Art. VIII.—Partial Impact: a possible Explanation of the Origin of the Solar System, Comets, and other Phenomena of the Universe.
[Read before the Philosophical Institute of Canterbury, 1st August, 1878.]
In the last paper which I submitted to the Institute, I gave a short sketch of some hypothetical cases of partial collisions, and suggested that such cases might possibly be of frequent occurrence throughout space, and might offer an explanation of many phenomena of the universe. I especially showed the application of the hypothesis to temporary and variable stars. To-night I intend to show that it appears competent to explain the formation of the solar system, of comets, of meteors, and of some variety of nebulæ. I shall, however, in the first place point out the very great difference which exists in the capabilities of cases of partial and complete collision, the first offering a field of possibilities of cosmical phenomena which is really surprising, the latter being probably confined to but a few rare cases.
In the last paper I assumed that the partial collision of two attracting bodies having an original proper motion in space, would be much more likely than entire coalescence. It appeared, however, to be a very general idea, that if the bodies struck at all, it must be that their mutual attraction would certainly produce complete coalescence. On the other hand, it was generally admitted that two bodies when attracted by each other would seldom come into contact, but would in most cases be carried by their original velocity away once more from each other's influence. It is only necessary to assume that the size of the bodies has increased enormously without increase of mass for a case of mere disturbance to become one of partial collision; the generality of the case is thus practically demonstrated. As cases of partial collisions may be of infinite variety, for the sake of simplicity I have in this paper (except where stated to the contrary) assumed that all the colliding bodies are of the same size; composed of the same chemical elements; with the same initial proper motions, the velocity of which is small compared with that developed by attraction; also that the mass of each of the two bodies of any one pair is the same.
If two bodies come into direct collision from rest, a definite energy of velocity will be acquired at the moment of contact, depending solely on the mass. After coalescence, if a single particle were attracted from infinite space, the particle being attracted by the whole coalesced mass, and this mass not appreciably moving towards the particle, twice the force would act through twice the space, and would develope twice the velocity, or four times the energy. Hence, also, a particle to leave the body must have this double velocity. Therefore, as it does not appear reasonable to expect that
after collision any portion will acquire much greater energy than before, we may reasonably assume that no part will acquire four times the energy of motion, and be thrown off into space. On the other hand, if two bodies come into partial collision, a piece of each would coalesce, and the rest would pass on into space. If the motion be entirely destroyed, the temperature developed by coalescence will be the same, no matter what proportion be struck off; whilst, if the pieces struck off be very small, the coalesced mass will have but little attractive power to keep the body together, and hence the velocity of each particle may be great enough to project the whole into space; whereas we have seen, in the case of complete coalescence, none would be able to be thus projected. This is a most important distinction between partial and complete collision.
Influence of Chemical Composition.
If two bodies, each a mixture of chemical elements, meet and destroy their motion of translation, then a molecular motion of identically the same energy must be developed (a small part will be converted into some form of potential energy, but this we will disregard). If a mass of small bodies have the same energy as an equal single mass, the velocity is also equal. Whence we must also assume that the velocity of the molecules, no matter what may be their respective weights, is not greater than the velocity of the whole body was before impact. Therefore, from what has been stated, in direct impact no particle will have sufficient velocity to leave the mass immediately after impact. But different elements having the same velocity are at different temperatures, inversely proportional to their molecular weight; the heavy atoms are therefore very much hotter than the light ones. We know by the laws of heat that these unequal temperatures will tend to equality; but it is worth while looking at this a little in detail. Let us suppose a hydrogen and a mercury particle to meet. The mercury is one hundred times as heavy as hydrogen, but the velocity of both is the same. The collision cannot produce heat, as it is heat motion already. The principle of energy at once tells us that the mercury will lose a part of its velocity, and the velocity of the hydrogen will be increased. Let this happen many times, and the temperature will become equal; in other words, the hydrogen will be moving ten times as fast as the mercury. Let both of these particles come to the surface of the body; their molecular motion will cause them to leave it; the hydrogen will probably have velocity sufficient to carry it away from effective attraction, which is impossible with the mercury, as initially its velocity was insufficient, and now it is less than before. Thus we see that at the surface of a mixed gaseous atmosphere there is a tendency the opposite to that of the diffusion of gases; probably the hydrogen and lighter atomic weight elements will be on the out-
side, and the heavier on the inside of bodies. Hence, the chief elements of the surface of bodies may reasonably be expected to be hydrogen, lithium, carbon, nitrogen, oxygen, magnesium, sodium, and sulphur. All these elements, except lithium (which may consequently be assumed to be universally rare), are the common elements of the surface of bodies; and hydrogen, the highest of all known bodies, is the most common off of all. Is not the element of 1474 line, which is found outside of hydrogen on the sun, an element of still less atomic weight than hydrogen? If this hypothesis be true, then it is reasonable to assume that diffused hydrogen must fill space. This would account for the retardation of comets and planets without the assumption of an ether resistance. It thus appears that the molecular motion of gases may become one of mere translation. There is accordingly a continuity of heat and mechanical motion. It is reasonable to suppose, that at a certain height above the sun the general motion of the particles of hydrogen may become more or less parallel; there would be no collisions of molecules, and consequently no luminosity would be then produced, and an apparent dissipation of the protuberances would occur. I have now shown the most striking points in the contrast of the energy of different cases of collision. I have also shown a possible reason why the small atomic weight elements are common on the surface of bodies; why we should expect to find hydrogen on the surface of all bodies, such as the sun and stars; lastly, that hydrogen, and probably the unknown element of the sun, may be the resisting substance which retards the motion of bodies in space.
On the Rotation of Systems.
It does not seem reasonable to expect rapid rotation in the case of entire coalescence of two bodies, as only the resultant of the two original rotations will tend to develops this motion. But, in the case of partial collision, we must have a rapid rotation of the mass, as each of the two bodies from which it was formed occupy chiefly one side of the new body, and as the velocity of each of the two bodies was originally opposite to that of the other, rotation is a necessary consequence.
There are two chief reasons for the inequality of the balance of momentum at the two sides of the coalesced mass: 1st. The piece cut off will be much thicker towards the middle of the original mass than at the outside. 2nd. The density of the inside is much greater than that of the outside, in consequence of the greater pressure, and also from the fact that it is probable the heavier elements are towards the centre of the mass. It may easily be seen that the resultant momentum on the two opposite sides are in opposite directions, consequently tending to rotation.
Comets and Solar System.
It is almost certain that the initially irregular shape of the two coalesced pieces would cause many smaller masses to fly off into space, producing possible visitants to other worlds, but in most cases the heat would be sufficient to cause all these masses to be converted into gas.
When two bodies of different size attract each other, the velocity acquired by the smaller body will be greater than that of the larger one (as an apple falling to the earth does not give the earth the same velocity as the apple itself acquires). With unequal bodies therefore, when collision occurs, the larger piece will have a smaller velocity than the smaller, hence there will be two orders of fragments. First, from the small piece, the high velocity of which may make comets and shooting stars of them.
Secondly, the fragments of the larger piece, whose small velocity may not take these bodies away from effective attraction, and they may thus become planets.
But the large mass of our sun shows that if the planets of our system have been formed in this way, one of two things must have occurred, either the original proper motion of the bodies must have been very much greater than the average is at present, or the bodies themselves must have been very large, so that even at impact the centres were a long distance from each other. There is, however, another reason why at impact the centres may have been at a distance from each other—namely, the great distortion of the bodies which must take place immediately before impact, in consequence of their mutual attraction. It is impossible to give even an approximate idea of how much this may influence the result. Generally, it is easy to see that the problems offered by partial impact are of extreme difficulty, the data being of necessity of infinite variety.
It is shown further on, that there is another partial impact hypothesis which may possibly explain the origin of our system.
All the following remarks apply equally to that hypothesis:—
At first the orbits of these bodies would be extraordinarily eccentric; on passing away on this first journey they would be in advance of the expelled gas, but would meet it on returning. This would tend to neutralise the force of attraction, and the orbit would become much more circular. Again, the passage of the planet through the gas would retard it. And lastly, on each of its orbits the attraction of gravitation would be greater on its outward journey than on its return, in consequence of the expelled matter passing outside its orbit into space. This fact would both tend to render the orbit more circular, and also tend to neutralise the action of the gaseous resistance in causing the body to approach the sun. It
is a well-known fact, that if a projectile revolves on one axis at right angles to the line of motion, there is a tendency to move in a curve. (The full discussion of this phenomenon would occupy much time.) It is possible to show that this force at first would have considerable effect in rendering the orbits circular, but finally with the planets near the sun its effect may be to render the orbits more elliptical. All these forces, therefore, tend to render the orbits more circular, but not as an average result to alter their mean distance from the sun. The larger masses would suffer less resistance in proportion than the smaller ones, and the general result would be, that if all started at the same distance the smaller bodies would be brought nearer the sun. It is easy to see that the centrifugal force and the attraction of nebulous mass would cause all the planets to travel approximately in the plane of the ecliptic, also why the sun's equator so nearly approaches it, and generally, why the rotations of the planets on their axes should be in the same direction. On the other hand, the pressure due to heat, the extreme want of symmetry of such a case of partial impact, combined with the original motion of rotation of the colliding bodies, if they had any, must all tell in the ultimate resultant motion, both orbital and axial. Almost certainly these forces would produce slightly inclined orbital planes, inclination of polar axes to these planes, and may as an extreme case produce a retrograde motion. It is also easy to see that the enormous atmospheres of those early days would effectually clear the bodies of all but very large masses of cosmical dust.
This fact appears of itself sufficient to show that the production of the asteroids must have been a subsequent event to the formation of the solar system. With respect to the asteroids, it is conceivable that the destruction of the planet which formed them may have been produced by a large meteoric visitant, with a high velocity. This hypothesis shows that such bodies may exist in considerable numbers. Such a mass might conceivably bury itself in another body, and when its motion of mass was stopped, its heat might be sufficient to produce a pressure of many thousand atmospheres. Such an explosion of developed gas might reasonably be expected to blow the body to pieces. It is generally considered that if the asteroids had been produced by the destruction of a planet, the fragments would have the same mean distance from the sun, and would pass the same points in their orbits where the destruction occurred; which is contrary to the observed motions of these bodies. The hypothesis that they are pieces of a planet is therefore not generally accepted; but these assumptions are only true if the velocity remain the same, the eccentricity of the orbit the same, and there is no resisting atmosphere. The first of these assumptions is
clearly not admissible in such a case as I have suggested, and the relative positions of the planets would influence the second. Or if this be considered to be insufficient, it is only necessary to assume that the destruction took place before the whole of the gas had been absorbed by the sun. Altogether, I think from the great eccentricity of the orbits of these bodies, from their positions, from the varying inclinations of the planes of their several ecliptics, from their varying intensity, and their small size, the only conceivable explanation of their formation is by a violent explosion. This would account for all their peculiarities. I am unacquainted with any force in nature that could produce such an explosion except the one here suggested.
It would appear also that the rings of Saturn cannot be considered to be a primary phenomenon; they may have been developed by the blowing to pieces of a moon, or by Saturn's atmosphere entrapping a train of meteors. This latter suggestion hardly appears so reasonable as the former. If the destroyed moon was brought to a very high temperature, mere liquid spray might have been produced, which would quickly cool and become a mass of solid particles revolving around in all eccentricities.
Comets and Meteors.
It is a necessity of this hypothesis that there should be large numbers of bodies travelling in space. Groups of these bodies may frequently have a common direction. Of these bodies it is probable that some may be very large, and even come within the solar system, yet remain invisible except as meteors. But it is conceivable that in some cases of collision bodies may leave, consisting chiefly of carbonic acid; which at certain stages of a body's heat, may form an important part of its atmosphere. It is not difficult to imagine that a portion of the atmosphere of such a body may have taken a common direction in space, and in its path become attracted by our system. If its nucleus, when near the sun, were volatilized carbon, and its atmosphere carbonic acid, the result of the sun's radiation on such an athermic substance as carbonic acid might certainly decompose it. Might it not be the case that the temperature of dissociation of carbonic acid may be lower than the temperature of the volatilization of carbon? There are certain peculiarities in the electric light supporting this. Thus the carbon might be liberated as a sublimate away from the sun, but in the direction towards the sun, the temperature may be sufficiently high to volatilize the carbon. This, or some other radiation theory, as Tyndall has suggested, seems the only one possible to explain the stupendous velocity of the growth of the tails, amounting in some cases to as much as 5,000 miles a second, a velocity which the energy of the sun would be incompetent to give to matter. Again,
this hypothesis agrees with some of the spectroscopic observations of comets, in which the tail gave a feebly continuous spectrum, showing it to be solid, and the nucleus a banded spectrum, showing it to be gaseous. It may be possible that there are other gases whose temperature of decomposition is lower than the temperature of volatilization of one of their constituents, such as fluoride of silicon and generally halogen compounds of infusible bases.
I shall now attempt to show that there may be agencies at work which may cause a great difference of temperature between the poles of the sun and its equator. This may give us an insight into the cause of the tremendous cyclones of the meeting solar trades, and these cyclones are possibly the cause of such spots. If this hypothesis really represents the formation of the solar system, then it is probable that radiation is greater in a direction perpendicular to the ecliptic than in its plane. Again, the combined energy of gravitation and centrifugal force would cause most of the absorbed matter to fall upon the sun about the equator; both of these causes may produce a great difference of temperature between the poles and the equator of the sun, sufficient, perhaps, to produce cyclonic spots. The projection of bodies upon the surface of the sun, bodies trapped by the sun itself, might probably produce the sea of flame which surrounds it, and the protuberances so often seen upon its limbs. The precipitation of bodies upon its surface appears to me to offer the only conceivable explanation of the high velocity which the hydrogen on the surface of the sun sometimes possesses. The speed of some comets proves that bodies in space may have a velocity of many hundred miles per second, and we know that a body at rest would acquire nearly 400 miles a second by the sun's attraction alone. Therefore many bodies may fall upon the sun with a velocity of 500 miles a second or more. Such a body would bury itself far down in the sun, clearing the gas by pressing it down before it and in a few minutes it would be many thousand miles into the sun, and, its motion of mass destroyed, a temperature of 100,000,000 might readily be developed, which, even if the density of the body were no higher than air, would amount to a pressure of 400,000 atmospheres, and would most likely be much greater than this. Here are all the conditions for a most powerful explosion, amply sufficient for all that has been observed of the prominences. It is quite evident that if there are trains of bodies, which have been brought into the orbits around the sun, most of the phenomena of periodical variations of spots and protuberances may be explained on the assumption that these bodies plunge obliquely into the body of the sun.
On Double and Multiple Stars.
When the original proper motion is small, and the proportions struck off large, after partial coalescence the greatly increased attraction acting on
the two retreating bodies will in many cases cause one or both of them to be attracted back to the coalesced mass; but as the force which produces this return is partially due to the other retreating body, and for reasons already mentioned, the returning body will not necessarily come into collision with the coalesced mass, but may revolve around it producing double stars, or, if both bodies returned, triple stars, and in many cases the coalesced mass would also separate and produce even quadruple, or still higher multiple stars. I need not say that many thousands of multiple stars exist. Generally the returning stars, although sometimes of greater magnitude, would be of less luminosity, but this body would collect much of the matter revolving around the more luminous body, and so have its own temperature raised. In the case of nearly complete collision, the two pieces leaving the coalesced mass might reasonably be expected to break into pieces. It is possible to show that the rotation of each of these pieces must generally be in the same direction as the rotation of the coalesced mass, and that most of the forces acting would tend to produce a system resembling the solar system.
I have already shown how a ring nebulæ may be produced by a case of partial collision. The cometic nebulæ would be produced when a high resultant velocity was produced in the coalesced mass. It is not difficult to conceive that in the collisions of approximately equal bodies the coalesced mass might separate chiefly into two other larger masses, and produce double nebulæ, and ultimately double stars revolving around each other. Again, a case of almost complete coalescence appears competent to give rise to the conditions we observe in the spiral nebulæ, as it will be seen that rotation will be very slow in this case, and the expulsion of matter irregular, although it must be confessed that it seems probable that generally a large nucleus of continuous nebulæ would be produced. At the same time possibly higher power observations may show this to be the case.