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The Origin of the Solar System

An Outline of the Three Principal Hypotheses

THE question of the origin of the solar system is one that has been a source of speculation for over a hundred years; but, in spite of the attention that has been devoted to it, no really satisfactory answer has yet been obtained. There are at present three principal hypotheses that appear to contain a large element of truth, as measured by the closeness of the approximation of their consequences to the facts of the present state of the system, but none of them is wholly satisfactory. These are the Nebular Hypothesis of Laplace, the Planetesimal Hypothesis of Chamberlin and Moulton, and the Capture Theory of See. Darwings theory of Tidal Friction is scarcely a distinct hypothesis, but is mentioned separately on account of its application to all of the others. The main features of these hypotheses will be outlined in the present paper. The Hypothesis of Laplace.According to Laplace, the solar system formerly consisted of a very much flattened mass of gas, extending beyond the orbit of Neptune, and rotating like a rigid body. In consequence of radiation of energy this slowly contracted, and in so doing gained so much in angular velocity that the centrifugal force at the equator became greater than gravity, and a ring of matter was left behind along the equator. Further contraction would detach a series of rings. These were then expected to break up in such a way that each produced a gaseous planet. This might later evolve in the same way as the original nebula, thus producing satellites. The criticisms of this hypothesis in its original form are very well known, and will only be summarized here. Forest ranger beating out a fire in one of the National Forests in Oregon FIGHTING FOREST FIRES [See page 200] The angular momentum of the system when the gaseous central body extended to the orbit of any planet can be calculated, and is not nearly sufficient to cause detachment of matter. Poincare showed that this objection could be met if the nebula were initially highly heterogeneous, with all but gAtj of its mass in the central body. The matter left behind would not form definite rings; for a gas has no cohesion, and consequently the separation of matter along the equator would be continuous and lead to another gaseous nebula, not rotating like a rigid body. A ring could not condense into a planet. According to the latest work of Jeans, viscosity is inadequate to make a mass of gas as large as a Lapla- cian nebula rotate like a rigid body. No satellite could revolve in a shorter time than it takes its primary to rotate: this condition is violated by Phobos, the inner satellite of Mars, and by the particles constituting the inner edge of Saturn's ring. All satellites should revolve in the same direction as their primaries rotate: this condition is violated by one satellite of Saturn and two of Jupiter. The second, third, and fourth objections seem quite unanswerable at present. The theory of Gravitational Instability, due to Jeans, is an attempt to pass directly from the symmetrical nebula to an unsymmetrical one with a secondary nucleus, without the ring as an intermediate stage. It will be noticed that Laplace's hypothesis implies that all the planets were formerly gaseous, and hence must have been liquid before they became solid. The question of the course of evolution of a gaseous mass initially heterogeneous with several strong secondary condensations has not hitherto been considered; such a mass would be free from at least the first four of the objections offered to the standard forms of Laplace's hypothesis, and its history would serve as a hypothesis intermediate between this and the Planetesimal Hypothesis. The Planetesimal Hypothesis.This hypothesis has been formulated by Chamberlin and Moulton1 to avoid the serious defects of the Nebular Hypothesis. It really consists of two separate assumptions, either of which could be discarded without necessarily invalidating the other. The first of these involves the close approach of some wandering star to the sun. This would raise two tidal projections at opposite sides of the sun, and if the disturbance was sufficiently violent, streams of matter would be expelled from them. On account of the perturbations of their paths by the second body, these would not fall back into the sun, but would go on revolving round it as a system of secondary nuclei, with a large number of very fine particles also revolving round the sun; each particle, however small, would revolve independently, so that the system would in this respect resemble the heterogeneous nebula mentioned at the close of the last paragraph. The mathematical investigation of this hypothesis would be extremely difficult, but there seems to be no obvious objection to it. It will be seen that the nuclei would be initially liquid or gaseous, having been expelled from the sun. Thus this hypothesis implies a formerly molten earth. The smaller particles would soon become solid, but the gaseous part initially expelled and not under the influence of a secondary nucleus would remain gaseous, although its density would be very small. The orbits would be highly eccentric. The second part of the hypothesis deals with the latef- evolution of the secondary nuclei. Its authors believe that these would steadily grow by picking up the smaller particles, which are called planetesimals, and in the process they would have the eccentricities of their orbits reduced. That this is qualitatively correct can easily be proved mathematically. There is, however, a serious objection to its quantitative adequacy. Consider any arbitrary planetesimal. Its chance of colliding with another planetesimal in a definite time is proportional to the sum of the surfaces of the planetesimals, while its chance of colliding with a nucleus is proportional to the sum of the surfaces of the nuclei. Further, if the eccentricities of the planetary orbits are to be considerably affected by accretion, the mass picked up by each planet must be at least as great as the original mass of the planet. Now the more finely divided the matter is, the more surface it exposes, and hence before accretion the mass picked up must have presented a much larger surface than the planet did. Hence collisions between planetesimals must have been far commoner than collisions between planets and planetesimals. Further, as the velocity of impact must have been comparable with an orbital velocity on account of the high eccentricity of the orbits, the colliding planetesimals must in nearly all cases have turned to gas; for it is known that meteors entering the earth's atmosphere at such velocities are volatized. Hence nearly all of the planetesimals must have turned to gas before the nuclei could be much affected by accretion. We are thus back to the heterogeneous gaseous nebula. If the planetesimals moved initially in nearly circular orbits this objection does not arise, but it can then be shown that the product of the mass and the orbital eccentricity of each nucleus would diminish with the time. It can thus be seen that Jupiter could never have been smaller than Uranus is now. There is no obvious objection to this form of the hypothesis, but there is no reason to suppose that solid planetesimals did originally move in nearly circular orbits.2 A further hypothesis that has come to be associated with the present one, although not an essential part of it, is the belief that the earth has always been solid. There are many serious difficulties in the way of this. The mode of formation of the nuclei described in the first part of the Planestesimal Hypothesis implies that they were initially liquid or gaseous. This is not, however, a direct objection; one part of the hypothesis might be true and the other false, as they are not interdependent. Only one satisfactory explanation of the elevation of mountains by the folding of the earth's crust has been offered; this attributes it to a horizontal compression at the surface. Now, if a solid earth grew by the addition of small particles from outside, these would be deposited in a layer on the surface, in a perfectly unstrained condition. Thus, during the whole process of growth the same surface condition would always hold, namely, that there is no horizontal compression at the surface, however much deformation may take place within. Hence any stresses available for mountain- building must have been accumulated after accretion ceased; if the theory that the earth was formerly molten should be proved to give insufficient surface compression to account for known mountains, then a fortiori the theory of a permanently solid earth gives insufficient compression, as the available fall of temperature is less. 3. It is by no means clear that a solid earth growing by accretion would remain solid. A particle falling from an infinite distance to the earth under the earth's attraction alone would develop a velocity almost enough to volatilize it on impact, and the actual velocities must have been considerably greater than this, as the planetesimals would have a velocity relative to the earth before entering its sphere of influence. If, then, the particles required to form the earth were all brought together at once, the resulting body would be gaseous. On the other hand, if the accretion were spread over a long enough time, heat would be radiated away as fast as it was produced, and the body would remain solid. In the absence of a criterion of the rate of growth it is impossible to state whether an earth growing by accretion could remain solid or not. Holmes3 has found that the hypothesis of a cooling earth, initially in a liquid state, leads to temperatures within the crust capable of accounting for igneous activity, whereas the view that the earth is now in a steady state, its temperature gradient being maintained wholly by radio-activity, is by no means certain to lead to adequate internal temperatures. Assuming the former fluidity of the earth, he has developed a wonderfully consistent theory of the earth's thermal state. The present writer, using Holmes's data, finds4 that the available compression of the crust is of the same order of magnitude as that required to produce the existing mountain-ranges. 2Monthly Notices of R.A.S. vol. lxxvn. 1916. It seems, then, that whatever we may assume about the origin of the earth, the hypothesis that it has at some stage of its existence been liquid or gaseous agrees best with its present state. The hypothesis of Laplace, however modified, implies the former fluidity of the earth, and so does the standard form of the Planetesimal Hypothesis. The Capture Theory of See.hLike the Planetesimal Hypothesis, this has been developed during the present century to avoid the objections that have been offered to that of Laplace. The main features of the two theories are very similar. Both involve the idea of a system of secondary nuclei revolving in independent orbits about the primitive sun, with sparsely distributed small particles between them, and the impacts of the small particles on the nuclei are supposed in course of time to act on the orbits of the latter in the same way as a resisting medium; namely, the eccentricities of the orbits tend to diminish, and satellites tend to approach their primaries. The Capture Theory is not, however, stated in so precise a form as the Planetesimal Theory. It is not definitely stated whether all the small particles would revolve in the same direction or not. If they did, then there would be little or no secular effect on the mean distance of a planet. If, however, they moved indifferently in the direct and retrograde senses, then their collective effect would be the same as that of a medium at rest, and the friction encountered by the planets in their motion would cause them to approach the sun. The fact that such a secular effect is stated by See to occur implies that the particles at any point are not on an average supposed to move with the velocity appropriate to a circular orbit at that point, so that the conditions would be such as to ensure that collisions between them would be violent. The small particles are described by the somewhat vague term of “cosmical dust”; if this means that they were solid, the Capture Theory, like the Planetesimal Theory, fails on the ground that the collisions between the small particles would cause the system to degenerate to a gaseous nebula long before any important effect had been produced on the nuclei. If, on the other hand, they were discrete molecules, then the system would be a heterogeneous gaseous nebula at the commencement, and this objection does not apply. It is clear, however, that the planets cannot have entered the system from outer space, for then their orbital planes would be inclined to one another at large angles, which the subsequent action of the medium could scarcely affect, whereas actually all the major planets keep very close to the ecliptic. All must, then, be regarded as having always been members of the solar system, however much their orbits may have changed. They are supposed to be derived from the secondary nuclei of a soiral nebula. The most important difference between the Planetesimal and Capture theories lies in the history attributed to the satellites. In the former, each satellite is supposed to have always been associated with its present primary, having been near it when originally expelled from the sun. In the Capture Theory, primaries and satellites are both supposed to have initially moved independently round the sun in highly eccentric orbits. If, in the course of its movement”, a small body came sufficiently near a large one, and had a sufficiently small relative velocity, then a permanent change would take place in the character of its orbit, and it is possible that, under the influence of the resisting medium, this would ultimately lead to its becoming a satellite. The mechanism of the process has not been worked out in detail, and, in view of the extremely complicated nature of the problem, it would be very dangerous to predict whether it is feasible. All the satellites in the system are supposed to have been captured in this way by their primaries. In both hypotheses the satellites are considered to have approached their primaries after becoming associated with them owing to the secular effect of the resisting medium. 3”Padio-activity and the Earth's Thermal History,” Geol. Mag. FebruaryMarch 1915, June 1916. *Phil. Mag. vol. xxxii. Dec m':er 1916. *>The Capture Theory of Cosmical Evolution, by T. J. J. See The Theory of Tidal Friction.All the theories so far mentioned agree in the fact that each commences with a particular distribution of matter, and tries to predict the course of the changes that would follow if this were left to itself. The success or failure of such hypotheses to lead to a system resembling the present solar system is the measure of their truth or falsehood. The method is thus essentially one of trial and error, and when a theory is found unsatisfactory, the next step is to modify it in such a way as to avoid the defects that have been detected. In this way a succession of different hypotheses may be Obtained, each giving a better representation of the facts than the previous one. Destructive criticism may thus be of positive value. Such a method must necessarily yield the truth very slowly, and must further involve a large number of assumptions concerning the initial conditions; in addition, the set of initial conditions that leads to the correct final state may not be unique. The Theory of Tidal Friction, due to Sir G. H. Darwin,6 is of a totally different character. It? starts with the present conditions, and by means of a single highly plausible hypothesis obtains relations that the properties of the system must have satisfied at any epoch, provided only that this is not too remote for the calculation to be possible, and that no unknown causes have operated that could invalidate the work. The initial conditions thus obtained are then unique, and the only way of disproving the hypothesis would be to discover some new agency of sufficient magnitude to upset the course of the involution. Whatever hypothesis may ultimately be found to account for the present solar system, the Theory of Tidal Friction must therefore form a part of it. The physical basis of the theory is very simple. The attractive force due to the moon is always greatest on the side of the earth nearest to it, and least on that farthest away, while its value at the center of the earth is intermediate. The center of the earth being regarded as fixed, then, the moon tends to cause the parts of the earth nearest to and farthest from it to protrude, thus forming a bodily tide. If the earth were perfectly elastic, the high tide would always occur with the moon in the zenith or nadir; no energy would be dissipated, and there would be no secular effect. If, however, it is viscous the tides would lag somewhat, and their attractions on the moon would, in general, produce a calculable secular effect on the moon's motion and the rotation of the earth. The only case where viscosity would produce no secular effect is when the deformed body rotates in the same time as the deforming one revolves. The tide then does not move round relatively to the body, but becomes a constant fixed deformation, directly under the deforming body, and ceases to produce a secular effect. In the ultimate steady state of a viscous system, then, the viscous body will always keep the same face turned towards the perturbing one. In the solar system system there are certainly two examples of this condition, and no other explanation of it has been advanced. Mercury always keeps the same face towards the sun, and the moon towards the earth; with less certainty it is believed that the same is true of Venus and the satellites of Jupiter. Now if the viscosity of a substance be zero, that substance is a perfect fluid, and there can be no dissipation of energy inside it. If, on the other hand, it be infinite, then we have the case of perfect elasticity, and again there can be dissipation. If the viscosity steadily increase from 0 to infinity, then the rate of dissipation of energy when the same periodic stress is applied increases to a maximum and then diminishes again to zero. The balance of probability seems to imply that the earth was formerly fluid, and, if this can be granted, the fact that most of it is now almost perfectly elastic at once indicates that dissipation of energy by tidal friction must have been important in the past. On this hypothesis Sir G. H. Darwin traced the system of the earth and moon back to a state where the moon was close to the earth, the two always keeping the same face towards each other, and revolving in some time between three and five hours. The lunar orbit was practically in the plane of the equator; the initial eccentricity is uncertain, as it depends altogether on the actual variation of the viscosity with the time. Scientific Papers, vol. ii. The question that next arises is, what was the condition just before this? The natural suggestion is that the two bodies formed one mass. The cause of the separation is, however, open to some doubt. It has been thought that the rapidity of the rotation would be enough to cause instability, in which case the original body might break up into two parts. Moulton, on the other hand, has shown that the actual rotation could not be so rapid as to make the system unstable. It is more likely that Darwin's original suggestion is correct, namely, that at the epoch considered the period of rotation was nearly double the period of one of the free vibrations of the mass; consequently the amplitude of the semidiurnal tide would be enormous, and might easily lead to fission in a system not possessing much strength. The Prevalence of Direct Motion in the Solar System. On all of the theories of the origin of the solar system that have here been described it is necessary that the planets should revolve in the same direction. On the Planetesimal Theory this would be the direction of the motion of the perturbing body relative to the sun at the time of the initial disruption. In addition to this, however, all the planets except probably Uranus and Neptune have a direct rotation, and all the satellites except those of these two planets and the outer ones of Jupiter and Saturn have a direct revolution. The fact that three satellites revolve in the opposite direction to the rotation of their primaries is in flagrant contradiction to the original form of the Nebular Hypothesis. It was, however, suggested by Darwin that all the planets might have originally had a retrograde rotation, and that the friction of the solar tides has since reversed the rotation of all except the two outermost. Jupiter and Saturn would then be supposed to have produced their outer satellites before the reversal took place, and the others afterwards. An objection to this theory has been raised by Moulton, who points out that the secular retardation of the rotation of Saturn due to solar tides is only about tsooo of that of the earth, so that there probably was not time for this to occur. On the other hand, this retardation is proportional to the seventh power of the diameter of the planets: if we can grant then that these planets were formerly much more distended than at present, the viscosity remaining the same, the available time may be adequate. At the same time, solar tidal friction may be adequate to explain the facts that one of the satellites of Mars and the particles at the inner edge of Saturn's ring revolve more rapidly than their primaries rotate, which would not be the case on the unmodified Nebular Hypothesis. Direct rotation and revolution of satellites on the Planetesimal Theory are shown by Moulton to be probable as a result of a very ingenious argument involving the mode of accretion. Whether it is quantitatively adequate is not proved, and the present writer would prefer to regard these motions as having been direct since the initial disruption. Let us suppose, for instance, that disruption would occur when the disruptive force had reached a definite fraction of surface gravity. It can easily be seen that both are proportional to the diameter of the disturbed body, and hence their ratio is independent of it. Other things being equal, then, a nucleus of any size would be equally likely to be broken up and give a set of dependent nuclei, which would then revolve round it in the direct sense. Secondary nuclei expelled at the same time and close together would remain together, and their relative motion might be in either sense. Thus we should expect both direct and retrograde revolution, but the former would predominate. The fact that the retrograde satellites are on the outside of their systems is to be attributed partly to the greater stability of retrograde orbits of larger size and partly to the fact that they would experience less resistance from the medium. Capture may be possible; in the present state of our knowledge we can neither affirm nor deny it. Direct rotation is presumably to be attributed to the attraction of the disturbing body on the tidal protuberance before and during expulsion, and to secondary nuclei with direct motions falling back into the parent body. Subsequent evolution would take place in a similar way to that indicated by Darwin. The Hypothesis of a Heterogeneous Nebula.A system of nuclei revolving in a tenuous gaseous nebula would experience a viscous resistance from it, and hence would probably evolve in much the same way as See has indicated in the Capture Theory; accretion must probably be almost negligible, so that the original nuclei must have had nearly their present masses. The original eccentricities of the orbits of both planets and satellites would be considerably reduced; the inclination to the plane of the ecliptic would be small at the commencement, and would remain so; if the medium revolved the effect on the major axes of the orbit, and hence on the periods, would probably be small. Direct satellites would approach their primaries, and retrograde ones would ultimately be left on the outskirts of their subsystems. Given suitable initial conditions, then, a system might be developed that would bear a strong resemblance to the existing solar system. The resisting medium itself would gradually degenerate and approach the sun on account of its internal friction; the zodiacal light may be the last remnant of it. It may, however, be regarded as certain that there has been no large amount of resisting matter near the earth's orbit for a very long time; there has probably been ample time for the evolution of the earth and moon to take place from the state that Darwin traced them back to. The moon was then probably formed from the earth by the disruptive action of the solar tides; but, as this would be a resonance effect, increasing in amplitude over thousands of vibrations, whereas the formation of a system of nuclei in the way suggested by Moulton would take place at once, there need be no surprise that the former event led to a single satellite of of the mass of the primary, while the latter formed several, the largest having a mass of tTjjfu of its primary. The unsymmetrical nebula here considered might have been produced in the manner described in the last section. A symmetrical nebula becoming gravitationally unstable would lead to an unsymmetrical one, as was proved by Jeans, but it is difficult to see how the phenomenon of retrograde and direct motions occuring to the same subsystem could occur on this hypothesis. On the whole, then, the most plausible hypothesis seems to be that a gaseous neubla with a system of secondary and tertiary nuclei was formed round the sun by tidal disruption owing to the close passage of another star, and that this has been subsequently modified by gaseous viscosity, and at a later stage by tidal friction. The moon was probably formed from the earth by solar tidal disruption, this method being abnormal in the system, and the later evolution of the earth and moon has been dominated by bodily tidal friction.

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