The Evolution of Satellites
After the explanation of this theory, I have added some comments on Mr. See’s views.
If familiarity does not always breed contempt, yet at least it generally breeds indifference. This is the case with most of us in regard to the rise and fall of the tide by the seashore, and so the problem as to whether the tide will serve conveniently to allow the children to dig in the sand or search for seaweed looms larger than that presented by the gigantic forces which now produce only these somewhat insignificant pulsations of the sea. Yet the tides should call forth in us a deeper interest, — I might almost say an emotion, — for, as I shall show, they are the feeble residue of influences which have probably exercised a predominant control over the history of the Earth and the Moon since an indeterminate but remote epoch in the past, and will continue that control into the distant future.
Newton was the first to prove that the tides are caused by the attractions of the Moon and the Sun. It would need much space to explain fully the manner in which those attractions operate, yet it is possible to give in a few words a rough sketch of the mode in which the tidegenerating forces arise. It will suffice for this purpose to confine our attention to the more important of the two bodies, the Moon, since the action of the Sun will then follow by parity of reasoning. According to the law of universal gravitation, the Moon attracts matter which stands near to her more strongly than that which is more remote. It follows that the attraction on the ocean, at the side of the Earth which is nearest to the Moon, must he greater than that exercised on the solid Earth itself. Hence there is a tendency for the sea to depart from its natural spherical shape, and to bulge outward toward the Moon. So far the matter is simple ; but it is perplexing to many that the Moon should apparently repel the water lying on the further side of the Earth. This action, however, is not due to any ideal repulsion from the Moon, but results from the fact that on the further side the Moon must attract the solid Earth more strongly than she does the water. On the nearer side the Moon pulls the water away from the Earth, and on the further side she pulls the Earth away from the water, thus producing an apparent repulsion of the water to an extent equal to the attraction on the other side. In this way there arises a tendency for the ocean to bulge equally toward and away from the Moon, and to assume an egg-like shape, with the length of the egg pointed toward the Moon.
If the whole planet were fluid, instead of being partly fluid and partly solid, the same tendency would still exist, but the tide - generating force would have the whole mass of the planet as its field of operation, instead of merely the superficial ocean. The fact that the Earth, the Moon, and the planets are all nearly spherical proves that in early times they were molten and plastic, and that they assumed their present round shape under the influence of gravitation. When the material of which any planet is formed was semi-liquid through heat, its satellites, or at any rate the Sun, must have produced tidal oscillations in the molten rock, just as the Sun and the Moon now raise tides in our oceans.
Molten rock and molten iron are rather sticky or viscous substances, and any movement which agitates them must be subject to much friction. Even water, which is a very good lubricant, is not entirely free from friction, and so our present oceanic tides must be influenced by fluid friction, although to a far less extent than the molten solid just referred to. Now all moving systems which are subject to friction gradually come to rest. A train will run a long way when the steam is turned off, but it stops at last, and a fly-wheel will continue to spin for only a limited time. This general law renders it certain that the friction of the tide, whether it consists in the swaying of molten lava or of an ocean, must be stopping the rotation of the planet, or at any rate stopping the motion of the system in some way.
It is the friction upon its bearings which brings a fly-wheel to rest; but as the Earth has no bearings, it is not easy to see how the friction of the tidal wave, whether corporeal or oceanic, can tend to stop its rate of rotation. The result must clearly be brought about, in some way, by the interaction between the Moon and the Earth. Action and reaction must be equal and opposite, and if we are correct in supposing that the friction of the tides is stopping the Earth’s rotation, there must be a reaction upon the Moon tending to hurry her onward. To give a homely illustration of the effects of reaction, I may recall to mind how a man riding a high bicycle, on applying the brake too suddenly, was shot over the handles. The desired action was to stop the front wheel, but this could not be done without a reaction on the rider, which sometimes led to unpleasant consequences.
The general conclusion as to the action and reaction due to tidal friction is of so vague a character that it is desirable to consider in detail how they operate.
The circle in the figure is supposed to represent the undisturbed shape of the planet, which rotates in the direction of the curved arrow. A portion of the orbit of the satellite is indicated by part of a larger circle, and the direction of its motion is shown by an arrow. I will first suppose that the water lying on the planet, or the molten rock of which it is formed, is a perfect lubricant, devoid of friction ; and that at the moment represented in the figure the satellite is at M艂. The fluid will then be distorted by the tidal force until it assumes the egg-like shape marked by the ellipse, projecting on both sides beyond the circle. When there is no friction, the long axis of the egg is always directed straight toward the satellite M艂, and the fluid maintains a continuous rhythmical movement, so that as the planet rotates and the satellite revolves, it always preserves the same shape and attitude toward the satellite.
But when, as in reality, the fluid is subject to friction, it gets belated in its rhythmical rise and fall, and the protuberance is carried onward by the rotation of the planet beyond its proper place. In order to make the same figure serve for this condition of affairs, I set the satellite backward to M ; for this amounts to just the same thing, and is less confusing than re-drawing the protuberance in its more advanced position. The planet then constantly maintains this shape and attitude with regard to the satellite, and the interaction between the two will be the same as though the planet were solid, but continually altering its shape.
We have now to examine what effects must follow from the attraction of the satellite on an egg-shaped planet when the two bodies constantly maintain the same attitude relatively to each other. It will make the matter somewhat easier of comprehension if we replace the tidal protuberances by two particles of equal masses, one at P, and the other at P艂. If the masses of these particles be properly chosen, so as to represent the amount of matter in the protuberances, the proposed change will make no material difference in the result.
The gravitational attraction of the satellite is greater on bodies which are near than on those which are far, and accordingly it attracts the particle P more strongly than the particle P艂. It is obvious from the figure that the pull on P must tend to stop the planet’s rotation, whilst the pull on P’ must tend to accelerate it. If a man pushes equally on the two pedals of a bicycle, the crank has no tendency to turn ; and besides, there are dead points in the revolution of the crank where pushing and pulling have no effect. So also in the astronomical problem, if the two attractions were exactly equal, or if the protuberances were at a dead point, there would be no resultant effect on the rotation of the planet. But it is obvious that here the retarding pull is stronger than the accelerating pull, and that the set of the protuberances is such that we have passed the dead point. It follows from this that the primary effect of fluid friction is to throw the tidal protuberance forward, and the secondary effect is to retard the planet’s rotation.
Action and reaction are equal and opposite, and if the satellite pulls at the protuberances, they pull in return at the satellite. The figure shows that the attraction of the protuberance P tends in some measure to hurry the satellite onward in its orbit, whilst that of P艂 tends to retard it. But the attraction of P is stronger than that of P艂, and therefore the resultant of the two is a force tending to carry the satellite forward more rapidly in the direction of the arrow. When the satellite is thus influenced, it must move in a spiral curve, ever increasing its distance from the planet. Besides this, the satellite has a longer path to travel in its circuit, and takes longer to get round the planet, than was the case before tidal friction began to operate.2
Now let us apply these ideas to the case of the Earth and the Moon. A man standing on the planet, as it rotates, is carried past places where the fluid is deeper and shallower alternately : at the deep places he says that it is high tide, and at the shallow places that it is low tide. In the figure it is high tide when the observer is carried past P. Now, it was pointed out that when there is no fluid friction we must put the Moon at M’, but when there is friction she must be at M. Accordingly, if there is no friction it is high tide when the Moon is over the observer’s head, but when there is fluid friction the Moon has passed his zenith before he reaches high tide. Hence he would remark that fluid friction retards the time of high water.3
A day is the name for the time in which the Earth rotates once, and a month for the time in which the Moon revolves once. Then, since tidal friction retards the Earth’s rotation and the Moon’s revolution, we may state that both the day and the month are being lengthened, and that these results follow from the retardation in the time of high tide. It must also be noted that the spiral in which the Moon moves is an increasing one, so that her distance from the Earth increases. These are absolutely certain and inevitable results of the mechanical interaction of the two bodies.
At the present time the rates of increase of the day and month are excessively small, so that it has not been found possible to determine them with any approach to accuracy. It may be well to notice in passing that if the rate of change of either element were determinable, that of the other would be deducible by calculation.
The extreme slowness of the changes within historical times is established by the records in early Greek and Assyrian history of eclipses of the Sun which occurred on certain days and at certain places. Notwithstanding the changes in the calendar, it is possible to identify the day according to our modern reckoning, and the identification of the place presents no difficulty. Astronomy affords the means of calculating the exact time and place of the occurrence of an eclipse even three thousand years ago, on the supposition that the Earth spun at the same rate then as now, and that the complex laws governing the Moon’s motion are unchanged. The particular eclipse referred to in history is known, but any considerable change in the Earth’s rotation and in the Moon’s motion would have shifted the position of visibility on the Earth from the situation to which modern computation would assign it. Most astronomical observations would be worthless if the exact time of the occurrence were uncertain, but in the ease of eclipses the place of observation affords just that element of precision which is otherwise wanting. As, then, the situations of the ancient eclipses agree fairly well with modern computations, we are sure that there has been no great change within the last three thousand years either in the Earth’s rotation or in the Moon’s motion. There is, however, a small outstanding discrepancy which indicates that there has been some change. But the exact amount involves elements of uncertainty, because our knowledge of the laws of the Moon’s motion is not yet quite accurate enough for the absolutely perfect calculation of eclipses which occurred many centuries ago. In this way it is known that within historical times the retardation of the Earth’s rotation and the recession of the Moon have been, at any rate, very slight.
It does not follow from this that the changes have always been equally slow, and indeed it may be shown by mathematical arguments that the efficiency of tidal friction increases with enormous rapidity as we bring the tide-raising satellite nearer to the planet. The law of tidal friction is that it varies according to the inverse sixth power of the distance ; so that with the Moon at half her present distance, the rate of retardation of the Earth’s rotation would be sixty-four times as great as it now is. Thus, although the action may now be almost insensibly slow, yet it must have proceeded with much greater rapidity when the Moon was nearer to us.
There are many problems in which it would be very difficult to follow the changes in the system according to the times of their occurrence, but where it is possible to banish time, and to trace the changes themselves in due order, without reference to time. In the sphere of common life, we know the succession of stations which a train must pass between New York and Boston, although we may have no time-table. This is the case with our astronomical problem ; for although we have no time-table, yet the sequence of the changes in the system may be traced accurately.
Let us then banish time, and look forward to the ultimate outcome of the tidal interaction of the Moon and the Earth. The day and the month are now lengthening at relative rates which are calculable, although the absolute rates in time are unknown. It will suffice for a general comprehension of the problem to know that the present rate of increase of the day is much more rapid than that of the month, and that this will hold good in the future. Thus, the number of rotations of the Earth in the interval comprised in one revolution of the Moon diminishes ; or, in other words, the number of days in the month diminishes, although the length of each day increases so rapidly that the month itself is longer than at present. For example, when the day shall be equal in length to two of our actual days, the month may be as long as thirty-seven of our days, and then the Earth will spin round only about eighteen times in the month.
This gradual change in the day and the month proceeds continuously until the duration of a rotation of the Earth is prolonged to fifty-five of our present days. At the same time, the month, or the time of a revolution of the Moon round the Earth, will also occupy fiftyfive of our days. Since the month here means the period of the return of the Moon to the same place amongst the stars, and since the day is to be estimated in the same way, the Moon must then always face the same part of the Earth’s surface, and the two bodies must move as though they were united by a bar. The outcome of the lunar tidal friction will therefore be that the Moon and the Earth will go round as though locked together in a period of fifty-five of our present days, with day and month identical in length.
Now, looking backward in time, we find the day and the month shortening, but the day changing more rapidly than the month. The Earth was therefore able to complete more revolutions in the month, although that month was itself shorter than it is now. We get back, in fact, to a time when there were twentynine rotations of the Earth in the time of the Moon’s revolution, instead of twentyseven and one third, as at present. This epoch is a sort of crisis in the history of the Moon and the Earth, for it may be proved that there never could have been more than twenty-nine days in the month. Earlier than this epoch, the days were fewer than twenty-nine ; and later, fewer also. Although measured in years, this epoch in the Earth’s history must be very remote ; yet when we contemplate the whole series of changes it must be considered as a comparatively recent event. In a sense, indeed, we may be said to have passed recently through the middle stage of our history.
Now, pursuing the series of changes further back than the epoch when there was the maximum number of days in the month, we find the Earth still rotating faster and faster, and the Moon drawing nearer and nearer to the Earth and revolving in shorter and shorter periods. But a change has supervened, so that the rate at which the month is shortening is more rapid than the rate of change in the day. Consequently, the Moon now gains, as it were, on the Earth, which cannot get round so frequently in the month as it did before. In other words, the number of days in the month declines from the maximum of twenty-nine, and is finally reduced to one. When there is only one day in the month, the Earth and the Moon go round at the same rate, so that the Moon always looks at the same side of the Earth, and as far as concerns the motion they might be fastened together by iron bands.
This is the same conclusion at which we arrived with respect to the remote future. But the two cases differ widely ; for whereas in the future the period of the common rotation will be fifty-five of our present days, in the past we find the two bodies going round each other in between three and five of our present hours. A satellite revolving round the Earth in so short a period must almost touch the Earth’s surface. The system is therefore traced until the Moon nearly touches the Earth, and the two go round each other like a single solid body in about three to five hours.
The series of changes has been traced forward and backward from the present time, but it will make the whole process more intelligible, and the opportunity will be afforded for certain further considerations, if I sketch the history again in the form of a continuous narrative.
Let us imagine a planet attended by a satellite which revolves in a circular orbit so as nearly to touch its surface, and continuously to face the same side of the planet. If now, for some cause, the satellite’s month comes to differ very slightly from the planet’s day, the satellite will no longer continuously face the same side of the planet, but will pass over every part of the planet’s equator in turn. This is the condition necessary for the generation of tidal oscillations in the planet, and as the molten lava, of which we suppose the planet to be formed, is a sticky or viscous fluid, the tides must be subject to friction. Tidal friction will then begin to do its work, but the result will be very different according as the satellite revolves a little faster or a little slower than the planet. If it revolves a little faster, so that the month is shorter than the day, we have a condition not contemplated in the figure above ; it is easy to see, however, that as the satellite is always leaving the planet behind it, the apex of the tidal protuberance must be directed to a point behind the satellite in its orbit. In this case the rotation of the planet must be accelerated by the tidal friction, and the satellite must be drawn inward toward the planet, into which it must ultimately fall. In the application of this theory to the Earth and the Moon, it is obvious that the very existence of the Moon negatives the hypothesis that the initial month was even infinitesimally shorter than the day. We must then suppose that the Moon revolved a little more slowly than the Earth rotated. In this case the tidal friction would retard the Earth’s rotation, and force the Moon to recede from the Earth, and so perform her orbit more slowly. Accordingly, the primitive day and the primitive month lengthen, but the month increases much more rapidly than the day, so that the number of days in the month becomes greater. This proceeds until that number reaches a maximum, which in the case of our planet is about twenty-nine.
After the epoch of maximum number of days in the month, the rate of change in the length of the day becomes less rapid than that in the length of the month ; and although both periods increase, the number of days in the month begins to diminish. The series of changes then proceeds until the two periods come again to an identity, when we have the Earth and the Moon, as they were at the beginning, revolving in the same period, with the Moon always facing the same side of the planet. But in her final condition the Moon will be a long way off from the Earth, instead of being quite close to it.
Although the initial and final states resemble each other, yet they differ in one respect which is of much importance ; for in the initial condition the motion is unstable, whilst finally it is stable. The meaning of this is that if the Moon were even infinitesimally disturbed from the initial mode of motion, she would necessarily either fall into the planet or recede therefrom, and it would be impossible for her to continue to move in that neighborhood. She is unstable in the same sense in which an egg balanced on its point is unstable; the smallest mote of dust will upset it, and practically it cannot stay in that position. But the final condition resembles the case of an egg lying on its side, which only rocks a little when we disturb it. So if the Moon were slightly disturbed from her final condition, she would continue to describe very nearly the same path round the Earth, and would not assume some entirely new form of orbit.
It is by methods of rigorous argument that the Moon is traced back to the initial unstable condition when she revolved close to the Earth. But the argument here breaks down, and calculation is incompetent to tell us what occurred before, and how she attained that unstable mode of motion. We can only speculate as to the preceding history, but there is some basis for our speculation ; for I say that if a planet, such as the Earth, made each rotation in a period of three hours, it would very nearly fly to pieces. The attraction of gravity would be barely strong enough to hold it together, just as the cohesive strength of iron is insufficient to hold a fly-wheel together if it is spun too fast. There is, of course, an important distinction between the case of the ruptured fly-wheel and the supposed break-up of the Earth ; for when the fly-wheel breaks, the pieces are hurled apart as soon as the force of cohesion fails, whereas when a planet breaks up through too rapid rotation, gravity must continue to hold the pieces together after they have ceased to form parts of a single body.
Hence we have grounds for conjecturing that the Moon is composed of fragments of the primitive planet which we now call the Earth, which detached themselves when the planet spun very swiftly, and afterward became consolidated. It surpasses the powers of mathematical calculation to trace the details of the process of this rupture and subsequent consolidation, but we can hardly doubt that the system would pass through a period of turbulence before order was reëstablished in the formation of a satellite.
I have said that rapid rotation was probably the cause of the birth of the Moon, but this statement needs qualification. There are certain considerations which prevent us from ascertaining the common period of revolution of the Moon and the Earth with accuracy; it may lie between three and five hours. I think that such a speed might not, perhaps, be quite sufficient to cause the planet to break up. Is it possible, then, to suggest any other cause which might have coöperated with the tendency to instability of the rotating planet ? I think that there is such a cause ; and though we are here dealing with guesswork, I will hazard the suggestion.
The primitive planet, before the birth of the Moon, was rotating rapidly with reference to the Sun, and it must, therefore, have been agitated by tidal oscillations due to the Sun’s attraction. Now, the magnitude of these solar tides is much influenced by the speed of rotation of the planet, and mathematical reasoning appears to show that when the day was about three or four hours in length the oscillations must have been very great, although the Sun stood no nearer to the Earth then than it does now. May we not conjecture that the oscillation of the molten planet became so violent that, in coöperation with the rapid rotation, it shook the planet to pieces, detaching huge fragments which ultimately were consolidated into the Moon ? There is nothing to tell us whether this theory affords the true explanation of the birth of the Moon, and I say that it is only a wild speculation, incapable of verification.
But the truth or falsity of this speculation does not militate against the acceptance of the general theory of tidal friction, which, standing on the firm basis of mechanical necessity, throws much light on the history of the Earth and the Moon, and correlates the lengths of our present day and month.
I have said above that the sequence of events has been stated without reference to the scale of time. It is of the utmost importance, however, to gain some idea of the time requisite for all the changes in the system. If millions of millions of years were necessary, the applicability of the theory to the Moon and the Earth would have to be rejected, because it is known from other lines of argument that there is not an unlimited bank of time on which to draw. The uncertainty as to the duration of the solar system is wide, yet we are sure that it has not existed for an almost infinite past.
Now, although the actual time-scale is indeterminate, it is possible to find the minimum time adequate for the transformation of the Moon’s orbit from its supposed initial condition to its present shape. It may be proved, in fact, that if tidal friction had always operated under the conditions most favorable for producing rapid change, the sequence of events from the beginning until to-day would have occupied a period of between fifty and sixty millions of years. The actual period, of course, must have been much greater. Various lines of argument as to the age of the solar system have led to results which differ widely among themselves, yet I cannot think that the applicability of the theory of tidal friction is negatived by the magnitude of the period demanded. It may be that science will have to reject the theory in its full extent, but it seems improbable that the ultimate verdict will be adverse to the preponderating influence of the tide on the evolution of our planet.
If this history be true of the Earth and the Moon, it should throw light on many peculiarities of the solar system. In the first place, a corresponding series of changes must have taken place in the Moon herself. Once on a time she must have been molten, and the great extinct volcanoes revealed by the telescope are evidences of her primitive heat. The molten mass must have been semi-fluid, and the Earth must have raised in it enormous tides of molten lava. Doubtless the Moon once rotated rapidly on her axis, and the frictional resistance to her tides must have impeded her rotation. She rotated then more and more slowly until the tide solidified, and thenceforward and to the present day she has shown the same face to the Earth. Helmholtz was, I believe, amongst the first in modern times to suggest this as the explanation of the fact that the Moon always shows us the same face.4 Our theory, then, receives a striking confirmation from the Moon ; for, having ceased to rotate relatively to us, she has actually advanced to that condition which may be foreseen as the fate of the Earth.
Thus far I have referred in only one passage to the influence of solar tides, but these are of considerable importance, being large enough to cause the conspicuous phenomena of spring and neap tides. Now, whilst the Moon is retarding the Earth’s rotation, the Sun is doing so also. But these solar tides react only on the Earth’s motion round the Sun, leaving the Moon’s motion round the Earth unaffected. It might perhaps he expected that parallel changes in the Earth’s orbit would have proceeded step by step, and that the Earth might be traced to an origin close to the Sun. But the smallness of the Earth’s mass compared with that of the Sun here prohibits the application of the theory of tidal friction, and it is improbable that our year is now longer, from this cause at any rate, by more than a few seconds than it was at the very birth of the solar system.
Although the solar tides can have had no perceptible influence upon the Earth’s movement in its orbit, they will have affected the rotation of the Earth to a considerable extent. Let us imagine ourselves transported to the indefinite future, when the Moon and the Earth shall be revolving together in fifty-five of our days. The lunar tide in the Earth will then be unchanging, just as the Earth tide in the Moon is now fixed ; but the Earth will be rotating with reference to the Sun, and, if there are unfrozen oceans, its rotation will still be subject to retardation in consequence of the solar tidal friction. The day will then become longer than the month, which for a very long time will continue to occupy about fifty-five of our present days. It is known that there are neither oceans nor atmosphere on the Moon ; but if there were, she would have been subject to solar tidal friction, and would have undergone a parallel series of changes.
Up to recent times it might have been asserted plausibly that the absence of any such mode of motion in the solar system afforded a reason for rejecting the actual efficiency of tidal friction in celestial evolution. But in 1877 Professor Asaph Hall discovered in the system of the planet Mars a case of the kind of motion which we have reason to foresee as the future fate of the Earth and the Moon ; for he found two satellites, one of which has a month shorter than the planet’s day.
In his paper on the discovery of these satellites, Professor Hall gives an interesting account of what had been conjectured, partly in jest and partly in earnest, as to the existence of satellites attending that planet. He quotes Kepler as writing, after the discovery of the satellites of Jupiter, “ I am so far from disbelieving the existence of the four circumjovial planets” (that is, satellites) “ that I long for a telescope to anticipate you, if possible, in discovering two round Mars, six or eight round Saturn, as the proportion seems to require, and perhaps one each round Mercury and Venus.” This, was of course, serious, although based on fantastic considerations. At a later date Swift poured contempt on men of science in his account of the inhabitants of Laputa, whom he describes as dexterous enough on a piece of paper, and in the management of the rule, the pencil, and the dividers, but as a clumsy, awkward, and unhandy people, and perplexed in their conceptions upon all subjects except mathematics and music. He writes, however, of the Laputans, 舠 They have likewise discovered two lesser stars or satellites, which revolve about Mars, whereof the innermost is distant from the centre of the primary exactly three of his diameters, and the outermost five.” In one of his satires, Voltaire also represents an imaginary traveler from Sirius as making a similar discovery.
These curious prognostications were at length verified by Professor Asaph Hall in the discovery of two satellites, which he named Phobos and Deimos, — Fear and Panic, the dogs of war. The period of Deimos is about thirty hours, and that of Phobos about eight hours, whilst the Martian day is of nearly the same length as our own. The month of the inner minute satellite is thus less than a third of the planet’s day ; it rises to the Martians in the west, and passes through all its phases in a few hours ; sometimes it must even rise twice in a single Martian night. As we here find an illustration of the condition foreseen for our own planet and satellite, it seems legitimate to suppose that solar tidal friction has slowed down the planet’s rotation. The ultimate fate of Phobos must almost certainly be absorption by the planet.
Several of the satellites of Jupiter and Saturn present faint inequalities of coloring, and telescopic examination has led astronomers to believe that they always present the same face to their planets. The theory of tidal friction would certainly lead us to expect that these enormous planets would have worked out the same result for these relatively small satellites that the Earth has effected in the Moon.
The efficiency of solar tidal friction must be far greater in its action on the planets Mercury and Venus than on the Earth. The determination of the periods of rotation of these planets thus becomes a matter of much interest. But the markings on their disks are so obscure that their rates of rotation have remained under discussion for many years. Until recently the prevailing opinion was that in each case the day was of nearly the same length as our own ; but a few years ago Schiaparelli of Milan, an observer endowed with extraordinary acuteness of vision, announced, as the result of his observation, that both Mercury and Venus rotate only once in their respective years, and that each of them always presents the same face to the Sun. These conclusions have recently been confirmed by Mr. Percival Lowell from observations made in Arizona, and are exactly conformable to our theoretical expectation. Whilst it is not easy to see how these astronomers can have been mistaken, yet it is proper to note that others, possessing apparently equal advantages, have failed to detect the markings on the planets. Accepting, however, this conclusion, we have the planets Mercury and Venus, the satellites of the Earth, and Jupiter and Saturn presenting evidence favorable to the theory of tidal friction, whilst the case of the Martian system is yet more striking as an instance of an advanced stage in evolution.
It would need another article to discuss the various aspects of this theory in relation to the histories of the planets and of their satellites. I may say, however, that it serves in great measure to explain the fact that the Earth is tilted over with reference to its orbit round the Sun, and that it throws light on the fact that the plane of the Moon’s orbit is not coincident with that of the Earth. The same cause may also be proved to tend toward making the orbit of a satellite eccentric, and it is this effect of tidal friction to which Mr. See has appealed. I shall not here repeat his arguments, but in section iv. I will make some comments on his theories.
With respect to the efficacy of tidal friction as a factor in the evolution of the Earth, it is not too much to say that if we postulate a planet consisting partly or wholly of molten lava, and rapidly rotating about an axis at right angles to its orbit round the Sun, and if that planet have a single satellite, revolving nearly as rapidly as the planet rotates, then a system will necessarily be evolved in time closely resembling our own.
A theory reposing on true causation, which brings into quantitative correlation the lengths of the present day and month, the obliquity of the ecliptic, and the eccentricity and inclination of the Moon’s orbit, must, I think, have strong claims to acceptance.
There are in the heavens many pairs of closely neighboring stars which revolve about each other under the influence of their mutual gravitation. The fact that both members of a pair are visible seems to indicate that they do not differ widely in mass, and it is also a striking peculiarity of these binary systems that the orbit is commonly very eccentric. The distinction is great between our solar system, with its large central mass and infinitesimal planets moving in nearly circular orbits, and these binary systems, and hence there is abundant reason for supposing that the course of evolution has been very different in the two cases.
Mr. See explains the high degree of eccentricity in these binary orbits by the influence of tidal friction. The tide undoubtedly operates under conditions which give it a wide scope, when two large masses are revolving about one another ; and tidal friction is the only known cause capable of converting a nearly circular orbit into a very eccentric one. But this does not afford quite sufficient reason for the acceptance of the theory, for the assumption is involved that orbits now very eccentric were formerly nearly circular. Mr. See accordingly also puts forward a theory of the method by which double stars originated, and to this I shall return later.
At first it may not be easy to see how the truth of this theory of the origin of the eccentricity is to be tested : it may be worth while, therefore, to point out the direction which, to me at least, seems the most promising in the search for confirmation or refutation.
It is thought by some spectroscopists that the ages of stars are already determinable by the nature of their spectra, and although the theories which have been advanced do not meet with universal acceptance, yet they foreshadow views which may some day be universally accepted. It has been plausibly contended that stars which are young in their evolution must consist of incandescent gas, and must therefore have spectra furrowed by bright lines ; later in their histories they are supposed to become more condensed and to give continuous spectra. Now if, from theories of this kind, we could ascertain the stage of evolution of a binary system, we should be able to form a judgment of the truth of the tidal theory; for the younger systems should present smaller eccentricity of orbit than the older ones, and the periodic times in the young systems should be shorter, on the whole, than those in the old ones. Delicate spectroscopic measurements make it theoretically possible to determine the relative masses of a binary pair, but hitherto the measurements have been carried to a successful issue in only a very few cases. It is to be expected, however, that the number of known masses will be largely multiplied in the future. A small star must cool more rapidly than a large one, and should present the appearance of greater age. We may hope, then, in time, not only to attain to crucial tests of spectroscopic theories of age, but also to be furnished with the materials for judging of the truth of the tidal theory of evolution of stellar systems.
The second and yet more speculative branch of Mr. See’s theory is that which concerns the mode of origin of binary systems. Man must ultimately be brought face to face with the incomprehensibility of the origin of matter and motion, but this consideration will never prevent him from peering into the past to the utmost of his powers. It is certain that the stars are continually undergoing change, and it seems impossible to accept their existence as an ultimate fact not susceptible of explanation. Thus we feel bound to trace their histories back to a past so remote that their preceding course of evolution becomes inscrutable.
The fact that two stars are now found to be revolving about each other leads to the conviction that their relationship is not a casual one, but that they have been connected from an early epoch, which for convenience we may call the origin of the system. It appears almost beyond question that this starting - point must have been at a time when the two stars were united in a single rotating mass. As the basis of his explanation of the manner in which a single mass may split into two, Mr. See takes certain theoretical investigations as to the shapes which a mass of gravitating and rotating fluid is capable of maintaining. I will not recapitulate his theories, but I wish to emphasize the uncertainties with which we are here brought face to face.
Many years ago Sir John Herschel drew a number of twin nebulæ as they appear through a powerful telescope. The drawings probably possess the highest degree of accuracy attainable by this method of delineation, and the shapes present evidence confirmatory of Mr. See’s theory of the fission of nebulæ. But since Herschel’s time it has been discovered that many details, to which our eyes must remain forever blind, are revealed by celestial photography. The photographic film is, in fact, sensitive to those photographic rays which we may call invisible light, and many nebulæ are now found to be hardly recognizable, when photographs of them are compared with drawings. A conspicuous example of this is furnished by the great nebula in Andromeda ; for whereas the drawing exhibits a cloud with a few dark streaks in it, the photograph shows a flattened disk surrounding a central condensation ; moreover, the disk is seen to be divided into rings, so that the whole system might have been drawn by Laplace to illustrate his celebrated nebular hypothesis of the origin of the solar system.
Photographs, however, do not always aid interpretation, for there are some which serve only to increase the chaos visible with the telescope. We may suspect, in fact, that the complete system of a nebula often contains masses of cool and photographically invisible gas, and in such cases it would seem that the true nature of the whole will be forever concealed from us.
Another group of strange celestial objects is that of the spiral nebulæ, whose forms irresistibly suggest violent whirlpools of incandescent gas. Although in all probability the motion of the gas is very rapid, yet no change of form has been detected. We are here reminded of a rapid stream rushing past a post, where the form of the surface remains constant, whilst the water itself is in rapid movement, and it seems reasonable to suppose that in these nebulæ it is only the lines of flow of the gas which are visible. Again, there are other cases in which the telescopic view may be almost deceptive in its physical suggestions. Thus, the Dumb-Bell Nebula (27 Messier Vulpeculæ), as viewed telescopically, might be taken as a good illustration of a nebula almost ready to split into two stars. If this were so, the rotation would be about an axis at right angles to the length of the nebula. But a photograph of this object shows that the system really consists of a luminous globe surrounded by a thick and less luminous ring, and that the opacity of the sides of the ring takes a bite, as it were, out of each side of the disk, and so gives it the apparent form of a dumb-bell. In this case the rotation must be about an axis at right angles to the ring, and therefore along the length of the dumb-bell.5
From what I have said it must be obvious that the subject is surrounded by difficulties and uncertainties ; Mr. See is therefore to be congratulated on having laid before the world an hypothesis which appears to explain the facts as far as we know them. The subject is necessarily a speculative one, and we must look forward to future spectroscopic and photographic researches for the confirmation or refutation of his theories.
G. H. Darwin.
- It was very natural that Mr. See should find in certain tidal investigations which I undertook for Lord Kelvin the source of my papers, but as a fact the subject was brought before me in a somewhat different manner. Some unpublished experiments on the viscosity of pitch induced me to extend Lord Kelvin’s beautiful investigation of the strain of an elastic sphere to the tidal distortion of a viscous planet. This naturally led to the consideration of the tides of an ocean lying on suck a planet, which forms the subject of certain paragraphs now incorporated in Thomson and Tait’s Natural Philosophy.↩
- It is somewhat paradoxical that, the effect of attempting to hurry the satellite is to make it actually move slower. It would be useless to attempt an explanation of this in such an article as the present one, but the converse case, where a retarding force acts on the body, may be more intelligible. When a meteorite rushes through the atmosphere it moves faster and faster, because it gains more velocity by the direct action of the Earth’s gravity on it than it loses by the friction of the air. And yet it is the friction of the air which allows gravity to have play ; so that we have the paradox of friction accelerating the motion.↩
- This must not be considered as a fair statement of the case when the oceans are as shallow as in actuality. The reader must accept the assurance that the friction of the tides of shallow seas also causes retardation of the planet’s rotation, although in a somewhat different manner from that explained above.↩
- Kant, in the middle of the last century, drew attention to the importance of tidal friction in celestial dynamics; but as he did not clothe his argument in mathematical form, he was unable to deduce most of the results which are explained in this paper.↩
- It is proper to state that. Mr. See does not refer to this nebula as confirmatory of his theory.↩