Modern cosmogonies

by Agnes M. Clerke

CRITICISMS OF THE NEBULAR HYPOTHESIS

Laplace's theory was a perfectly definite conception. In this lay its distinctive merit; in this also its special susceptibility to attack. Here was no question of condensation round nuclei arising at discretion amid the large possibilities of boundless elemental confusion; but of an orderly succession of occurrences, rendered inevitable by the steady operation of mechanical laws, and harmonizing, in their outcome, with the array of ascertained phenomena visible in the planetary system. These accordingly ceased to be regarded as arbitrary or casual; they became linked together in the present, and with the past, as joint products of one grand scheme of development. The mode of origin of the bodies exhibiting them accounted, its inventor claimed to have shown, simply and entirely for them all; and at least the fundamental propositions laid down by him could not be gainsaid.

Clearly, the unanimity of planetary movements is no result of chance; it represents quite obviously a survival of the general swirl of an inchoate mass, occupying primitively the whole recognised sphere of solar influence. Ambiguities set in only when details come to be considered. The engendering nebula devised by Laplace was provided with a vast endowment of heat and a slow movement of rotation; hence cooling, contraction, and acceleration advanced pari passu, the last as a consequence of the mechanical law by which the algebraic sum of the areas described by any number of bodies round a given axis, multiplied by their several masses and projected upon a single plane, remains constant to the end of time. In other words, to repeat what has been stated a few pages back, the moment of momentum of a congeries of particles can neither increase nor diminish through the effects of their mutual interactions, however varied and prolonged.

The nebula then quickened its pace until a stage was reached at which centrifugal speed could no longer be controlled by gravity; separation became inevitable, and an equatorial ring was abandoned, which thenceforward revolved on its own account in the period conformed to by the undivided mass at the epoch of its secession. This was the first of many subsequent crises of instability, each eventuating in the detachment of a nebulous ring. These rings, however, were regarded as merely transitional forms. They survived, just for illustrative purposes, in the Saturnian system; elsewhere they broke up into fragments, which ultimately coalesced into globes, and the globes were embryo planets. There was, indeed, a hitch in the line of argument which did not escape the acumen of the French geometer. The direction of the axial movement imparted to the members of the solar family depended essentially upon the relative velocities of the portions of matter brought together for their construction. If the inner sections of the self-shaping mass moved faster than the outer, the resulting rotation should have been retrograde; if slower, direct rotation would have ensued. Now, in a ring like that of Saturn, composed of discrete particles, linear speed decreases continuously outward, each of its minutest constituents obeying independently Kepler's law of periods and distances. Such a formation, since it would necessarily have yielded backward-spinning planets, would have been unfit for the purpose in view, and Laplace accordingly substituted an annulus endowed with a considerable amount of cohesion, and capable of rotating, like a solid, in a single period. It is true that such unanimity of movement was incompatible with the other postulated conditions; but the anomaly escaped notice for above half a century.

Professor Darwin has moreover pointed out[10] that a ring of matter distributed with any approach to uniformity must concentrate, if at all, round its own centre of gravity. It should accordingly collapse upon, and become re-absorbed by, the parent-body. If markedly unsymmetrical and ill-balanced, its materials might certainly collect at an interior point more or less remote from the centre; but in no case could the focus of condensation be situated in any part of the annular circumference, where it was located by Laplace.

Whether workable or not, the genetic plan traced out by him was a strictly regulated one; its steps were marked with characteristic precision. Yet by this very determinateness it gave hostages to the future. It challenged the application of tests which designs more vaguely sketched might have evaded. The primary criterion of its truth was the prevalence of concordant motion throughout the solar domain. Counter-currents were formally excluded; their possibility was not even contemplated. Hence, the discovery of the retrograde systems of Uranus and Neptune flatly contravened its pretensions to unconditional acceptance. With less evidence, but equal certainty, Laplace's hypothesis, strictly interpreted, involves the consequence that each planet circulates in the identical time occupied by the rotation of the undivided nebula just before instability toppled over into separation. Each of the planetary periods should accordingly bear a certain ratio, prescribed by inexorable mechanical law, to the actual period of the sun's rotation. In point of fact, however, the periods in question are much shorter than comports with the necessity for the conservation from age to age of the system's moment of momentum. The discrepancy was adverted to nearly half a century ago by M. Babinet.[11] He showed in March, 1861, that the axial movement of the solar mass, when distended to fill the sphere of Neptune, should have been, by the law of areas, so excessively slow that more than 27,000 centuries would have been needed for the completion of a single rotation; while the period, even when the shrinking nebula had come to be bounded by the terrestrial orbit, must still have been protracted to 3,181 years. Under these circumstances, centrifugal force would never have overbalanced central attraction; no rings could have separated, and no planets could have been formed.

Quite recently, Mr. F. R. Moulton, of Chicago,[12] has reconsidered the subject in the course of a careful and candid discussion of the difficulties besetting the nebular cosmogony as viewed from the standpoint of modern science, and he comes to essentially the same conclusion. His calculations, though founded on data expressly chosen so as to give the classic theory the benefit of every doubt, made it perfectly clear that the moment of momentum of the embryo planetary system should have exceeded its present value no less than 213 times if, when it extended to the distance of Neptune, it rotated in what is now the period of Neptune. But moment of momentum is a constant. The lapse of millions of years makes no difference to it; it is not, like energy, subject to 'dissipation'; it can neither have gained nor lost value since the sky was first flecked with the 'breath-stain' appointed to condense into our sun, which, in this respect at least, must at every stage of its subsequent evolution have maintained immutability. On the other hand, this being so, its primeval wheeling motion would have been much too leisurely to permit the occurrence of accesses of instability. Gravity would have steadily kept its supremacy over the forces tending to disruption until the nebula had contracted to less than the compass of the Mercurian sphere, and its overthrow at that epoch would have been too late for the origination of any of the sister orbs of the earth. These results, it is true, depend in part upon the mode of variation in density ascribed to the progressively shrinking nebula; but the law adopted by Mr. Moulton has a consensus of authorities in its favour. Nor could its deviation from exactitude—if it be inexact—possibly suffice to account for the enormous discrepancies which calculations based upon it have brought to light.

The nebular hypothesis stipulates further that satellites must revolve more slowly than their primaries rotate. The reason is patent. In the periodic time of a body detached by centrifugal acceleration the rate of gyration of the original mass is, if the theory be valid, perpetuated. Subsequent contraction tends to quicken, and very greatly to quicken, the rotation of the planet, while the period of the satellite survives unaltered as a standing record of what the joint period was. This relation may indeed be modified by the effects of tidal friction, but it is more than doubtful whether it can ever be reversed. It is, then, a characteristic feature of the mode of evolution described by Laplace that no month—so to call it—can be shorter than the corresponding day. And the rule is conformed to in nearly every part of the solar system. Nevertheless, two flagrant violations of it have lately obtruded themselves upon notice, and can scarcely be explained away by supplementary hypotheses. The first ascertained anomaly of the kind was met with in the swift circulation of Phobos, the inner satellite of Mars, which completes three revolutions and enters upon a fourth while the planet attended by it wheels once on its axis. The fact is most perplexing, and the confident persuasion that solar tidal friction would avail to remove the difficulty has not proved well grounded. Solar tidal friction, it may be remarked, acts as an external force upon subordinate systems submitted to its influence. Within their precincts moment of momentum may be destroyed by it; it tends, so far, to abrogate the law of conservation; and the supposition was hence feasible that the rotation of Mars had, in the course of ages, greatly slackened through the retarding effect of sun-raised tides. But the agency was demonstrably inadequate to the task assigned to it.

The reduction of the rotational moment of Mars to about one twenty-fifth its primitive amount[13] would have brought other consequences in its train, at least one of which did clearly not ensue. At an early stage of the process Phobos should have been re-engulfed in the mass of its primary.[14] For the pull of the small tidal wave raised by it on the surface of that body would have been backward from the instant that the balance of periods became inclined, through solar compulsion, in a direction contrary to that it would have naturally taken; and the ensuing loss of velocity must have entailed the descent of the little satellite along a spiral path towards an inevitable doom. Its continued existence, then, closes this way of escape from the difficulty raised by the shortness of its period. M. Wolf had recourse to a different explanatory subterfuge.[15] He believed that Phobos might have owed its origin to one of Roche's 'elliptic sheddings' of nebulous matter dropped downward from near the polar regions of the distended Martian spheroid, and rotating, owing to its low rate of linear speed, in the immediate vicinity of the cooling planet. The explanation, though ingenious, is too recondite to be satisfactory. The mind takes no grip of it; it evades distinct apprehension.