The universe around us

Observational astronomy leaves no room for doubt that a great number of stars, possibly even all stars, follow the sequence shewn in fig. 11. No other mechanism, so far as we know, is available for the formation of the numerous spectroscopic binary systems, in which two constituents describe small orbits about one another. In these stars, then, the central condensation of mass must be below the critical amount just mentioned; to this extent they behave like liquids rather than gases.

We have relied entirely on mathematical analysis in tracing out the details of the process of fission just described. And we are totally unable to check our theoretical results by observation. There is not a single star in the sky of which we can say: here is a star which has certainly started to break up by fission, and will certainly end as a binary system. It is perhaps not altogether surprising. The breaking up process is in all probability of very short duration by comparison with the lives of the stars, so that in any case we should have to investigate a great many stars before catching one in the act of breaking into two.

On the other hand, a star in the act of breaking up ought to be very easily differentiated from ordinary stars. Mathematical analysis shews that its interior would be in a state of considerable turmoil, so that it would hardly be likely to shine with a steady light: it would be a “variable” star. Further, its condition ought to shew a progressive change, although it is an open question whether this would be rapid enough to be detected in a few years of observation. Finally, if any group or class of stars were suspected of being stars in process of fission, it ought to be possible to arrange them in an order corresponding to the extent to which the fissional process had advanced, and the sequence so formed ought to end with stars in the physical condition of newly formed binaries.

I have recently suggested that the Cepheid variables, whose unknown mechanism of light-variation renders such valuable service to the astronomer, are merely stars in the act of fission. Want of space prevents our entering here into the intricate question of how far they exhibit the peculiarities which mathematical analysis requires of stars in process of fission, but it is easily seen that they satisfy the three simple tests outlined above. They are certainly variable stars, and the light-variations of different stars are so similar as to suggest very strongly that they all arise from the same cause. The periods of a number of Cepheids are suspected of change, and Hertzsprung has estimated that the prototype star, δ Cephei, which has now been observed for 126 years, is decreasing its period of light-fluctuation at the rate of about a tenth of a second per annum; thus a million years would reduce its present period of 5⅓ days by over a day. Finally Dr Otto Struve has found that the sequence of Cepheids fits almost perfectly on to that of newly formed binaries. Thus the prospects for the “fission theory” of Cepheid variables seem hopeful, but the theory must be very thoroughly tested before it can be accepted, and it cannot be claimed that it has been so far either tested thoroughly or accepted extensively.

An alternative view, first propounded by Plummer and Shapley, regards Cepheid variables as pulsating spheres of gas. The behaviour of such masses of gas has been investigated mathematically by Eddington and others, but it does not appear that it can be reconciled with the observed behaviour of Cepheid variables.

THE DEVELOPMENT OF
BINARY SYSTEMS

Whatever the process of formation of binary systems may be, we experience fairly plain sailing in attempting to trace out the subsequent development of such systems. Three factors are simultaneously in operation.

TIDAL FRICTION. The first of these three factors, which is only of brief duration, was designated “tidal friction” by Sir George Darwin, who first drew attention to it, and investigated the manner of its operation. When first a rotating mass breaks up and forms a binary system, the two components are so near that they necessarily raise tremendous tides on one another; Darwin shewed that these drive the two bodies apart, and equalise their rates of rotation in so doing. After these processes have been in operation for millions of years, the rates of rotation of the two bodies and their rate of revolution about one another must all become equal, so that each body perpetually turns the same face to its companion, and the two rotate about one another like the two masses of a dumb-bell joined by an invisible arm.

Although a sun and planet do not form a binary system in the strict technical sense, they are necessarily subject to the same forces as true binary systems. Thus we can see the operation of tidal friction in the fact that Mercury always turns the same face to the sun, and that Venus rotates so slowly on its axis that it turns the same face to the sun day after day, and probably also week after week. As we pass further out into space the effects of tidal friction rapidly diminish, but it is probably significant that the nearer planets, Earth and Mars, have days of about 24 hours each, while the remote planets Jupiter, Saturn and Uranus each have days of only about 10 hours. The periods of rotation of Neptune and Pluto are unknown. Apart from these we find, in a general way, that the further we recede from the sun the more rapidly the planets rotate, which is precisely the effect that ought to be produced by tidal friction.

In the same way, tidal friction has in all probability been mainly responsible for the present configuration of the earth-moon system, driving the moon away to its present distance from the earth and causing it always to turn the same face towards us. Tidal friction must of course still be in operation. The moon is responsible for the greater part of the tides raised in the oceans of the earth; these, exerting a pull on the solid earth underneath, slow down its speed of rotation, with the result that the day is continually lengthening, and will continue to do so until the earth and moon are rotating and revolving in complete unison. When, if ever, that time arrives, the earth will continually turn the same face to the moon, so that the inhabitants of one of the hemispheres of the earth will never see the moon at all, while the other side will be lighted by it every night. By this time the length of the day and the month will be identical, each being equal to about 47 of our present days. Jeffreys has calculated that this state of things is likely to be attained after about 50,000 million years.

After this, tidal friction will no longer operate in the sense of driving the moon further away from the earth. The joint effect of solar and lunar tides will be to slow down the earth’s rotation still further, the moon at the same time gradually lessening its distance from the earth. When it has finally, after unthinkable ages, been dragged down to within about 12,000 miles of the earth, the tides raised by the earth in the solid body of the moon will shatter the latter into fragments (p. 250 below), which will form a system of tiny satellites revolving around the earth in the same way as the particles of Saturn’s rings revolve around Saturn, or as the asteroids revolve around the sun.

We have already noticed how the present arrangement of the earth-moon system enables us to calculate the earth’s age; Jeffreys estimates that the system must have taken something of the order of 4000 million years to reach its present configuration (p. 155).

This period, which seems so long when judged by terrestrial standards, is only a moment in the life of a star. The components of the true binary star attain a configuration like that of the earth-moon system in a brief fraction of their lives, and, passing on, reach in time the configuration in which each perpetually turns the same face to the other. Up to now, tidal friction has been driving the masses ever further apart, but as soon as this stage is attained, the tides become stationary on both components, so that tidal friction goes out of operation. Thus the separation produced by tidal friction has now reached its limit, and, so far as tidal friction is concerned, the two bodies might rotate in the way just described to all eternity.

LOSS OF WEIGHT. As tidal friction becomes inoperative, a new agency takes hold. We have calculated that the sun is losing weight at the rate of 250 million tons a minute, that it has been losing weight at this rate, or some comparable rate, for millions of millions of years, and will continue so to do for millions of millions of years yet to come. The earth is at its present distance from the sun because this distance is exactly suited to the present weight of the sun. If the sun’s weight were suddenly reduced to half, its gravitational pull on the earth would also be reduced to half, and the earth would move to a greater distance from the sun[22].

The sun’s weight is not likely to be suddenly reduced to half, but it has been reduced by a thousand million tons in the last four minutes, with the result that its gravitational grip on the earth has been weakened and the earth has moved out to a wider orbit; at this moment the radius of the earth’s orbit is greater than it was four minutes ago. The details can be traced out mathematically with complete precision. It appears that the earth’s orbit round the sun is not a circle, or even an ellipse of small eccentricity; it is a spiral curve, like an uncoiled watch spring. Every year the earth moves a tiny step further out into the outer cold and darkness; exact calculation shews that its average distance from the sun increases at the rate of about a metre (39·37 inches) a century. The effect is of course of precisely the same kind as we have seen must be produced in the galactic system by the loss of weight of the stars. The only difference is that in the galaxy a system of thousands of millions of stars is expanding, whereas the sun-earth system consists of only two members.

Precisely similar effects must be produced by the loss of weight in the two components of a binary star. Here both components are radiating away energy, and so are simultaneously losing weight. Detailed calculation shews that they must continually recede from one another, but that the shape of their orbit will undergo no change.

Neither separately nor in combination do the two effects just described explain either the shapes or the sizes of the observed orbits of binary stars as a whole. To interpret these we must call on yet a third agency, the gravitational forces from passing stars. We have already seen how these account for the statistical distribution of orbits which is actually observed.

The combination of all three agencies, tidal friction, extending over millions of years, loss of weight, extending over millions of millions of years, and disturbance from passing stars, extending over a similar period, is responsible for the evolution of binary star systems. Their aggregate effect is to widen the distance between the two stars, while at the same time knocking the orbit out of shape.

SUBDIVISION. While these changes are going on in the orbital arrangement of a binary system, the two components are themselves changing their physical condition on account of their continual loss of weight, and, as with the parent stars, this loss of weight will generally result in a shrinkage in the size of the star. The shrinkage of either component of the system causes its shape to run through the sequence of configurations we have already enumerated, and if the shrinkage continues for long enough, the component may end by further dividing into two separate masses. Either or both of the constituents of a binary system may subdivide into binary sub-systems in this way, resulting in a system of either three or four stars. H. N. Russell has shewn mathematically that when a binary system P, Q divides into a triple system, P, q, qʹ, through Q breaking up into two constituents q, qʹ, the distance between q and qʹ cannot be more than about a fifth of the original distance PQ. This theoretical law is well confirmed by observation. Fig. 13 shews a typical multiple system, and we notice that the separations in each of the various sub-systems are all quite small in comparison with those of the main systems.

The development of the hypothetical primitive chaos has now been traced through five generations of astronomical bodies,

chaos—nebulae—stars—binary systems—sub-systems,

to which a sixth generation must be added if the stars of the sub-system happen to fission further, as, for instance, they have done in the star shewn in fig. 13. The genealogy of the stars begins with a vast tenuous nebula filling all space; the last generation consists of small, shrunken, dying stars with no capacity for further subdivision. The genealogy has been traced out primarily on theoretical grounds alone, but we need have no doubts as to its general accuracy, since observation confirms it repeatedly and at almost every step. Indeed it is hardly too much to say that the evolutionary sequence could have been discovered almost equally well from observational evidence alone, except for the hypothetical primaeval chaos, about which, from the nature of the case, observation cannot have anything to say.

THE ORIGIN OF THE
SOLAR SYSTEM

Almost all observed astronomical formations can be placed in the evolutionary sequence we have just discussed, either with fair certainty or with reasonable plausibility, except for one outstanding and conspicuous exception—the Solar System. Cosmogony came into being as an attempt to discover the origin of the solar system. The reasons why it limited its efforts to this particular problem are chronological; in the early days of cosmogony, astronomy was barely conscious of anything outside the solar system. The sketch just given of the findings of modern scientific cosmogony has been remarkable in that it has exhibited cosmogony taking us a tour round the whole universe, explaining the origin and life-history of practically every object we encounter on this tour, and then becoming speechless when it is brought back home and confronted with its birthplace, the solar system.

LAPLACE’S NEBULAR HYPOTHESIS. The first serious scientific cosmogony was that embodied in the famous Nebular Hypothesis of Laplace. In 1755 Kant had pictured a primaeval chaos condensing into spinning nebulae, and, identifying one of these nebulae with the sun, had imagined the planets to be formed by the solidification of masses of gas shed from the nebula, much in the way in which we have supposed the stars to be born. In 1796, Laplace advanced similar ideas, which he developed in detail with a mathematical precision quite beyond the capacities of Kant. He shewed how, as its shrinkage made it spin ever faster and faster, a rotating mass of gas would flatten out, develop the lenticular form we have already discussed (fig. 3 of Plate XVI), and then proceed to eject matter in its equatorial plane, or rather to leave it behind as the shrinkage of the main mass continued. At this stage it would look somewhat like the nebulae shewn in figs. 4 and 5 of Plate XVI, although Laplace, being unacquainted with nebulae of this type, adduced Saturn surrounded by its rings as an example of the formation to be expected at this stage (Plate XXIV, p. 250). Laplace imagined that the fringe of abandoned gas would then condense and form a single planet. As the main mass shrunk further, more gas was abandoned in the equatorial plane, which in due course condensed into another planet, and so on, until the sun left off shrinking and no more planets were born. A repetition of the same process, but on a far smaller scale, resulted in the satellites being born out of the planets.

That the hypothesis is prima facie plausible, is evident from its having survived, and indeed been generally accepted, for nearly a century before it encountered any serious opposition. Recently criticisms have accumulated, of so vital a nature as to make it clear that the hypothesis must be abandoned.

The sun, according to Laplace, broke up and gave birth to planets through excess of rotation. Yet both theory and observation indicate quite clearly the fate in store for a star which rotates too fast for safety; it does not found a family, but merely bursts, like an overdriven fly-wheel, into parts of nearly equal size. Spectroscopic binary and multiple systems are the relics of stars which have broken up through excess of rotation, and they do not in the least resemble the solar system.

Again, the principle of “conservation of angular momentum” requires that the rotation of the primaeval sun shall persist in the rotation of the present sun, and in the revolutions of the planets around it. On adding together the contributions from all of these, we obtain a total which ought to represent the angular momentum of the primaeval sun. In strictness a further contribution ought to be added on account of the weight of all the radiation which the sun has emitted since the planets were born. We can calculate the amount of this contribution, because we know the age of the earth with tolerable accuracy, but it proves to be entirely negligible.

The total angular momentum of the primaeval sun can be calculated with very fair accuracy, because more than 95 per cent. of the total angular momentum of the present solar system resides in the orbital motion of Jupiter. This contribution can be calculated with great exactness, so that some uncertainty in the minor contributions which make up the remaining 5 per cent. can have but little influence on the total.

When this total is calculated the startling fact emerges that the primaeval sun cannot have had enough rotation to cause break-up at all. Clearly the sun is very far from being broken up by its present rotation. Flattening of figure is the first step towards break-up, and the sun’s figure is so little flattened by its present rotation that the most refined measurements have so far failed to detect any flattening at all. On adding the further angular momentum now represented in the motions of Jupiter and all the other members of the solar system, we arrive at a primaeval sun rotating about as fast as Jupiter now rotates, and shewing about the same degree of flattening of figure as Jupiter—enough to measure quite easily in a telescope, or even to detect with the eye alone, but nothing like enough to cause break-up.

The sun is hardly likely to have altered much since its planets were born, for the intervening 2000 million years or so represent but a minute fraction of the sun’s total life. If, however, we imagine it to have shrunk appreciably in the interval, then the available amount of angular momentum would have been even more unable to break up the large primaeval sun than it is to break up the present shrunken sun. Whichever way we look at it, we reach the conclusion that the sun cannot have broken up, as Laplace imagined, through excess of rotation; indeed it can never have possessed more than a quite tiny fraction of the amount of rotation needed to break it up.

A third objection is of a somewhat different character. Laplace was a very great mathematician, and there was nothing the matter with his abstract mathematical theory, so far as it went. More refined modern analysis has confirmed it at every step, and observation does the same, as photographs of rotating nebulae (Plate XVI) bear witness. These photographs exhibit a process taking place before our eyes, which is essentially identical with that imagined by Laplace, except for a colossal difference of scale. Everything happens qualitatively as Laplace imagined, but on a scale incomparably grander than he ever dreamed of. In these photographs the primitive nebula is not a single sun in the making, but contains substance sufficient to form hundreds of millions of suns; the condensations do not form puny planets of the size of our earth, but are themselves suns; they are not eight or so in number, but must be counted in millions.

We may ask why the same thing cannot happen on the smaller scale imagined by Laplace—for are not the conclusions of mathematics applicable independently of the size of the body with which we are dealing? The answer has in effect been given already (p. 218). Everything happens on the smaller scale according to plan until we come to the formation of the condensations; here the question of scale proves to be vital. We have seen (p. 196) how the molecules which form the sun have condensed into a star because of their great number; the molecules in a room do not condense into anything at all because they are too few. In the same way, the molecules left behind by the slow shrinkage of a sun (assuming this for the moment to rotate rapidly enough to leave molecules behind) would not condense, because at any instant there would be too few of them available for condensation. They would be shed by driblets, and a driblet of gas does not condense but scatters into space. A mathematical calculation decides the question definitely, and the decision is entirely adverse to the hypothesis of Laplace. Apart from minor details, the process imagined by Laplace explains the birth of suns out of nebulae; it cannot explain the birth of planets out of suns.

SECOND BODY THEORIES. Laplace imagined his sun to be alone in space, even its nearest neighbours being too remote to influence it in any way. It was the natural supposition to make; we have already remarked how exceedingly rare an event it must be for two stars to approach near enough to influence one another. Yet no possible mode of evolution of a star which remains alone in space seems able to explain the origin of the solar system. As far back as 1750, Buffon had suggested that the solar system might have been produced through the disruption of the sun by another body, which he described as a “comet.” In propounding his Nebular Hypothesis, Laplace mentioned Buffon’s idea, but dismissed it somewhat curtly on the grounds that it seemed unable to account for the nearly circular orbits of the planets—an ill-founded objection, as we shall soon see. Yet when we find that a single star cannot of itself give birth to a solar system, it becomes natural to investigate what happens on the rare occasions on which the evolution of a star is directed along other paths by the near approach of a second star.

In 1880, Bickerton of New Zealand, reviving Buffon’s idea, supposed that the solar system had been formed by the collision of the sun with another star. He imagined the débris of the collision to form a third nebulous body, condensations in which formed the planets. He shewed how the resistance which the planets would encounter as they moved through the surrounding nebula would gradually make their orbits more circular, and so account for their present nearly circular shapes. Ten years earlier, the English writer, R. A. Proctor, had advanced similar ideas, although with less precision. In 1905 Professors Chamberlin and Moulton of Chicago advanced a modification of the same ideas, under the name of the “Planetesimal Hypothesis.” Discarding the idea of material collision, they supposed that a passing star exerted a powerful tidal pull on the sun, with the result that the ordinary solar prominences temporarily attained an extraordinary violence; the ejected matter was supposed to rise to unusual heights and condense into small solid bodies, the “planetesimals,” out of the aggregation of which the planets were ultimately formed. These various theories were all purely speculative. They have shewn very little capacity either for surviving the acid test of mathematical analysis, or for explaining the more salient features of the solar system; none of them, for instance, explains why the larger planets in the solar system are accompanied by families of satellites.

Three years before Chamberlin and Moulton advanced their planetesimal theory, I had speculated as to the possibility of tidal forces breaking up a star, and generating a solar system. In 1916, I investigated mathematically what would actually happen when one star raised violent tidal forces on another. The results I obtained seemed to me to demolish the planetesimal theory of Chamberlin and Moulton, and led me to put forward the present-day “Tidal Theory,” which I believe a large proportion of astronomers now accept as giving the most probable origin of the solar system; it can of course make no claim to finality or certainty.

TIDAL THEORY. When two stars or other bodies pass close to one another without collision, the primary effect must be that each raises tides in the other. The closer the approach, the higher the tides in general, although something must depend also on the speed with which the bodies pass one another, because this determines the length of time during which they influence one another.

It is likely that the two spiral arms which give their name and characteristic appearance to the spiral nebulae may owe their inception to a somewhat similar tidal action. Conditions here are different in that the rotation of the nebulae in any case causes them to emit matter in their equatorial planes, so that even small tidal forces should then cause this matter to concentrate in two symmetrical arms. Under stellar conditions a far closer approach is necessary to draw matter out from the star, and it is then most likely that there will be two unequal and dissimilar arms, or possibly only one arm.

If the approach is very close indeed, the tides may assume an entirely different aspect from the feeble tides which the sun and moon raise in our oceans; they may take the exaggerated forms of high mountains of matter moving over the surface of the star. An even closer approach may transform these mountains into long arms of gas drawn out from the body of the star. If, as will generally be the case, the two stars are of unequal weights, the lesser will in general suffer more disturbance than the weightier.

THE BIRTH OF PLANETS. The long arm or filament of matter drawn out of a star by tidal action is at first continuous in its structure, but analysis shews that it provides a fit subject for the operation of what we have called “Gravitational Instability.” Condensations begin to form in this long arm of gas, in the way already described. As before, the smaller condensations are dissipated, while the larger increase in intensity until finally the filament breaks up into a number of detached masses—planets have been born out of the smaller star. The pairs of nebulae shewn in Plate XXII and the upper half of Plate XXIII are very probably under one another’s tidal influence, and may serve to suggest the general nature of the process we are now considering, although it must be remembered that whatever is happening here is on an enormously greater scale than that of the solar system—if it were not, the telescope would be utterly unable to shew it to us.

When the new-born planets first begin to move as separate and independent bodies, they are acted on by the gravitational pulls of both stars, and so describe highly complicated orbits. Gradually the bigger star recedes until its gravitational effect becomes negligible, and the planets are left describing orbits around the smaller star alone. If the planets moved in a clear field of empty space, these orbits would be exact ellipses. But the great cataclysm which has just occurred must have left all sorts of débris behind. Comets, meteors and other minor bodies which still survive in the solar system may represent a small part of it, but probably the main part was left in the form of dust or gas, so that the new-born planets had at first to plough their way through a medium which offered some resistance to their motions. Under these circumstances their orbits would not be strict ellipses. It can be proved that a resistance of the kind just described would change the shape of the orbits, and that with the progress of time they would become more circular, finally becoming absolutely circular if the medium should last long enough.

The débris of gas and dust would, however, continually be swept up by the planets and would disappear completely in time, probably leaving the planetary orbits something short of absolute circles. Assuming that all this has happened in the solar system, very little of the original débris can now remain, its last vestiges being probably represented by the particles of dust which are responsible for the zodiacal light. Nevertheless, the resisting medium appears to have existed for long enough to make the orbits, both of the planets and of their satellites, very nearly circular for the most part.

The exceptional cases are fully as significant as the cases of conformity. Comparatively elongated orbits still exist in just those regions where we should expect the primaeval resisting medium to have been most sparsely spread in space, namely on the outermost confines of the solar system and of the various satellite system. Pluto, the outermost planet of all, has a more elongated orbit than any other planet. Again, in the systems of Jupiter and Saturn, the satellites with the most elongated orbits are those which are furthest away from their primaries. In addition to this, a general tendency may be discerned for elongated orbits to be associated with small weights, both in planets and their satellites. Mercury, with a weight of only a twenty-fifth that of the earth, has a quite elongated orbit, as also to a less degree has Mars with a ninth of the weight of the earth. An explanation of this has been suggested by Jeffreys. Massive planets such as Jupiter and Saturn must have collected a large mass of the resisting medium round them, and carried it through space with them as a far-reaching envelope. The massive planets would have their motion checked by the interaction of the whole of this big envelope with the remainder of the medium, and so would attain circular orbits more rapidly than the lighter planets which had accumulated envelopes of very much smaller dimensions. And the same, with the appropriate modifications, is true of the satellite systems.

Jeffreys has calculated the rate at which planetary orbits would change their shape under the action of this resisting medium. The data of the problem are necessarily uncertain, and this uncertainty naturally affects his conclusions, but his study has yielded a valuable confirmation of other estimates of the length of time which has elapsed since the planets were born.

We may next turn our attention to the physical changes which must all this time be affecting the various planets. The long filament of matter pulled out of the sun is likely to have been richest in matter in its middle parts, these parts having been pulled out when the second star was nearest and its gravitational pull was strongest. Diagrammatically at least, we may think of this filament as shaped like a cigar—thick near the middle, thin at the ends—so that when condensations begin to form, those near the middle are likely to be richer in matter than those at the ends. This probably explains why the two most massive planets, Jupiter and Saturn, occupy the middle positions in the sequence of planets.

Fig. 14 shews the planets arranged in the order of their distances from the sun, with their sizes drawn roughly to scale. The thousands of asteroids whose orbits now fill the space between the orbits of Mars and Jupiter are represented as a single planet, it being generally supposed that these asteroids were formed by the break-up of what was originally a single planet in a way we shall shortly describe.

If we surround the planets by a continuous outline, as in the diagram, we can reconstruct in imagination the cigar-shaped filament out of which they were produced, and we see at once how the biggest planets were produced where matter was most abundant.

The tidal theory which predicts all these features had been propounded, and its consequences worked out, many years before the new planet Pluto had been discovered. Valuable support for the theory may thus be found in the circumstance that Pluto behaves in every way according to the requirements of the tidal theory.

THE BIRTH OF SATELLITES. We have already noticed how the great disparity of weight between the sun and planets distinguishes the sun-planet formation from that of the normal binary star, and so suggests entirely different origins for the two formations. Exactly the same disparity repeats itself in the planet-satellite systems. Just as the parent sun is enormously more massive than its children the planets, so these in turn are far more massive than their satellite children. The sun has 1047 times the weight of its most massive planet and many millions of times the weight of the smallest. In the system of Saturn the corresponding figures are 4150 and about 16,000,000. The nearest approach to equality of weights is provided by the earth-moon system, the earth having only 81 times the weight of the moon. And, like the planetary system of the sun, the satellite systems of Saturn and, to a lesser degree, of Jupiter shew a general tendency for the weights of the various satellites to increase up to a maximum as we pass outwards from the planet, and then to decrease again. This again suggests formation out of a cigar-shaped filament with matter occurring most richly near the middle. In conjunction with the repetition of the great disparity of weights between primary and secondaries, this indicates very forcibly that the satellites of the planets must have been born by the same type of process as had previously resulted in the birth of their parents.

We can imagine the process in a general way. Immediately after their birth, the planets must begin to cool down. The largest planets, Jupiter and Saturn, naturally cool most slowly and the smallest most rapidly. The latter may lose heat so speedily that they liquefy, and perhaps even solidify, almost immediately after their birth. While these events are in progress, the planets are still pursuing somewhat erratic orbits, in describing which they may pass so near to the sun that a second series of tidal disruptions occurs. In these the sun itself plays the rôle originally played by the passing star from space, the planets playing the part originally taken by the sun. The sun may now tear long filaments of matter out of the surfaces of the planets, and these, forming condensations, may give birth to yet another generation of astronomical bodies, the satellites of the planets. In some such way the tidal theory imagines the planetary satellites to have come into being.

Mathematical investigation shews that the more liquid a planet was at birth, the less likely it would be to be broken up by the still gaseous sun. If, however, such a break-up occurred, the weights of primary and satellites would be more nearly equal than if the planet had been more gaseous. Thus, on passing from wholly gaseous planets to planets which liquefied at or immediately after their birth, we should expect at first to find planets with large numbers of relatively small satellites, and then, after passing through the border-line cases of planets with small numbers of relatively large satellites, we should expect to come to planets having no satellites at all.

We have already seen that the big central planets, Jupiter and Saturn, ought to have remained gaseous for longest and the smaller planets to have liquefied earliest; we now see that this prediction of theory exactly describes what is actually found in the solar system. Starting from Jupiter and Saturn, each with nine relatively small satellites, we pass Mars with only two satellites, and come to the earth with its one relatively large satellite, followed by Venus and Mercury which have no satellites at all. Proceeding in the other direction we leave Jupiter and Saturn each with their nine tiny satellites, to discover Uranus with four small satellites and Neptune with one comparatively big satellite. The number placed under each planet in fig. 14 gives the number of its satellites. When the numbers are exhibited in this way, the law and order in the arrangement of the satellite systems becomes very apparent, and this arrangement is seen to be exactly in accordance with the prediction of the tidal theory. The cigar-shaped arrangement applies not only to the sizes of the planets, but also, as it ought, to the numbers of their satellites.

The earth and Neptune, with only one satellite each, and those comparatively large ones, form the obvious lines of demarcation between planets which were originally liquid and those which were originally gaseous. This leads us to conjecture that Mercury, Venus and Pluto must have become liquid or solid immediately after birth, that the earth and Neptune were partly liquid and partly gaseous, and that Mars, Jupiter, Saturn and Uranus were born gaseous and remained gaseous at least until after the birth of their families of satellites.

We may perhaps find further evidence confirmatory of the tidal theory in the circumstance that the weights of Mars and Uranus are abnormally small for their positions in the sequence of planets. If, as we have supposed, the planets were all born out of a continuous filament of matter, the weight of Mars at birth would in all probability have been intermediate between those of the earth and Jupiter, and the weight of Uranus intermediate between those of Neptune and Saturn. But if, as we have already been led to suppose, the two anomalous planets Mars and Uranus were the two smallest planets to be born in the gaseous state, they would be likely to lose more of their substance than the other planets through their outermost layers of molecules dissipating away into space before they had cooled down into the liquid state. If Mars and Uranus are supposed to be mere relics of planets which were initially far more massive than they now are, the anomalies begin to disappear and the pieces of the puzzle to fit together in a very satisfactory manner.

ORBITAL PLANES. Every rotating mass, whether gaseous, liquid or solid, has a definite axis of rotation, and, perpendicular to this, a definite equatorial plane which divides the mass symmetrically into two exactly equal and similar halves. When a mass breaks up under its own rotation, the equatorial plane and the symmetry still persist. Illustrations of this can be found in any set of photographs of rotating nebulae, as, for instance, those shewn in Plates XV and XVI. In more humble life an illustration is provided by the splashes of mud thrown off by a spinning bicycle-wheel, which all keep in the plane in which the wheel is spinning.

If the sun’s equatorial plane had proved to be a plane of symmetry for the solar system, so that the whole system was similarly arranged as regards the two sides of this plane, it might have been possible to explain the system as the result of a rotational break-up. But the sun’s equatorial plane is not a plane of symmetry. The planets do not move in it, most of them moving in a plane which makes an angle of 5 or 6 degrees with it. In terms of our humble analogy, the splashes of mud are not flying about in the plane in which the bicycle-wheel is spinning.

The hypothesis that the planets came into being through a rotational break-up of the sun fails completely before this fact, but the tidal theory provides a simple explanation of it at once. The sun is still rotating much as it was before the planets were born, and so retains its original equatorial plane. The quite different plane in, or very close to, which the planets are describing orbits must clearly be the plane in which the long tidal filament was originally drawn out by the passing star. Thus the plane in which the outer planets now move must record the position of the plane in which the two stars, the sun and the wandering star, the second parent of the sun’s family of children, described orbits about one another 2000 million years ago. It is the only clue the latter has left of his identity, and is of course far too slight to make identification possible after this long lapse of time.

To sum up, we have seen that the normal mechanism by which the greater part of the universe has been carved out is the birth of successive generations of astronomical bodies through the action of “gravitational instability.”

The normal genealogy runs somewhat as follows:

chaos—nebulae—stars—binary systems—sub-systems.

Not all stars have passed on to the last two generations; where only a small amount of rotation was present, a star might well live its whole life without further subdivision. Our sun would have provided an instance of this had it not been for the rare accident of the close approach of a second star. From the interaction of these, two other generations came into being, still through the mechanism of gravitational instability. For our solar system, as for any other similar systems there may be in the sky, the genealogy runs as follows:

chaos—nebula—sun—planets—satellites.

Both types of genealogy shew five generations, each born from its parent through the action of gravitational instability, and between them the two genealogies include practically all the large size astronomical objects with which we are acquainted. It is then fair to say that “gravitational instability” appears to be the agency primarily responsible for the main architecture of the universe.

ROCHE’S LIMIT. The reign of gravitational instability must end with the birth of planetary satellites, since gaseous bodies of less weight than these could not hold together. Even under the most favourable circumstances their feeble gravitational pulls would be unable to restrain their outermost molecules from escaping, so that the whole mass would speedily scatter into space. Yet astronomy provides many instances of smaller bodies; we have already mentioned the asteroids, meteors or shooting-stars, and the particles of Saturn’s rings. As all these are too small to have been born in the gaseous state, we must suppose them to be the broken-up fragments of larger masses. This accords with the circumstance that these small bodies as a rule do not occur individually but in swarms.

The asteroids occur as a single swarm. If these were found scattered throughout the solar system, their origin might present a difficult problem. As things are, the whole swarm can be explained quite simply as the broken fragments of a primaeval planet. Saturn’s rings again admit of a natural explanation as the fragments of a former shattered moon of Saturn. Comets, which we have hardly had occasion to mention so far, are in all probability swarms of minute bodies which are just held together sufficiently by their mutual gravitational attraction to describe a common orbit in space. At its apparition in 1909, Halley’s comet was estimated to reflect as much of the sun’s light as a single body 25 miles in diameter. Yet its apparent surface was 300,000 times that of such a body, and was quite transparent. It is difficult to resist the conclusion that the comet consisted of a widely-spaced swarm of small bodies, and such a swarm again admits of a simple explanation as the broken fragments of a single mass.

Shooting-stars, or meteors, also are encountered in swarms. As we shall see later, the motion of many of these swarms makes it possible to identify them as broken-up comets. Thus the broken fragments which compose a comet are identical with the meteors which we see as shooting-stars when they penetrate into the earth’s atmosphere. Shapley has estimated that the earth’s atmosphere must catch thousands of millions of shooting-stars every day, of which at most only one in a hundred is bright enough to be visible to the naked eye. Generally they dissolve into vapour before they reach the earth’s surface (see p. 176); occasionally one is so big that the earth’s atmosphere fails to dissipate it entirely, and what remains of it strikes the earth as a solid body—a meteorite. Every shooting-star and meteorite may be regarded as a miniature comet, consisting of only a single fragment. On occasions a whole group of fragments, moving in parallel paths at only small distances apart, may strike the earth’s atmosphere and appear as a “fireball.” Generally speaking all the small fry of the solar system move in swarms, and can be naturally interpreted as the broken-up fragments of larger bodies.

If the meteorites are broken fragments of bodies which were born out of the sun at the same time as the planets, they must have solidified at about the same time as the earth, at an epoch which we have placed at about 2000 million years ago. But if they had been born out of some other star, the time of their solidification might have been anywhere up to millions of millions of years ago.

Professor Paneth and two colleagues at Königsberg have recently estimated the ages of various meteoric stones by methods similar to those employed to fix the age of the earth (p. 154). They obtain ages which range from a few million years up to 2900 million years, but there is nothing beyond this last figure. Not a single stone suggests an age even approaching millions of millions of years. This provides very strong evidence that these stones were products of the same cataclysm as produced the earth, and incidentally provides valuable confirmation of our previous estimate of the earth’s age.

We can easily see how larger bodies might be broken up into swarms of meteors. We have supposed the sun to have been broken up, at least to the extent of ejecting a family of planets, by the tidal pull of a passing star. What would have happened if the passing star had not passed, but had come to stay? So long as it remained within a certain distance of the sun, its tidal forces were pulling the sun to pieces. We can imagine how a longer visit from it would have resulted in a greater upheaval in the sun, and the birth of a larger family of planets. Finally a visit of unlimited duration would have shattered the sun into fragments.

In 1850 Roche gave a mathematical investigation of this process of tidal break-up. His discussion dealt only with solid or liquid bodies, but the underlying mechanism is the same whether the bodies are solid, liquid or gaseous. We have seen that the smaller of the two bodies involved in a tidal encounter suffers the most. Roche dealt only with the case in which one body was very small in comparison with the other; in such a case the small body was completely broken up, while the larger one remained unscathed. Roche imagined the small body to describe an orbit of gradually decreasing size around the big body. If the two bodies were of equal density, he calculated that the small body would be broken up as soon as the radius of its orbit fell to 2·45 times the radius of the large body. If the bodies are of different density the matter is slightly more complicated. We must imagine the larger body to expand or contract until it has the same average density as the smaller body; the critical distance is then 2·45 radii of the larger body in its imaginary expanded or contracted state.

This distance is generally known as Roche’s limit. A satellite can with safety describe a circular orbit about its primary so long as this orbit lies beyond Roche’s limit, but it is broken into fragments as soon as it trespasses within the limit. The following figures confirm Roche’s mathematical analysis:

At the same time they suggest very forcibly that Saturn’s rings are the broken-up fragments of a former satellite which ventured into the danger-zone marked out by Roche’s limit. We have seen how our own moon is destined in time to contract its orbit, until it is finally drawn within the Roche’s limit surrounding the earth and broken into fragments. After this the earth will have no moon, but will be surrounded by rings like Saturn.

We speak of Saturn’s rings in the plural, because two distinct circular gaps cause an appearance of three detached rings. There is a tendency to jump to the hasty inference that the rings are the shattered remains of three distinct satellites, but it is not so. Goldsbrough has shewn how certain orbits around Saturn are rendered unstable by the motions of the larger satellites of Saturn, so that no particle could permanently remain in such an orbit. He has calculated positions for these unstable orbits, and these are found to agree exactly with the positions of the observed divisions between the rings. Thus Saturn’s rings were in all probability produced by the breakage of a single satellite. The ring of small satellites which our moon will ultimately form round the earth will contain no divisions, because the earth has no other moons to render certain orbits unstable.