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THE ORIGIN OF THE SOLAR SYSTEM1
J. Jeans.
Modern astronomers have telescopes whose apertures range from that of the human pupil (one fifth of an inch) to the aperture of the giant telescope on Mount Wilson—more than 100 inches in diameter. If we lived in the midst of infinite space uniformly filled with stars, or if their distribution could be regarded as uniform on the scale of existing telescopes, then the number of stars visible in different telescopes could be taken as proportional to the cube of the aperture.
In reality, our unaided eye distinguishes about 5,000 stars; with the aid of a one-inch telescope this number rises to about 100,000, with the aid of a ten-inch telescope—to 5 million, and with the aid of a hundred-inch telescope, probably, to 100 million. These numbers increase far more slowly than the cubes of the apertures. Hence it may be concluded that we are surrounded by a non-uniform field of stars. We live in a finite universe, the distribution of bodies in which becomes very noticeably thinner even at the small distances attainable by our telescopes. It is supposed that the whole universe contains approximately 1,500 million stars; our Sun is situated not very far from its center.
Let us imagine the various celestial bodies in the order of their distance from us. Neglecting all bodies much smaller than our Earth, we must first of all dwell on Venus and Mars, which approach us to distances of 26 and 35 million miles. Next comes Mercury, whose nearest distance from us is 47 million miles. The most distant planet (Neptune) is separated from us by a distance of about 2,800 million miles.
But then there comes a great gap. The first luminary beyond it is the dim star Proxima Centauri, at a distance of 24 trillion miles, that is, 8,000 times farther than Neptune; after it comes $\alpha$ Centauri, at a distance of 25 trillion miles from us. Then, in order, come the faint red star Munich 15 040, at a distance of 36 trillion miles, and another faint star—Lalande 21 185—at 47 trillion miles. Thus the nearest group of stars is millions of times farther from us than the group of planets near to us. Then comes Sirius, the brightest star in the sky, at a distance of 50 trillion miles. Farther on begins a whole series of celestial bodies, more than 20,000 times farther from us than Sirius; but much earlier than these bodies there are spiral and spheroidal nebulae and primary star clusters. The nearest of the latter, whose distance is known more or less accurately, is the star cluster N. G. C. 7006, which, according to Shapley, is 25,000 times farther from us than Sirius. The light from this star cluster reaches us after 200,000 years; meanwhile, to pass through the entire thickness of this cluster, light requires several hundred years. Apparently, the star cluster N. G. C. 6822 is considerably farther away. According to Shapley, its distance from us is about 6,000,000,000,000,000,000 ($6 \cdot 10^{18}$) miles—this distance light traverses in a million years. As one may now think, the light emitted by these stars at the present moment will reach us by the end of the existence of our solar system; the light, however, observed now was emitted in the epoch of the formation of our planets.
It is not easy to juxtapose and compare all these different distances at once, but we shall nevertheless try to do so. The Earth moves around the Sun at a speed of about twenty miles per second; in a year it describes an orbit about six hundred million miles long.
If we represent the area of the Earth’s orbit in the form of a pinhead or a point with a radius of one-hundredth of an inch, then the Sun will be equal in size to an invisible speck of dust, and the Earth—an ultramicroscopic particle with a diameter of one-millionth of an inch. Neptune’s orbit, enclosing within itself the entire solar system, will appear as the circumference of a small coin, while the distance to the nearest star, Proxima Centauri, will be equal to 75 yards, and to Sirius—160 yards. On the same scale, the distance to the nearest star cluster N. G. C. 7006 will appear as a length of 2,400 miles, and to the cluster N. G. C. 6822—about 12,000 miles; and, consequently, roughly speaking, the entire universe can be represented within the volume of our Earth.
From this it is evident that we are going to study the origin and history of a system whose dimensions stand in relation to the dimensions of the universe as the dimensions of a three-pence coin stand to the dimensions of the Earth. Why, then, have we become so interested in this small coin? First of all because, for all its insignificance, it is our own—our собствен-
...ness, or at least a part of it, a millionth of an inch in diameter, is our property. But there are also historical motives here, not at all so sentimental.
We have already pointed out that between our system and its neighbors there lies a colossal space. For the development of astronomical knowledge this space has always served as a great hindrance. Even in the last century mankind’s conception of the world beyond the limits of this space was extremely meager; the stars appeared to be no more than shining points, “fixed luminaries.” At that time the problem of the universe was of necessity reduced to the problem of the origin of our system.
Recent investigations have changed all this, and modern astronomers possess a large stock of information about the nature, structure, and motions of bodies lying beyond the limits of our system. A cosmogonist of the last century could assert that the solar system arose in such and such a way without fearing that his theories would suffer a fiasco when compared with other systems. But if I now propose to you a theory of the origin of the solar system, you may at once demand its application to the explanation of the properties of one and a half billion systems lying beyond the interval mentioned above. Did their development proceed along the same path, and if not, why? It is well to begin the study precisely with these systems.
Among these one and a half billion objects there is a certain, comparatively small, number of classes whose nature and behavior remain mysterious: these are the planetary nebulae, variable Cepheids, long-period variables of the Mira Ceti type, and a few others. With the exception of them, all the remaining known objects can be arranged in one simple continuous series. This series may be composed, for example, according to increasing density; it will begin with especially rarefied nebulae and end with solid stars having the density of iron. But there can be no doubt that such a series is an evolutionary one; according to the laws of physics, the density of a body increases if it radiates heat, and, besides this, the density does not increase. Let us begin our survey, then, with the very first links of the chain accessible to us—with the nebulae.
If we exclude the enigmatic “planetary” nebulae, then all the rest fall into two sharply delimited classes, which may be called nebulae of regular and irregular form.
Representatives of nebulae of irregular form are, for example, the great nebulae of Orion and the nebulae surrounding the Pleiades. Until quite recently, nebulae of irregular form were assigned a very great role in the evolution of worlds. It was observed that they are usually associated with especially hot stars; hence there followed a beautiful, simple cosmogony, which looked upon these stars as...
on the product of the condensation of nebulae and allowing, in their subsequent life, a gradual, continuous cooling. This cosmology was too simple to last for long—it was created several decades ago by the investigations of Russell, Hertzsprung, and others. Thanks to the latter, we now know that very hot stars are associated with irregular nebulae and that they are at the threshold of their life, beginning to decline toward old age.
Let some mass of rarefied gas contract and radiate heat. If the mass radiated without contracting, it would cool; if, on the contrary, the mass contracted without radiating, it would begin to heat up. But if radiation and compression occur simultaneously, then without mathematical investigation it is unknown which of the two tendencies will prevail. In 1870 Homer Lane showed that a mass of gas, at sufficiently low pressures, when it approximately obeys the ordinary laws, must in fact heat up while radiating. Cooling cannot begin until the moment when the density reaches a certain limit, when deviations from the laws of a perfect gas begin; this occurs when the nebula is already not far from the stage of cooling. From this we see that the maximum temperature pertains to the middle age of the star—to an age when its substance can no longer be considered a perfect gas. In this middle period of a star’s life, the temperature at its surface must be about 25,000° C, whereas the temperature at its center may reach millions of degrees. Its mean density is probably equal to about one-tenth the density of water. It is still unknown why stars with such a maximum temperature are in some close connection with nebulae of irregular form. It is possible that certain stars, at very high temperatures, are able to illuminate the surrounding accumulations of matter, which otherwise would be invisible. In any case, apparently, nebulae of irregular form do not serve as an indispensable link in the evolutionary chain. It is more probable that they are a by-product, and, as such, we shall consider them in the further exposition.
Let us now return to nebulae of regular form. Most of them have the appearance of circles or ellipses, sometimes smoothly outlined at the ends of the major axes, and sometimes possessing pointed ends. An example of the latter type is shown in Fig. 1. (Nebula N. G. C. 3115.) A whole series of nebulae of regular form have been studied spectroscopically, and in some cases a rapid rotation was found around an axis coinciding with the shortest diameter of the nebula. A mathematician can calculate the form assumed by a mass of rarefied gas when rotating. If the rotational motion
absent, the mass would take the form of a sphere. With slow rotation the form passes into a slightly flattened ellipsoid of revolution—that is, one resembling an orange, just as our Earth resembles one. As the rotation accelerates, the spheroid begins to stretch out along the equator and, finally, at very high velocities, assumes a form resembling a biconvex lens with a sharp edge along the equator, as is seen in the photograph of the nebula presented in Fig. 1. Such a sequence of forms is observed quite clearly in examples of various nebulae (of regular form). There is therefore every reason to suppose that nebulae are rotating gaseous masses; but we shall try to confirm this before finally adopting such an assumption.
When a mass of gas radiates energy, it must contract. If this takes place during rotation, then the moment of momentum must remain constant, and in order to preserve the former moment, the contracting gaseous mass must rotate at a speed greater than the initial one. This circumstance, which served as the cornerstone of the Kant–Laplace cosmogony, retains deep significance for the cosmogonist of our own day as well. Every nebula, as its age increases, begins to rotate ever faster and faster and, finally, if nothing accidental interferes, assumes the form seen in Fig. 1. Such a form marks a turning point in the life of a nebula. After reaching it, the nebula continues to contract, and the speed of rotation must increase in order to preserve the former angular momentum. But mathematical analysis of the motion shows that beyond this limit the form can no longer stretch out along the equator while preserving equilibrium. Further contraction entails the rupture of the nebula, with part of the matter being drawn outward from the equatorial region.
Fig. 1.
Up to now we have been saying that the equator of the nebula has the form of a circle, which undoubtedly would be true if the nebula were isolated in space. But in reality nebulae have neighbors, and these neighbors must produce on the surface of the nebula—
ness, tides and ebbs, just as the Sun and the Moon cause tides and ebbs on the surface of the rotating Earth. Wherever there are neighboring bodies, there must always be two opposite points of maximum tides and two points, situated on two sides between them, of greatest ebbs. Therefore the equator, instead
Fig. 2.
of the form of a circle, will take an elliptical form. If the equator of the nebula were an ideal circumference, and the nebula were entirely symmetrical with respect to the axis of rotation, then the ejection of matter would begin simultaneously at all points of the equator. In fact, there could be no grounds here for this process to begin at one point earlier than at another. But in nature there is nowhere such
Fig. 3.
perfect equilibrium; if the principal factors compensate one another, then there will always be small factors disturbing the equilibrium in one direction or another. In the present case, there would be no difference between all points of the equator if such secondary factors were absent, but as soon as they appear, a difference immediately arises. It may quite justly be supposed that such factors, causing the initial ejection of matter at individual points, are tides, and mathematical investigation shows that, in this case, the ejection of matter will begin
in two antipodal points, at which the tide is maximal. These points lie at the ends of the major axis of the equator, which has an approximately elliptical form. After the nebula passes the critical limit (Fig. 1), its form continues to remain lenticular, but now at two antipodal points of its equator the separation of matter begins.
This coincides perfectly with what we observe in spiral nebulae. Fig. 2 (N. G. C. 5866) depicts a nebula in which the ejection of matter is only just beginning; we observe here a swelling near the equator and a dark band which, probably, owes its origin to ejected matter that has already had time to cool.
Fig. 4.
Fig. 3 (N. G. C. 4594) represents a further stage of development, and Fig. 4 (N. G. C. 891) an even more advanced stage, when the separated matter, although not yet entirely, has very strongly exhausted the mass of the nucleus.
Fig. 5.
In all these figures we have seen nebulae very close to one another. Fig. 5 (M. 51) shows the well-known “Whirlpool” in Canes Venatici—a nebula physically similar to the nebula of Fig. 4, but seen this time from the front: we observe it along the direction of the axis of rotation. Here the central nucleus occupies only a small part of the whole picture. Figures 6 (M. 101) and 7 (M. 81)
depict nebulae whose development has gone further, so that in the last of them there remains only a very small nucleus, while all the rest of the space is occupied by matter ejected, according to our assumption. In both of the latter nebulae the streams of separated matter are situated at two diametrically opposite points, as follows from the dynamical theory. Until now we have said that the elements of a spiral nebula are composed of matter ejected by the nucleus, as the theory indicates; but we shall not be satisfied with theory alone: quite direct experiments confirm the same thing. Various astronomers, especially Van Maanen, have discovered motion in the arms of many spiral nebulae, including those shown in Figures 5, 6, and 7. Their observations have shown that the arms of the nebulae do in fact consist of matter ejected by the nucleus. Figure 8 shows the motion found by Van Maanen in 100 points of the nebula M. 81; the arrows show the displacements over a period of 1,300 years1; studies of various other nebulae gave approximately the same result; it is therefore difficult to doubt that the arms of nebulae consist of matter flowing out from the nucleus.
Fig. 6.
Measurements of the actual velocities in the nebula M. 51 (Fig. 5) have shown that its particles make a complete revolution around the nucleus in 45,000 years; in M. 81 (Fig. 7) the corresponding period is 58,000 years, and in M. 101 (Fig. 6)—about 85,000 years. From this one can determine the density of the matter in the nucleus. It has been found that this density is on the order of \(10^{-16}\) grams per cubic centimeter, which corresponds to a vacuum more perfect than that which can be achieved in laboratories. If an insignificant volume of gas
if one were to spread the matter in an ordinary electric incandescent bulb over the volume of a large church, its density would still be 10,000 times greater than the density of the nucleus of a nebula.
The nebula shown in Fig. 4 has a granular structure. In M. 51 (Fig. 5) condensation is already clearly expressed, while in the outer regions of M. 101 (Fig. 6) and M. 81 (Fig. 7) this condensation has proceeded still further, isolating individual star-like points. When gas bursts from an ordinary sun into a vacuum, it immediately expands, striving to occupy the entire volume offered to it. Why does this not occur when gas flows out from the nucleus of a nebula? The expansion would assume gigantic dimensions if the indicated process took place here. But as the scale increases, the influence of gravitation begins to tell, until, finally, on the scale of nebulae, gravitation begins to prevail over the tendency of the gas to expand and merges the ejected matter into separate streams. After this has occurred, phenomena will take place which the dynamical theory can also predict. As regards the distribution of density along the threads of the currents, the elasticity of the gas tends to equalize this density; on the contrary, under the influence of gravitation, the streams tend to condense into separate clumps. When the usual dimensions of nebulae are reached, the latter tendency predominates, and the ejected matter breaks up into drops, much as water flowing from a tube breaks up into drops, but, of course, for entirely different reasons. In the photographs reproduced in Figures 4, 5, 6, and 7, we can trace the course of this process.
Fig. 7.
The dynamical theory not only predicts the formation of such gas drops, but even makes it possible to calculate their dimensions, masses, and mutual distances. Comparing these distances, expressed in kilometers, with the angular distances observed directly in the sky makes it possible to calculate the distance from us to the nebula. It may be noted with satisfaction that the distances calculated by this method are in excellent agreement with other determinations. Calculations of the masses of condensed gas drops lead to still more interesting and important results. In some nebulae for which the corresponding calculations have been made, the mass of such separate clumps has proved equal to the average mass of a star.
Fig. 8.
This, it seems to me, gives the key to deciphering the evolution that interests us—we are present here at the creation of new stars. In Fig. 1 we saw raw material—an extremely rarefied gaseous mass, continuously contracting and at the same time rotating ever faster and faster, until, finally, the system disintegrates. The contraction and acceleration go further, and in Figs. 2 and 3 we see the beginning ejection of matter, from which stars will subsequently arise. In Figs. 4 and 5 one can see the initial germination of individual stars, owing to the condensation of the ejected mass. Finally, in the outer regions of Figs. 6 and 7 the final products of condensation are noticeable—separate masses which, although they have not yet reached the density of ordinary stars, have already begun to lead an independent existence. Each of these masses will traverse the whole path already described by us in detail. It will contract, heating up in the process—until those times
until the laws of an ideal gas still continue to be obeyed; subsequently, upon reaching a certain critical point corresponding to the maximum temperature, the star will continue to contract, but already cooling as it does so and gradually turning into a dead, dark mass.
The number of stars born from a single nebula may reach
Fig. 9
millions. They may either mix with the entire mass of surrounding stars, or form their own independent family—if the original nebula is sufficiently remote from the other worlds. Examples of the first possibility may be the Pleiades and the stars of Ursa Major, in which all the stars have a common velocity and, generally speaking, identical physical properties. All the stars of such groups have been wandering together in space, apparently, from the very moment of their origin. An example of the second possibility—the formation of a separate colony of stars—may be the so-called “globular” star cluster
clusters, similar to the well-known Hercules star cluster (Fig. 9). It is globular only in name; in fact Shapley found that it has the form of an ellipsoid possessing a plane of symmetry, as indeed should be the case if it is the product of a rotating nebula.
It is apparently impossible to assert that the two cases indicated are exclusively possible. It is more probable that they serve as the ends of a continuous chain of all possible types of stellar groups born from a single nebula. It is even possible that the so-called “great star cloud” is nothing other than an assemblage of star clusters that have arisen from a single nebula. The clusters here are so intermingled that it is difficult to discern separate groups of stars, but nevertheless our conjecture is not without probability on certain grounds. In 1905 Kapteyn noticed that near the Sun the stars form two “star streams,” each of which moves with its own velocity in space.
Leaving aside the question of the extent of these streams in space, one may suppose that they are moving star clusters. Soon afterward, independently of one another, Eddington and Holm (Halm) found a third “stream,” or moving star cluster, consisting of very hot stars, which astronomers assign to classes B and O. In this case we know the dimensions of the cluster and its approximate shape. According to Charlier, its shape resembles a round biscuit lying parallel to the Milky Way, its diameter being 2.8 times its thickness. Some star clusters have a common origin, but their original form changes sharply as soon as they enter the surrounding stellar medium. Dynamical theory shows that, after entering the stellar world, a cluster must assume the form of a round biscuit parallel to the Milky Way, with the diameter 2.5 times greater than the thickness. This agrees rather well with the observations and shows that all the stars in the “stream” are of one origin; the same also applies to certain small moving clusters, for example to the already mentioned cluster of the Great Bear. We cannot, of course, claim complete certainty for our assumptions, but there is nevertheless reason to think that the “great star cloud” is a lump of intermingled star clusters, each of which formed from a separate nebula. This, of course, has no bearing on the question of the origin of the solar system; we have touched upon it only in order to complete the aggregate of ideas concerning the evolution of the stars.
Such evolution is similar, and in its first stages completely identical, to that which Laplace adopted in his famous hypothesis on the origin of the solar system. Before our eyes there has passed the rotation and contraction of nebulae; we have noted the condensation of matter
into separate masses; finally, we have witnessed the beginning of the wanderings of these separate masses in space, and all this agrees exactly with what Laplace had depicted.
Only one difference may be noted. We have traced the evolutionary process on a scale of which Laplace never dreamed. He supposed the dimensions of the original nebula to be equal to the orbit of Neptune, and I have already said at the beginning of this article what the difference in scale is between it and the distances of stellar worlds. If we again take the diameter of Neptune’s orbit as the diameter of a small coin, then the nucleus alone of the nebula in Figures 6 and 7 will fill the whole of the Albert Hall, and the corolla will cover all of Hyde Park and Kensington. If we wished to change the scale so that bodies the size of our Earth would become visible to the naked eye, then on this scale the nebula would extend over the whole district, and perhaps over the whole continent.
But if the original nebula is incomparable in size with that of Laplace, nevertheless the gaseous condensations into which it breaks up approach in their mass Laplace’s assumptions, and their dimensions differ from Laplace’s only rather insignificantly. If we admit that these young formations behave in the same way as the original nebula, then the origin of planets can be explained; if, however, we take into account the tertiary disintegration of matter, repeating the history of its ancestors, then the origin of satellites can also be explained. But mathematical investigation and direct observation contradict such a simple hypothesis concerning the origin of the solar system. As we have seen, the filaments of spiral nebulae attain enormous dimensions, and, at such dimensions, gravitation prevails over the elasticity of the gas, forcing it to condense. Nebulae whose mass is comparable with the mass of the Sun at first follow the same course of life until the expulsion of matter begins from their equator. After this their cycle of development differs from that described above. The ejected matter cannot condense into filaments, still less into clumps; it forms a rarefied atmosphere surrounding the nebula. Such a system begins to contract more and more, radiating heat; at the same time the constancy of angular momentum is maintained by the ejection of ever new gaseous masses from the center into the atmosphere.
Mathematical investigation shows that, after the central star has contracted to a certain critical density—approaching one tenth of the density of water—a catastrophe occurs, in which the whole system is transformed into a binary star: two stars of commensurable mass begin to revolve around one another in a very close, approximately circular orbit. This is a formation with which practical astronomers are well acquainted. They have found that a very considerable part—probably more than half—of the stars in the sky turn out to be
are called double. Initially they are found, as was mentioned, at a very close distance from one another. Subsequently they move farther and farther apart, while the eccentricity of the orbit increases. Theory shows that the process of division which led to the splitting of one star into two can also be repeated with each of the companions, whereby a “complex”—triple, quadruple, etc.—star is formed. Russell, who investigated this question theoretically, found certain numerical relations between the mutual distances of complex stars; he also showed that the predictions of the theory are confirmed by observations.
Thus far, therefore, theory and observation go hand in hand. We have followed the course of development of astronomical objects along the path from the finest nebulae to the densest complex stars, and at all stages of this path observations have confirmed the theoretical predictions. But not all astronomical objects traverse this entire path. The guiding cause on this path is rotation in conjunction with the contraction caused by the radiation of heat. After a sufficiently prolonged contraction, hardening begins; the rate of rotation can no longer increase, and the evolution of the body, from the physical point of view, is arrested. The duration of the development of each given body depends on the stock of living force of rotation it initially possessed. If, at the beginning of its life, a nebula does not rotate at all, it will forever preserve a spherical form, gradually turning into a cold, non-radiating mass. Such a nebula will never leave its initial condition. This is apparently improbable, but we do nevertheless know that some nebulae freeze and die without reaching the critical stage (Fig. 1), at which the birth of a star begins. In exactly the same way, many stars cool and cease to develop, never reaching the stage of the formation of double stars. Likewise, many double systems can never pass into more complex systems. Let us turn here to observations: pure double systems are known in numbers ten times greater than complex systems that have passed through the double stage. Theory has given us the possibility of tracing the whole cycle of the development of objects, but both theory and observations show that only a few systems can pass through this entire cycle.
We now approach the very essence of the question. Nowhere in this cycle have we found the solar system, or anything even slightly resembling it. If our Sun were not surrounded by planets, we should without difficulty ascertain its origin. It could be supposed that it was born from an ordinary nebula, and that its development proceeded along the normal path, but that it possessed a small store of the living force of rotation, and therefore deviated from the usual evolutionary path before it had time to split into a system of a double star. Indeed, it could be admitted that its history is the same as the history of half
stars in the sky. An argument in favor of this assumption may be the circumstance that the mass of the Sun is equal to the mass of stars born from nebulae, and that, with the exception of the planets, it is in all other respects similar to millions of other stars which apparently originated from nebulae. Confirmation of the hypothesis of a small store of angular momentum, which halted its further development, may be furnished by the slowness of its rotation at the present time. A simple calculation shows that the Sun possesses only a small part of the total angular momentum necessary for disintegration. Even if we add the angular momenta of all the planets, supposing that they once separated from the Sun, we shall arrive at the same conclusion: the angular momentum of the whole system constitutes only a small part of that required for the disintegration of the Sun and the formation of a binary-star system. The origin of the Sun, therefore, is understandable to us. Difficulties arise when we attempt to explain the origin of the planets and their satellites.
It has already been noted more than once that certain astronomical systems do not fit into our conception of the ordinary evolutionary path. Particular examples may be planetary nebulae, Cepheids, and long-period variables. Since the development of some systems does not coincide with the path described above for the majority of the luminaries, we must suppose that various branchings can adjoin this main path, along which development may proceed under the influence of various causes. This is the only thing that can be assumed. We can expect that two stars will meet with one and the same fate with still less probability than if we were speaking of two people. We assumed that our normal star develops in the universe quite independently, while its angular momentum remains constant and is not subject to perturbations from neighboring suns. Mathematicians find it convenient to assign to each star an entirely boundless world, but in nature this is not so. However, never do the ideal assumptions of mathematicians come so close to the truth as in our case. On the scale that we have already used, and in which the Sun appeared as a microscopic particle—one ten-thousandth of an inch in diameter—the most gigantic of the known stars would appear as a pinhead, one thirtieth of an inch in diameter. The space allotted to the stars, on this same scale, would appear as the interior space of the cathedral of Peter and Paul. This space is not easy to fill, although one may imagine that, in their motions, some stars can disturb the motion of others when they meet; but it is perfectly clear that any serious interactions can take place here only in rare, exceptional cases. Obviously, we were right in considering the evolution of a star as entirely undisturbed by neighboring bodies; we now see why the enormous majority of stars develop precisely along this normal path.
In all probability, the number of stars that have strayed from this normal path is very small. The number of stars in the sky is approximately equal to the number of people on Earth; the number of exceptional systems known to us corresponds to the population of a small town, although, of course, one may suppose that some of these exceptional systems are still unknown to us. There is no reason to think that the cause which diverts a star’s development from the normal path can be only the influence of neighbors—but there are sufficiently few systems that constitute an exception for this to be regarded as true in the majority of cases.
But we have to concern ourselves not with exceptions in general, but with our solar system in particular. What neighboring star diverted it from the general path of development? Here, for the first time, astronomical observations cannot help us. No system is known in the vicinity of the solar system that could in one way or another have exerted this influence. But there is no reason to think that such a system does not exist: it is possible that we simply do not see it, as being dead. Astronomers of some distant star would observe our Jupiter as the brightest body, after the Sun, in our system, but even its brightness would amount to only one three-hundred-millionth of the brightness of the Sun. From the nearest known star to us, Proxima Centauri, the Sun would appear as a star of the first magnitude, while Jupiter would be a star of magnitude 22.2, the angular distance between them being equal to four seconds of arc. A star of magnitude 22.2 is completely inaccessible to observation in our telescopes, all the more so because it is located at a distance of four seconds from a star of the first magnitude. We must take care to increase the power of our telescopes considerably before we can hope to notice in the sky systems similar to ours and, moreover, no farther from us than Proxima Centauri. It is therefore clear that here our investigations pass beyond the limits of that domain in which observations can confirm or refute our conclusions: from here begin exclusively theoretical constructions.
In beginning our investigations, let us note that the solar system possesses certain very striking characteristic features. It is by no means a collection of bodies accidentally grouped together—otherwise one would have to renounce the idea of unraveling their origin. But characteristic features are possessed not only by the system of the Sun and the planets; the same features are repeated in the smaller systems of Jupiter and Saturn with their satellites. Each of these small systems is a reduced copy of the solar system, and therefore one cannot be satisfied with an explanation of the origin of only one of these systems if the origin of the other two is not explained at the same time. The chief common features of these three systems are that their orbits, with few exceptions, lie in one plane, and that these orbits are everywhere described in one
and in the same directions, and that the masses of the satellites in relation to the planets are just as small as the masses of the planets in relation to the Sun. For example, the mass of the Sun is 1047 times greater than the mass of the largest planet, Jupiter, while the mass of the latter is 11000 times greater than the mass of the largest of its satellites. The smallest difference in masses is found in our Earth–Moon system, where the mass ratio is \(81:1\). In systems with a large number of satellites (for example, the Sun, Jupiter, Saturn) there is observed a general tendency for the masses to increase up to a certain maximum and then subsequently decrease—as the distance from the central body increases. Thus, in the principal system there is a regular sequence: Mercury, Venus, Earth, Mars, Jupiter, where only Mars violates the regularity, having an anomalously small mass, and a descending sequence: Jupiter, Saturn, Uranus, Neptune, in which Neptune likewise represents an exception, since its mass is several percent less than that of Uranus.
In describing the principal evolutionary path, we had in mind a contracting and rotating mass—initially gaseous, then liquid, and finally solid—developing independently in space. Such a system must possess noticeable characteristic features throughout its entire life; namely, it must have a plane of symmetry. In its most primitive state, while it was only a chaos of independent molecules, this plane must coincide with what mathematicians call the “invariable” plane of the system. Later, when the mass assumes the regular form of a rotating nebula, this plane becomes equatorial, and in it gradually appear clots which then condense into individual stars. The symmetry of spiral nebulae with respect to the equatorial plane shows of itself that they developed from rotating masses in the absence of extraneous, disturbing influences.
If our solar system had developed from a rotating mass not subjected to perturbations, then it would possess a common plane of symmetry. The orbits of almost all the planets and satellites would, indeed, lie approximately in one plane, which therefore may be taken as the plane of symmetry. But the axis of rotation of the Sun is not perpendicular to this plane. The Sun has its own equatorial plane of symmetry, which is inclined at an angle of \(7^\circ\) to the plane of the planetary orbits.
The noncoincidence of these two planes already in itself shows that our system could not simply have developed from a rotating, unperturbed mass. Therefore, in looking into the remote past of our system, we must take into account both the rotation of the masses and the external influence upon them. In the first, rough approximation, it will naturally be assumed that the plane of the solar equator coincides with the plane of rotation of the original system, while the plane of the planetary orbits was determined by external influences.
Of all the interactions between two separate astronomical bodies, gravitational attraction is the most significant. The Moon was once credited with influence over the most varied phenomena on Earth, for example, over the weather, over the fate of people, over their feelings and even over their health; but the only influence that has deserved scientific investigation is gravitational attraction, which causes periodic tides. Undoubtedly, collisions between two astronomical bodies will entail more tragic results than a tidal wave, but we shall not consider them here. Such collisions probably occur extremely rarely; they also may cause a system to deviate from its principal evolutionary path, but it cannot be admitted that our solar system deviated from its principal path precisely under the action of such a catastrophe. Since, for lack of time, we cannot investigate all possible branchings of the evolutionary path, we shall turn to the branching most probable for our system—one caused by a very powerful tidal action.
The height of the tide caused on the Earth by the Moon reaches, on average, several feet. This height is approximately one ten-millionth part of the radius of the Earth—a part which we shall call the tidal fraction. If the Moon were ten times heavier, the tidal fraction would increase tenfold; if its distance from the Earth were reduced by half, the tidal fraction would increase eightfold. If we agree to measure masses in fractions of the mass of the body on which the tides arise, and if as the unit of length we take the radius of that same body, then the tidal fraction will be equal to the mass of the tide-producing body divided by the cube of the distance, i.e. \(\dfrac{M}{R^3}\). From this formula we shall find that the nearest star to us, Proxima Centauri, produces on the Sun a tide of immeasurably small magnitude; the tidal fraction here is \(10^{-26}\), and the actual height of the tide is \(10^{-15}\) cm, i.e. one fiftieth part of the radius of an electron. This simple illustration shows that under normal conditions interactions between neighboring stars are exceedingly insignificant. In order for tidal forces to acquire importance in cosmogony, anomalous conditions are necessary.
Our Sun at the present moment has no sufficiently close neighbors; but it is possible that at some time, in its wanderings among the stars, it passed by one of them at a distance smaller than the present distance to Proxima Centauri. The most trustworthy methods of judging the age of the Earth, provided by geology and by the study of radioactivity, indicate figures from 800 to 1,100 million years. For reliability, let us take the age of the Sun to be 1,000 million years. Let us make an assumption, departing little from the truth—that during the-
in the course of all this billion years the Sun and all the stars moved exactly as they do now, with the same average velocities, maintaining the same mean distance from one another. During this billion years the distance of the Sun from the nearest stars must have gradually changed, and consequently different stars, one after another, found themselves in the role of nearest neighbors. But there was once a time when the Sun was closest of all to some one of the stars. A calculation based on the theory of probability shows that this nearest distance must have been of the order of \(7 \times 10^{15}\) cm,—a distance which is, in any case, one six-hundredth of the distance of Proxima Centauri and exceeds the radius of Neptune’s orbit by fifteen times. Even if the Sun filled the entire orbit of Neptune, the tidal part caused by such a nearby star, with mass equal to the mass of the Sun, would be equal to
\[ \frac{1}{(15)^3}, \quad \text{or} \quad \frac{1}{3375}, \]
i.e. the height of the tide would be altogether insignificant from the standpoint of cosmogony. As matters stand, tidal interaction between individual stars must be recognized as inessential in cosmogony, unless by chance these two stars pass at an exceptionally close distance from one another.
It is possible, therefore, that our Sun became the victim of such an exceptionally close encounter. There are no grounds for considering such a case a priori improbable. As a result of such a close encounter, as we shall see, there could have arisen a system in many respects resembling our solar system.
Our calculations of probabilities were based on the erroneous assumption that the conditions of the stellar world remained similar to the present ones over a period of a billion years. Looking into the remote past of the universe, we encounter an epoch when all conditions differed sharply from the present ones. We shall reach an epoch which we have already investigated, and in which the Sun had not yet acquired its present characteristic features. It was one of the satellites in the wreath of a spiral nebula, moving together with thousands of similar condensations. Its density was incomparably less than at present, and its dimensions correspondingly larger. It was, perhaps, much closer to its neighbors than it is now. In this ancient period of its existence the tidal effect caused by its neighbors was enormous; we shall touch on this more closely.
Generally speaking, when one star passes near another, the tide disappears as soon as the tide-producing body recedes. Even if the luminaries approached so closely that the height of the tide exceeded the radius of the first star, then, after the recession of the second, the first again assumes its initial spherical form. But there exists a limit beyond which the initial form can no longer be restored. The limiting distance depends, first of all, on the mass of the perturbing body; to a lesser degree it depends on the velocity of rotation,
The form and distribution of the density of the first star; it also depends slightly on the velocity of one star relative to the other. We shall obtain a sufficiently correct picture of the course of events if we imagine the first star surrounded by a certain fictitious sphere, whose radius depends on the mass of the perturbing star. If its mass is equal to the mass of the first star, then the radius of the imaginary sphere will be equal to \(2^{1/4}\) actual radii of the first star; if the perturbing star is seven times heavier than the first, then the radius of the imaginary sphere will exceed the actual radius of the first star by a factor of \(4^{1/2}\). Until the center of the passing star enters inside such an imaginary sphere, the tide disappears when the perturbing forces are removed; but as soon as the center of the perturbing star penetrates inside the imaginary sphere, completely new phenomena begin.
As the perturbing body approaches, the tide rises higher and higher, while at its highest point the force of attraction toward the center of the first star keeps decreasing and decreasing. At the same time, the attraction toward the center of the perturbing body begins to make itself felt ever more strongly. Finally, precisely when the center of the passing body moves along the periphery of the critical sphere, the gravitational forces of the two bodies acting on the tide balance one another—this condition determines the dimensions of the critical sphere. If the passing star pierces this sphere, then the particles of the tidal wave are torn away from the first star, for the resultant gravitational force is now directed toward the perturbing body. As a result, at the point of the highest tide a stream or clump of gas is torn away. Each ejected particle of gas begins to move under the combined action of the first and second stars, and the problem of determining its orbit is a special case of the three-body problem, which, unfortunately, is insoluble. But, generally speaking, the path of the ejected matter, undergoing various curvatures, will all the time lie in the plane containing the orbit of the perturbing star.
If such an ejection of matter from the Sun occurred simply under the influence of rotation and contraction, then the gravitational attraction would be, as we have seen, insufficient to counteract the elastic expansion of the gas, and the matter would quickly be dispersed in space. In the case we are now examining, the conditions are essentially quite different: contraction with emission of heat is a very slow process, whereas the catastrophe associated with the tide can occur very rapidly. The effect of the star’s rotation will manifest itself after thousands of years, whereas a decade is quite sufficient for the tide-producing body to appear, do its work, and depart. The gaseous stream ejected when the rotational speed increases is extremely thin; the stream ejected in a tidal catastrophe may easily exist independently, and its gravitational field is quite sufficient for it to condense into a compact mass.
If gravitation is able to accomplish this, then it can also break up the jet into separate condensations, as happens in the condensation of spiral nebulae. But here one must take into account an essential difference. The compression of nebulae is a slow, age-long process. Year after year, century after century, the outflow of jets of uniform form continues—a process that may be compared with the twisting of a rope. But a tidal catastrophe, on the contrary, proceeds rapidly: within a few years the ejection of the jet begins, reaches its maximum development, and then ceases. When a jet of such a form disintegrates, it forms not a long chain of equal masses, but a small number of unequal masses. It is natural to suppose a priori that the largest masses will arise from the central parts of the filament, richer in matter, and the smallest from the end parts, where matter is most strongly rarefied. This assumption may be confirmed by the fact that the largest planets of our solar system, Jupiter and Saturn, are located close to the middle of the series of all the planets.
If the origin of the planets can be explained by a tidal catastrophe, then, obviously, the origin of their satellites can also be explained in general terms. Indeed, immediately after the birth of some planet—for example, Jupiter—the same initial conditions arise, but reproduced in miniature. Jupiter now falls to the lot of the Sun, while either one of the neighboring stars, or the Sun itself, produces a tide on it and the catastrophe connected with it. Since Jupiter, the Sun, and the perturbing star moved in one and the same plane—the plane of Jupiter’s orbit—its satellites, after their formation, must also move in this plane, which is confirmed by observation.
So long as we are investigating our question only in general terms, it is natural to think that the process may go on farther and farther, from one birth to the next birth, that each member of the family of satellites can produce still smaller satellites, which will revolve around it—and so on to infinity. But an inner sense suggests that this cannot continue without end: there must be some limit. Exact calculation confirms the arguments of this inner sense, but shows that we would pass beyond this limit if we applied to all satellites one and the same method of reasoning. I have already mentioned the mathematical formula that permits the calculation of the masses of bodies formed during the condensation of the wreath of spiral nebulae. The same formula will serve us also for calculating the masses of planets that arose from jets ejected by the Sun. Suppose that, at the epoch of the catastrophe, the radius of the Sun was equal to the radius of Neptune’s orbit, and therefore its density was \(5.5 \times 10^{-12}\). Let us assume that, in the middle of the ejected jet, the mean density was ten times smaller, i.e. \(5.5 \times 10^{-13}\). Let us further assume that the temperature of the ejected matter corresponded to the molecu-
velocities of \(4 \times 10^4\), such as are possessed by molecules of hydrogen or oxygen near their boiling points. Then our formula will show that the mass of planets formed from the middle parts of the streams should be about \(10^{30}\) gr., i.e. intermediate between the masses of Jupiter and Saturn. We note with satisfaction that our arguments, on which the calculations were based, have not led us to erroneous conclusions, and that the path we have indicated has proved to be correct. To confirm the “tidal” theory of the birth of these planets, we could reverse the course of the calculations and, taking as given their presently known masses, calculate what the density of the matter that gave rise to them must have been.
Of course, reverse calculations of this kind are applicable not only to Jupiter and Saturn; if the tidal hypothesis is correct, then such calculations can also be carried out with respect to all the planets and their satellites. For example, the first five satellites of Saturn have a mass of about \(5 \times 10^{23}\) gr.; our calculations show that, if these satellites had condensed from gaseous streams ejected by Saturn, then the density of this gas would have had to lie within the limits from the density of lead to a million times greater. Such an assumption is, consequently, absurd: the only thing that can be concluded is that Saturn’s satellites did not arise from a condensed gaseous stream.
Such a conclusion is not unexpected or unforeseen. Since even now these satellites, in view of their small size, could not retain a gaseous atmosphere, they could never have been in a gaseous state. They were born either in a liquid or in a solid state.
In this way we have finally reached the limit beyond which the formation of new satellites is already impossible. This limit is determined above all by the small size of the satellites. The process may also end because matter may pass into a liquid or even a solid state before it has yet had time to break up into parts, as probably happened with the satellites of the planets and with the minor planets.
What, then, is to be said about our Earth, which interests us more than all the other planets? Its present mass is too small to admit of its origin from a gaseous stream, but we must remember that if it was born in a gaseous state, then a large part of its mass would have been dispersed in space, so that the present Earth is perhaps only the remnant of a former, more massive planet. But such an approach to the investigation will give us nothing. More productive may be an investigation of our satellite, the Moon. If some planet was born in a liquid state, then under the influence of tides caused by the Sun it would have had to separate off a satellite; but the difference in masses between it and the satellite is not as great as in the case of gaseous planets. Consequently, in passing from planets born in a gaseous state to planets born...
having arisen in the liquid state, we shall encounter, instead of a large number of small satellites, a small number of relatively large ones and, finally, planets having no satellites at all. This is precisely what we observe in the solar system. Leaving Jupiter and Saturn, each possessing nine relatively small satellites, we pass to Mars with its two satellites and to the Earth with its one relatively large satellite; then follow Venus and Mercury, entirely devoid of satellites. Proceeding in the opposite direction from Jupiter and Saturn, we arrive at Uranus with its four small satellites and, finally, at Neptune, with its one relatively large satellite. From this point of view, the Earth–Moon system represents the boundary between planets born in the gaseous state and those born in the liquid state; in the other half of the chain the same connecting role is played by Neptune. Hence we may conclude that Mercury and Venus were born in the liquid or solid state, the Earth and Neptune partly in the liquid and partly in the gaseous state, and Mars, Jupiter, Saturn, and Uranus in the gaseous state.
We have already noted that Mars and Uranus possess masses that are too small in relation to their place in the series of planets. If the planets were born from a stream of gradually changing density, then the mass of Mars should be intermediate between the masses of the Earth and Jupiter; likewise the mass of Uranus should be intermediate between the masses of Neptune and Saturn. On the other hand, we have seen that, in all probability, Mars and Uranus are the smallest planets born in the gaseous state; it is therefore quite probable that both these anomalous planets in their time cast off into outer space more matter from their surfaces than did the other planets. Let us suppose, then, that Mars and, to a lesser degree, Uranus cast off into space a large part of their mass; let us suppose that they are merely the remnants of some heavier planets—and all the anomalies disappear, all the difficulties will be excellently removed.
Nevertheless, for all the great achievements of tidal theory, it by no means lays claim to a complete, final explanation of the origin of the solar system; it is only a theory that, it seems to me, most clearly depicts the history of this system and is freer than all others from insurmountable difficulties.
Translated by Vas. Shulykin.