately the same time, and that time certainly not far different from, and quite possibly identical with, the critical period of instability for the terrestrial spheroid. "Is this," Professor Darwin asks, "a mere coincidence, or does it not rather point to the break-up of the primeval planet into two masses in consequence of a too rapid rotation?"[1175]

We are tempted, but are not allowed to give an unqualified assent. Mr. James Nolan of Victoria has made it clear that the moon could not have subsisted as a continuous mass under the powerful disruptive strain which would have acted upon it when revolving almost in contact with the present surface of the earth; and Professor Darwin, admitting the objection, concedes to our satellite, in its initial stage, the alternative form of a flock of meteorites.[1176] But such a congregation must have been quickly dispersed, by tidal action, into a meteoric ring. The same investigator subsequently fixed 6,500 miles from centre to centre as the minimum distance at which the moon could have revolved in its entirety; and he concluded it "necessary to suppose that, after the birth of a satellite, if it takes place at all in this way, a series of changes occur which are quite unknown."[1177] The evidence, however, for the efficiency of tidal friction in bringing about the actual configuration of the lunar-terrestrial system is not invalidated by this failure to penetrate its natal mystery. Under its influence the principal elements of that system fall into interdependent mutual relations. It connects, casually and quantitatively, the periods of the moon's revolution and of the earth's rotation, the obliquity of the ecliptic, the inclination and eccentricity of the lunar orbit. All this can scarcely be accidental.

Professor Darwin's first researches on this subject were communicated to the Royal Society, December 18, 1879. They were followed, January 20, 1881,[1178] by an inquiry on the same principles into the earlier condition of the entire solar system. The results were a warning against hasty generalisation. They showed that the lunar-terrestrial system, far from being a pattern for their development, was a singular exception among the bodies swayed by the sun. Its peculiarity resides in the fact that the moon is proportionately by far the most massive attendant upon any known planet. Its disturbing power over its primary is thus abnormally great, and tidal friction has, in consequence, played a predominant part in bringing their mutual relations into their present state.

The comparatively late birth of the moon tends to ratify this inference. The dimensions of the earth did not differ (according to our present authority) very greatly from what they now are when her solitary offspring came, somehow, into existence. This is found not to have been the case with any other of the planets. It is unlikely that the satellites of Jupiter, Saturn, or Mars (we may safely add, of Uranus or Neptune) ever revolved in much narrower orbits than those they now traverse; it is practically certain that they did not, like our moon, originate very near the present surfaces of their primaries.[1179] What follows? The tide-raising power of a body grows with vicinity in a rapidly accelerated ratio. Lunar tides must then have been on an enormous scale when the moon swung round at a fraction of its actual distance from the earth. But no other satellite with which we are acquainted occupied at any time a corresponding position. Hence no other satellite ever possessed tide-raising capabilities in the least comparable to those of the moon. We conclude once more that tidal friction had an influence here very different from its influence elsewhere. Quite possibly, however, that influence may be more nearly spent than in less advanced combinations of revolving globes. Mr. Nolan concluded in 1895[1180] that it still retains appreciable efficacy in the several domains of the outer planets. The moons of Jupiter and Saturn are, by his calculations, in course of sensible retreat, under compulsion of the perennial ripples raised by them on the surfaces of their gigantic primaries. He thus connects the interior position of the fifth Jovian satellite with its small mass. The feebleness of its tide-raising power obliged it to remain behind its companions; for there is no sign of its being more juvenile than the Galilean quartette.

The yielding of plastic bodies to the strain of unequal attractions is a phenomenon of far-reaching consequence. We know that the sun as well as the moon causes tides in our oceans. There must, then, be solar, no less than lunar, tidal friction. The question at once arises: What part has it played in the development of the solar system? Has it ever been one of leading importance, or has its influence always been, as it now is, subordinate, almost negligible? To this, too, Professor Darwin supplies an answer.

It can be stated without hesitation that the sun did not give birth to the planets, as the earth has been supposed to have given birth to the moon, by the disruption of its already condensed, though viscous and glowing mass, pushing them then gradually backward from its surface into their present places. For the utmost possible increase in the length of the year through tidal friction is one hour; and five minutes is a more probable estimate.[1181] So far as the pull of tide-waves raised on the sun by the planets is concerned, then, the distances of the latter have never been notably different from what they now are; though that cause may have converted the paths traversed by them from circles into ellipses.

Over their physical history, however, it was probably in a large measure influential. The first vital issue for each of them was—satellites or no satellites? Were they to be governors as well as governed, or should they revolve in sterile isolation throughout the æons of their future existence? Here there is strong reason to believe that solar tidal friction was the overruling power. It is remarkable that planetary fecundity increases—at least so far outward as Saturn—with distance from the sun. Can these two facts be in any way related? In other words, is there any conceivable way by which tidal influence could prevent or impede the throwingoff of secondary bodies? We have only to think for a moment in order to see that this is precisely one of its direct results.[1182]

Tidal friction, whether solar or lunar, tends to reduce the axial movement of the body it acts upon. But the separation of satellites depends—according to the received view—upon the attainment of a disruptive rate of rotation. Hence, if solar tidal friction were strong enough to keep down the pace below this critical point, the contracting mass would remain intact—there would be no satellite-production. This, in all probability, actually occurred in the case both of Mercury and Venus. They cooled without dividing, because the solar friction-brake applied to them was too strong to permit acceleration to pass the limit of equilibrium. The complete destruction of their relative axial movement has been rendered probable by recent observations; and that the process went on rapidly is a reasonable further inference. The earth barely escaped the fate of loneliness incurred by her neighbours. Her first and only epoch of instability was retarded until she had nearly reached maturity. The late appearance of the moon accounts for its large relative size—through the increased cohesion of an already strongly condensed parent mass—and for the distinctive peculiarities of its history and influence on the producing globe.

Solar tidal friction, although it did not hinder the formation of two minute dependents of Mars, has been invoked to explain the anomalously rapid revolution of one of them. Phobos, we have seen, completes more than three revolutions while Mars rotates once. But this was probably not always so. The two periods were originally nearly equal. The difference, it is alleged, was brought about by tidal waves raised by the sun on the semi-fluid spheroid of Mars. Rotatory velocity was thereby destroyed, the Martian day slowly lengthened, and, as a secondary consequence, the period of the inner satellite, become shorter than the augmented day, began progressively to diminish. So that Phobos, unlike our moon, was in the beginning farther from its primary than now.

But here again Mr. Nolan entered a caveat. Applying the simple test of numerical evaluation, he showed that before solar tidal friction could lengthen the rotation-period of Mars by so much as one minute, Phobos should have been precipitated upon its surface.[1183] For the enormous disparity of mass between it and the sun is so far neutralised by the enormous disparity in their respective distances from Mars that solar tidal force there is only fifty times that of the little satellite. But the tidal effects of a satellite circulating quicker than its primary rotates exactly reverse those of one moving, like our moon, comparatively slowly, so that the tides raised by Phobos tend to shorten both periods. Its orbital momentum, however, is so extremely small in proportion to the rotational momentum of Mars, that any perceptible inroad upon the latter is attended by a lavish and ruinous expenditure of the former. It is as if a man owning a single five-pound note were to play for equal stakes with a man possessing a million. The bankruptcy sure to ensue is typified by the coming fate of the Martian inner satellite. The catastrophe of its fall needs to bring it about only a very feeble reactive pull compared with the friction which the sun should apply in order to protract the Martian day by one minute. And from the proportionate strength of the forces at work, it is quite certain that one result cannot take place without the other. Nor can things have been materially different in the past; hence the idea must be abandoned that the primitive time of rotation of Mars survives in the period of its inner satellite.