Popular Science Monthly/Volume 13/July 1878/On the Formation of Nebulae
| ON THE FORMATION OF NEBULÆ. |
By WILLIAM M. DAVIS, Esq.
THE close proximity of the satellites of Mars to their primary has led me to investigate the lesson taught by them and other satellites of short periods.
This investigation has enabled me to demonstrate:
I. That the nebular hypothesis fails to account for the present condition of the solar system, without the additional hypothesis of a resisting medium in space.
II. It has enabled me to show, also, that, although this medium tends to bring the solar and all other systems to a state of quiescence, it has no such tendency on the material universe as a whole, provided that the ponderable matter thereof be of infinite extent. If, however, the ponderable matter—as distinguished from the ether—be of finite extent, it should come to rest, as will be shown in the sequel.
The first proposition will be established by taking the first satellite of Mars as an example, and proving that it must have been at least fifteen or twenty times as far as it now is from its primary when it was able to take on the globular form from the nebulous ring out of which it was made. This being established, it follows, as a necessity, that its orbit must have contracted into its present dimensions since it was thus formed; and the satellite during this time has condensed into its present condition.
As the same cause which contracts the orbits of the satellites should produce a like result upon those of the planets, it follows that they, too, must have been farther away from the centre of the system than they now are, when they took on the globular form from their nebulous rings.
The hypothesis of a resisting medium has been adopted to account for this contraction of orbits, as no other hypothesis seems competent to do so.
That this satellite of Mars and others in our system were much farther away from their primaries than they now are, will be proved, by proving that, if a nebulous satellite revolved around any primary in the short period in which most of the solid ones now do, the tidal energy—or tendency to elongation and disruption—which would, in that case, be generated on its opposite sides by such rapid revolution, would be sufficient to tear it into atoms. These atoms would be distributed around the primary in the form of a nebulous ring, which ring would be in a state of stable equilibrium, and therefore could not be reconverted into the globular form.
Permit me, then, to bring forward some imaginary experiments, for the purpose of illustrating certain dynamical principles (and methods) to be employed in proving the fact just stated.
Assuming the density of the earth to be 512 times that of ice, it follows that, if a globe of ice—say ten miles in diameter—be isolated in space, a small dense body, as a bullet, near its surface, should fall toward it—by the action of its gravity alone—through 160 inches during the first minute of its descent. Now, if this icy globe be made to revolve around any large planet in the short period of 5 hours and 4234 minutes, and on its axis in the same time and in the same direction, then the tidal energy (which is, in this case, the difference between the force of the planet's attraction for the particles at the centre of the icy satellite and for those at the two opposite points of its surface which are nearest to and farthest from the planet, added to the difference of the tangential force on the particles)[1] would exactly counterbalance the icy satellite's interior gravity along this diameter; i. e., if the tidal energy could be made to act alone on the aforesaid bullet, at either end of this diameter, it would force it outward through 160 inches during the first minute of such action; hence, if a particle at either end of this diameter should be acted upon both by the gravity and the tidal energy at the same time, it would have no tendency to move in either direction; but if it were raised a few inches above the surface, then the tidal energy would prevail over the gravity and take it away.
To get a clear conception of the peculiar condition under which this icy globe is now placed, let us call this last-named diameter its axis of tension, and the plane passing through its centre and perpendicular to it the plane of compression.
Now, along this axis there is no force to prevent the elongation of the icy globe in that direction, except only the force of cohesion in the ice itself, as its gravity in that direction is exactly counterbalanced by the tidal energy.
Around the plane of compression, however, the case is different; here the interior gravity is unopposed by the tidal energy, and every atom is pressing inward on the central mass; and this pressure tends to force the tensible regions outward, and thus to make the tensile axis longer.
When this elongation begins, the disruptive energy rapidly increases in virtue of the increased diameter in that direction, and the diminution of the internal gravity, produced by the same operation. By such action as this the icy globe should be quickly torn into pieces and distributed around its primary in the form of a ring of fragments.
Prof. Daniel Vaughan has shown that such is the origin of the rings of Saturn, and ascribed the close approach of the two satellites which formed them to the action of a resisting medium.[2]
If this were a globe of water instead of ice, it is very evident that much less disruptive energy would be required to tear it to pieces, on account of the greater mobility of its parts; most probably not more than one-seventh of the above-named force would be required to accomplish this result.
If this force be sufficient, and the globe of water be made to revolve around any large planet in fifteen hours or less, the tidal energy will tear it into atoms by virtue of the following law:
It can be demonstrated—1. That the tidal energy generated on a spherical satellite of small but constant mass, when revolving around a large primary, varies directly as its diameter; 2. That it varies, also, inversely as the square of its periodic time; and 3. That the ability of the same satellite to resist the disruptive tendency of this tidal energy varies inversely as the square of its diameter; provided there be no cohesive force to aid in resisting this tendency, and in a nebulous satellite there would be none to do so.
As the first and third propositions relate to the diameter, they may be included in one, and then the law may be stated as follows:
The disruptive ability of the tidal energy of a primary planet on a nebulous satellite of small but unvarying mass varies directly as the cube of the diameter and inversely as the square of the periodic time. Let us apply this law to the case in hand. To do this it may be very safe to estimate that a ten-mile globe of water, while yet in the state of a nebulous satellite, would occupy the globular space of at least one hundred miles in diameter. This would give it a density of only 11000 of that of water, which, however, would still be millions of times greater than that of the original nebula out of which the entire system was made.
According to the above law, the disruptive ability of the tidal energy on the nebulous satellite must be 103, or 1,000 times as effective as on the ten-mile liquid one, if revolving in the same time. Now, to find the shortest time by the above law in which this nebulous globe could revolve around its primary without disruption, we must multiply the fore-named fifteen hours by the square root of 103; the product of this multiplication amounts to about 1934 days. As this is the shortest time in which any small nebulous satellite of this density can revolve around any large primary without disruption, it becomes very evident that nearly all the solid ones in our system must have been much farther than they now are from their primaries, when they were able to take on the globular form from the nebulous rings or collection of nodules out of which they were made.
Taking the above estimates, and applying the law to the case of Mars's nearest satellite, we find that its orbit must have been at least 1723 its present diameter when it was able to take on its globular form from its nebulous ring.
This establishes beyond doubt the fact to be proved, and gives us some idea of the vast dimensions of the solar system when this last nebulous satellite of Mars was formed.
What, then, must have been the distance of the first nebulous planet from the centre of the system, when it was formed? This, of course, can be only vaguely guessed, as we have no reliable criterion to judge by.
The Resisting Medium.—The introduction of the hypothesis of a resisting medium to account for this contraction of planetary orbits seems at first sight to involve a condition fatal to the continued activity of the material universe; for, if there be a resisting medium, which is gradually bringing our system to a state of rest by its reaction on the bodies moving in it, it is but reasonable to suppose that it should produce like results on all other systems, and thus ultimately bring the entire universe of matter into the quiet sleep of death. But that this is not the normal tendency, however, when applied to the universe as a whole, we have the most abiding assurance, without any investigation of this kind; for, if such be the tendency now, it always would have been the tendency, in which case the end would have been accomplished during the eternities of the past, and we would not be here to-day to dread its approach.
Still the following question, or its equivalent, will press itself on many minds: How can the perfect conservation of force, which is so essentially necessary for the continued activity of the material universe, be reasonably accounted for, if there be a resisting medium in all space through which it must ever move? This pressing yet interesting question leads directly to the second division of our subject, which will now be discussed.
In order to give this question a suitable reply, as well as to show how the perpetual activity of the material universe may be maintained, while moving in this resisting medium, we will trace the history of some given solar system from its original nebulous state, down through its life-sustaining period, thence to its final destiny; and then discover, if possible, a means by which it may be reinvigorated or resurrected to a new planetary life. For this purpose it seems necessary to present—very briefly, however, for want of space—one illustration, reaching through the various stages in the grand round of successive changes through which all planetary systems seem to be passing. Our solar system will be taken as the illustrative example.
In tracing the history of the system from its nebulous state down to the present time, the path pointed out by the illustrious Laplace will be closely followed.
More recent writers have suggested other modes for the formation of such systems, some of which, however, would seem to be the exception instead of the rule here presented, as the sequel will show.
No definite explanation will be given in this paper as to how the out-thrown masses of nebulous matter—which will hereinafter be described—may be utilized in forming other systems; and no suggestion given as to the formation or structure of the globular or other clusters of stars, which are so bewildering to investigate, and yet so interesting to look upon; but the formation of these, and of that great galaxy of stars of which our sun seems to be a member, may be accounted for on the same dynamical principles that are employed in this discussion.
Following Laplace, it is assumed, then, that our planetary system began its evolutions as a great nebulous sphere of perfectly dissociated matter of almost inconceivable rarity, and of nearly uniform density.
At this time it was not quiescent, but most probably was agitated by the movement of internal currents and counter-currents, the resultant motion of which caused the entire mass to revolve around one of its diameters.
From the nature of the case, this rotation must have been very slow indeed, probably one rotation in millions of years. If its diameter were 500 times that of Neptune's present orbit, it would require more than 36,000,000 years to make one revolution; even this velocity would slightly flatten it at the poles.
During these revolutions it was radiating heat, not only from its surface, but, on account of its extreme rarity,[3] from regions far below its surface. This radiation, combined with the gravitation of its parts, caused contraction; and this contraction, by well-known mechanical laws, increased the rate of rotation, and a consequent further flattening at the poles, while a correspondingly greater increase of density in the central parts took place.
This process continued till the rate of rotation of the bulging equatorial belt generated sufficient tangential force, by virtue of the rapid rotation of those particles, to counterbalance the gravitating force of the disk-like mass within, at which time further contraction of the outer edge of this nebulous belt, or beginning of a ring, ceased, except that infinitesimal portion due to resistance alone; for, at this time, each particle in this outer belt revolved in its own orbit around the central mass.
As radiation continued, contraction also continued, thereby conferring a planetary character on each particle of the successive layers of the equatorial ring of particles thus left out by the contracting nebulous spheroid.
Let us now confine our attention, to this out-left ring, for its conduct will show how planets and satellites are formed from rotating nebulous masses:
As radiation still continued, the repulsive force between the particles diminished, which allowed them to approach nearer to each other; and this tendency to agglomeration resulted in the formation of small centres of local attraction near the surface of the ring, where radiation was most rapid.
As condensation continued, new centres of local attraction were formed within, while the outer and older nodules continued to increase in size, and to coalesce into larger masses; till, finally, the outer edge of this ring had changed from an homogeneous and continuous nebulous disk to a multitude of nebulous planetoids of great volume, but of small mass; while the succeeding interior particles, as fast as they were left out by the contracting spheroid, were preparing to undergo a like change.
Now, as these planetoids have various periods of revolution, they will occasionally come into conjunction, and then, on account of the great volume and small mass of each, they should coalesce without crash; till, finally, some preponderating mass should collect all the little ones exterior to its orbit into itself, together with as many of those within its orbit as its gravitating force could control.
In like manner will all succeeding rings be collected into nebulous planets; and, if the masses of these planets be sufficiently large, they too, in a like manner, will develop nebulous secondaries after their own likeness, both in form and motion.
It is the satellites so formed of the out-left rings of the condensing nebulous planets in our system that have been under discussion in this paper.
That the nebulous planet thus formed will be given a motion of rotation in the same direction as that of its primary is due to the fact that the exterior planetoids have a greater virtual velocity than the interior ones have. This will become evident from the following considerations:
Let us consider, first, the effect produced on its rotation by one of the outer planetoids as it coalesces with this preponderating mass. As the two bodies approach conjunction, the small one will be drawn inward to meet the larger one, and this contraction of its orbit so increases its orbital velocity that, at the time of meeting, this velocity is greater than that of the controlling mass, and on striking it will give the latter an impulse to rotate in the direction of its orbital motion; while, on the other hand, one of the interior planetoids, by being drawn outward, will have its motion diminished to such a degree that, on meeting, it will give the larger one an impulse to rotate in the same direction as that which the outer one gave to it.
Now, if this nebulous globe be not disturbed by some external force, it will form the outer planet of the then future solar system.
This is the general rule for the formation of secondary bodies in all systems. In our system there seems to have been one exception to this general rule, viz., the asteroids. From some cause—most probably from external disturbance—this ring did not collect into a single mass, or, if so, was dashed into many fragments afterward by some meteoric or cometary body which, thrown out from some previously-formed nebula, had been wandering through space till it reached our system.
There are indications in other parts of the system of such external disturbances, notably in the satellitious system of Uranus.
From the manner in which the solar system has been formed, it seems most probable that all the bodies in it should both revolve and rotate in the same plane and direction that the sun does, had there been no external disturbance to prevent it.
Having examined the mode in which a planet is formed, and thus learned how a solar system may be formed out of nebulous matter, and having discovered that the system must be contracting into smaller dimensions from some sufficient cause, let us next inquire what consequences are most likely to follow the operation of such cause.
Consequences of Contraction.—It has been shown, by the foregoing investigation, that our system is expending its life-giving energy on some resisting medium which causes this contraction.
This, at first sight, seems saddening to contemplate; but there may be another point from which to view it. For, while it is seemingly wasting its life-giving power in this struggle with resistance, it may, in reality, be storing up a new supply of potential energy, by which a future activity may be insured. Or, in other words, it may be forming a new bud, which, when properly vivified by another one, may blossom forth with the most brilliant rainbow hues, and finally ripen into planetary fruit which shall become the happy home of future intelligent races.
Modus Operandi of Conservation.—It is well known that the stars are not fixed, but that they are moving in various directions with various velocities, relatively to our galaxy, at least.
Now, if the stars be moving, it is very probable that some of them are moving in such directions that they will finally meet, either in pairs or otherwise.
Let us direct our attention to two of them which are very like our star in mass and attendants, or we may suppose our sun to be one of them, and that they are so moving as to approach each other at the very slow rate of one mile a week; and let us further suppose that, before meeting, each will have arrived at that state of quiescence to which all systems are tending.
The object of assuming such slow original motion for the meeting bodies is to make a test case, as it were, in order to show clearly that the gravitative force of two such large bodies is sufficient to convert them both into a nebulous mass, besides throwing large portions of this mass into the attracting spheres of surrounding stars, and thus beyond the possibility of return.
It may be proper, here, to point out the modus operandi by which such systems reach the state of quiescence alluded to above, which is, substantially, as follows:
The planets absorb their satellites by first converting them into fragmentary rings—as Saturn has already transformed two of his. These rings gradually approach the planets, till finally they fall upon their surfaces, and become part of them; while the planets themselves are approaching their primaries to succumb to a like fate.
Having absorbed their planetary attendants, and having cooled off so as to become cold, dark bodies, like the earth, they enter the sphere of each other's sensible attraction, and begin to approach with continually increasing velocity, till finally they meet, each arriving at the point of contact with a velocity of from 400 to 500 miles a second, depending on their mass and density.
Of the heat generated by such a collision, we can have no adequate conception. It may, however, be calculated, and written down in thermometric degrees;[4] still the figures are meaningless to us except as representing an inconceivable intensity of heat.
It may be stated as so many thousand times the heat generated by the explosion of an equal weight of gunpowder, still we are unable to form an idea of the unit of measure here given.
If the doctrine of the "correlation and conservation of forces" be true, then the heat thus generated, if it could all be applied in the form of moving force to these two bodies while yet intact, should be sufficient to throw them back again to the points at which their motions began to be accelerated, if there were no resistance; but, owing to the resistance met with, they will not rebound fully to those points.[5]
It will not, however, be expended in that manner, but in expanding the entire mass of these two globes into a thin, nebulous vapor; large portions of which, most probably, will be thrown out beyond the sphere of sensible attraction of that which remains, and into those of the surrounding stars.
This great probability will much resemble a certainty when we come to subject the question to the following speculative illustration:
If the entire nebulous mass could be preserved in the form of an expansible spherical shell, while the entire amount of heat-force should be acting upon its interior surface to force it outward, then, according to the above-named law of conservation, the entire mass would be thrown nearly to the limit of its sphere of sensible attraction; i. e., nearly to those points at which the motion of the two bodies began to be accelerated.
For the sake of convenient reference in the following difficult illustration, let us imagine the entire mass of expanding vapor to be divided into two equal parts, called respectively the inner mass and the outer mass; and let us imagine the heat-force to be divided into two equal parts also, called the inner force and the outer force.
Now, as these two forces are sufficient to drive these two masses very nearly to the aforesaid points of acceleration, and whereas only a part of the inner force can be expended in distributing the inner mass throughout the space surrounded by such limits, it follows that that part of the inner force so conserved will expend itself in helping the outer force to throw the outer mass beyond this sphere of sensible attraction, and, most probably, into those of the surrounding stars.
If such be the case, then some of these out-thrown masses may become cometary bodies and meteoric showers to the inhabitants of "other worlds than ours," besides forming abundant material for the "cosmical dust," so much discussed of late; and, possibly, some of the largest of these fragments may be able to produce asteroidal groups, in some ripening planetary system, by disrupting one of its planets while yet in the nebulous state. This seems to supply a deficiency in this hypothesis which has long been felt.
Density of the Newly-formed Nebula.—If, now, we fix our attention on the condition of this nebula at the moment when the explosive force had expended its last effort to throw these outside masses into surrounding space, we can readily see that it must have been of very nearly uniform density, in consequence of the tendency of the out-moving particles to continue their motions outward.
Confirmation.—It is very probable that many such explosions as that described above have been witnessed from our planet, and have been recorded in history as temporary stars; an interesting account of some of which may be found in Herschel's "Outlines of Astronomy."[6]
In May, 1866, such a phenomenon was observed in the Northern Crown. This collision, however, seems to have been, not with the star itself, but with one of its planets, or with some other dark body lying in that direction, which contained a large amount of water, the hydrogen of which, being dissociated from its oxygen, shone out with such brilliancy as to be seen at this distance.
That this was a planetary collision seems probable, from the fact that the star continued to shine with its normal light during the time of, and after, this brilliant display of hydrogen, which is proved by the spectrum analyses of its light during that time.
The "new star" lately discovered in the constellation of Cygnus seems to be a complete confirmation of this theory.
A very interesting account of this star, by Richard A. Proctor, may be found in The Popular Science Monthly for December, 1877. From this account the star seems to have passed through all the various changes which should naturally be expected from such a collision; first, a very great augmentation of light, with a continuous, rainbow-tinted spectrum arising from the intense pressure to which the rapidly expanding mass of gas was at first subjected; gradually passing through various changes and gradations, till, finally, it took on the "spectrum of a true nebula," which should naturally occur after a large part of the intense heat of percussion had taken on the form of latent heat of expansion.
"As the stars are moving with various velocities in various directions," it may be asked, "What would be the consequences if two of them should enter each other's sphere of sensible attraction with very great velocities?"
In order to secure definite results, in replying to this question let us assume definite conditions:
Suppose them to be equal, and of such mass and density that each would approach the point of meeting with a velocity of 400 miles a second, by virtue of their mutual gravitation alone; and, further, that each one had an original velocity of 300 miles a second toward that point, when they entered each other's sphere of sensible attraction.
Now, they would meet, not with a velocity of 700 miles a second, as might, at first, be supposed, but with the velocity represented by , or 500 miles a second.
According to a previous mode of reasoning, the heat-force generated by such a collision should be sufficient to throw these two bodies outward beyond the possibility of return; therefore, the greater portion of the resulting nebulous mass would be thrown out with a corresponding velocity, and be distributed among the surrounding stars, leaving but a small portion of it to occupy the place of meeting; which, consequently, without further additions, would make but a small solar system.
Conclusion.—Let us now consider what would most likely be the result of such collisions, if the matter of the universe were of finite instead of infinite extent.
For this purpose we may assume the last-named pair of stars to constitute the entire amount of ponderable matter in the universe. It is supposed, then, that they are both moving directly toward the point of future meeting with a velocity of 300 miles a second, when each begins to be affected by the other's accelerating force; which, consequently, increases that velocity to 500 miles a second at the time of meeting.
It will readily be seen, from previous considerations, that large masses of the resulting nebula will be thrown out from the sphere of sensible attraction of the remaining mass, with velocities exceeding 300 miles a second, while other portions will emerge with less and less velocities, till finally some portions barely reach those limits.
The remaining nebula should then begin to contract, and might, possibly, form a small planetary system. Of the out-thrown masses, those which moved with the greatest velocity would retire to the greatest distances; but even they must finally stop, because they could not overcome perpetual resistance.
The resistance which these masses have to contend with is of two kinds: first, the feeble, insensible attraction of the remaining mass; second, the resistance of the ether.
The first diminishes with the square of the increasing distance, but is never reduced to absolute zero; the second, however, diminishes with the diminishing speed, and finally becomes nothing, at which time the body stops.
Now, would these farthest masses return? Most certainly they would; for no distance can be named so great that the force of gravity shall become absolutely nothing.
If it took millions of years for the most distant body to move one inch, after it had stopped it would eventually return to the central mass, which would itself finally become quiescent.
It will be readily seen that if any number of such bodies were put in motion in the boundless ether, they, too, would finally come to rest.
Another very well-known and much shorter path leads to this same conclusion; it is this:
If the ponderable moving matter of the universe be limited, then, by constant collision, its motion would all be converted into heat and light, and be radiated into the outer realms of space, never to return again, leaving all the ponderable matter to collect into one great mass, and to cool off to a state of perfect quiescence.
But, if matter be infinite, then there can be no "outer realms" into which this heat-force can radiate; consequently there will be no motion lost, and matter, since it has ever been moving, will continue in motion forever.
- ↑ The above is the formula usually given for computing the tidal energy under the assumed conditions; but I incline to believe that the real disruptive power exerted on the satellite is just double that, for the following reasons:
One (1) pound of ice placed on the surface of this icy globe should press it with the force of 1.6 grain, of our standard.
Now, the tidal energy, as above calculated, causes the planet to pull the nearest pound with 1.6 grain greater force than it does the central pound, while, at the same time, it pulls the central pound with practically 1.6 grain greater force than it does the farthest pound; consequently the tensile pull between these two surface-pounds, which would be required to resist the tidal energy, must be equal to 2 x 1.6 grain, while they are drawn toward each other by the gravity of the satellite with the force of only 1.6 grain. - ↑ "Popular Physical Astronomy," by Prof. Daniel Vaughan. Cincinnati: Freeman & Spofford. 1858.
- ↑ It should be here remarked that the heat thus radiated from the nebula is not lost, but continues as wave-motion in the ether, until it is again converted into molecular motion in ponderable matter.
- ↑ Assuming the average specific heat of cosmic matter to be one-fifth that of water, then the calculated temperature due to a velocity of 400 miles a second is equal to nearly 450,000,000° Fahr., or 250,000,000° Centigrade.
- ↑ It may be well to remark just here that the resistance here spoken of is assumed to be caused by the so-called ether of space, through which all bodies must move. Now, this resistance may be due to the inertia of the ether alone, in which case we must suppose that the ether is perfectly fluent, and receives a kind of mass-motion from the bodies moving through it. Or, on the other hand, we may conceive it to be a friction between the moving body and the ether. In this case the ether will be given a wave-motion of some kind, while the ponderable matter acquires a molecular motion. In either case there will be no motion lost.
- ↑ Philadelphia edition, 1861, p. 472.