THE THIRD CONCORD

The Earth's Beginning by Robert S. Ball is part of the HackerNoon Books Series. You can jump to any chapter in this book here. THE THIRD CONCORD

CHAPTER XVI. THE THIRD CONCORD

Rotations of the Planets on their Axes.—The Older Planets—No Information about Uranus or Neptune or the Asteroids—The Speed of Rotation is Arbitrary so far as Kepler’s Laws are concerned—The Third Concord—A Remarkable Unanimity—Kant’s Argument—Illustration of the Rotation of the Moon on its Axis—How the Nebular Theory explains the Rotation—The Moon’s Evolution—Special Action of Tides—The Evolution of the other Satellites—The case of Mars—Jupiter and Saturn as Miniatures of the Solar System—Uranus and Neptune offer Difficulties.

We have seen in the last chapter how the rotation of the sun beat time, as it were, for the planets, by giving to them an indication of the direction in which the revolutions round the sun should be performed, and we have observed with what marvellous unanimity the planets follow the precept thus given. We have now to consider yet another concord, which has perhaps not the great numerical strength of that last considered, but is, nevertheless, worthy of our most special attention. The earth revolves about an axis which is not very far from being perpendicular to the principal plane to which the movements of the solar system are related. From a dynamical point of view it would, of course, have been equally possible for the earth to revolve on its axis in the same direction as the rotation of the sun, or in the opposite direction. There is nothing so far as the welfare of man is concerned to make one direction of rotation preferable to the other, but, as a matter of fact, the earth does turn round in the same way as the sun turns.

Jupiter also turns on its axis, and Jupiter again, like the earth, might turn either with the sun or it might turn in the opposite direction. Here, again, we find a unanimity between the earth and Jupiter; they both turn in the same direction, and that is the direction in which the sun rotates. The same may be said of Mars, and the same may be said of Saturn. In the case of the planets Mercury and Venus we cannot speak with equal definiteness on the subject of their rotations about their axes. The circumstances of these planets are such that there are great difficulties attending the exact telescopic determination of their periods of rotation. The widest variations appear in the periods which have been assigned. It has, for instance, been believed that Venus rotates in a period not greatly differing from the period of twenty-four hours in which our earth revolves. But it has been lately supposed that the period of Venus is very much longer, and is in fact no less than seven months, which is, indeed, that of the revolution of Venus about the sun. According to this view, Venus rotates round the sun in a period equal to its revolution. If this be so, then Venus constantly turns the same face to the sun, and the movement of the planet would thus resemble the movement of the moon around the earth. As a matter of observation, the question must still be considered unsettled, though there are sound dynamical reasons for believing that the long period is much more probable than the short one. We do not now enter into this question, or into the still more difficult matter of the rotation of Mercury; it suffices to say that whichever period be adopted for either of these planets is really not material to our present argument. In both cases it has never been doubted that the direction of the rotation of the planets is the same as the direction in which Jupiter and Mars and the earth rotate, these being also the same as the direction of the solar rotation.

As to the rotations of Uranus and Neptune about their respective axes, the telescope can show us nothing. The remoteness of both these planets is such that we are unable to discern objects on their discs with the definiteness that would be required if we desired to watch their rotations. We have also no information as to the rotation of the several asteroids. No one, I think, will doubt that each of these small planets, equally with the large planets, does rotate about its axis; but it is impossible for us to say so from actual knowledge.

But undoubtedly the five old planets, Mercury, Venus, Mars, Jupiter, and Saturn, as well as the earth, all rotate in the same direction as the sun. Each planet might rotate twice as fast, or half as fast, as it does at present. They might all rotate in the opposite direction from that in which they do now, or some of them might go in one direction, and some in the other, with every variety in their diurnal periods, while the primary condition of Kepler’s Laws would have still been complied with. We may also note that the direction in which the rotation takes place seems quite immaterial so far as the welfare of the inhabitants on these planets is concerned.

The fact that the planets and the sun have this third concord demands special attention. The chance that the earth should rotate in the same direction as the sun is, of course, expressed by one-half. It is easy to show, that out of sixty-four possible arrangements of the directions of rotation of the five planets and the earth, there would be only one in which all the movements coincided with the direction of the rotation of the sun. If, therefore, it had been by chance that the direction of these motions was determined, then Nature would have taken a course of which the probability was only one sixty-fourth. No doubt this figure is by no means so large as those which expressed the probabilities of the other planetary concords; it is, however, quite sufficient to convince us that the direction of the rotation of the planets on their axes has not been determined merely by the operation of chance.

We are to see if there is any physical agent by which the planets have been forced to turn round in the same direction. And here comes in one of those subtle points which the metaphysical genius of Kant suggested. Let us take any two planets—say, for instance, the earth and Jupiter—and let us endeavour to see what the nature of the agent must have been which has operated on these planets so as to make them both rotate in the same direction. Kant urged that there must have been some material agent working on the materials in Jupiter, and some material agent working on those of the earth, and that to produce the like effect in each planet there must have been at one time a material connection existing between that body which is now Jupiter and that body which is now the earth. In like manner Kant saw this material connection existing between the other planets and the sun, and thus he was led to see that the whole material of our solar system must once have formed a more or less continuous object. The argument is a delicate one, but it seems certainly true that in the present arrangement of the orbits it is impossible for us to conceive how, with intervals of empty space between the tracks of the planets, a common influence can have been exerted so as to give them all rotations in the same direction.

The nebular theory at once supplies the explanation of the unanimity in the rotation of the planets, just as it supplied the explanation of the unanimity in the directions of their revolutions. To explain the rotation of a planet on its axis, let us imagine that one portion of the contracting nebula has acquired exceptional density. In virtue of its superior attraction it absorbs more and more material from the adjacent parts of the nebula, and this will ultimately be consolidated into the planet, though in its initial stages this contracting matter will remain part of the nebula. We have shown that the law which decrees that the moment of momentum must remain constant will require that, after a certain advance in the contraction, all the parts of the nebula shall rotate in the same direction. Thus we find that the sun, or rather the parts of the nebula that are to form the sun, and the parts that are to form the planets are all turning round together.

Fig. 51.—An elongated irregular Nebula (n.g.c. 6992; in Cygnus).
(Dr. W. E. Wilson, F.R.S.)
(From the Astronomical and Physical Researches at Daramona Observatory.)

At this point we may consider a geometrical principle which, though really quite simple, is not always easily understood. It has indeed presented considerable difficulty to many people. Suppose that an ordinary card is laid on a flat board, and that, with a bradawl, a hole is made through the card into the board. The hole may be at the centre, or at one of the corners, or a little way in from one of the edges, or in any other position whatever on the card. Now suppose that a postage stamp is stuck upon the card anywhere, and that the card is then moved around the bradawl. How are we to describe the motion of that postage stamp? It would certainly be revolving around the bradawl; but this motion we may consider as composed of two others. At any instant we may accurately represent the movement of the postage stamp by considering that its centre was moving in a direction perpendicular to the line joining that centre to the hole made by the bradawl, and that it also had a rotation around its centre, the period of that rotation being just the same as the time the card would take to go round the bradawl. Thus we see that the movement of the postage stamp contains at any moment a movement of translation and a movement of rotation.

We may illustrate the case we have supposed by the movement of the moon around the earth. If the centre of the earth be considered to be at the centre of rotation the moon may be considered to be in the position of the postage stamp. As our satellite revolves, the same side of the moon is continually turned towards the earth, but this is due to the fact that the moon, at each moment, really possesses two movements, namely, a movement of translation of its centre, in a direction perpendicular to the line from the moon’s centre to the earth’s centre, coupled with a slow rotation of the moon round its axis.

The contracting nebula we may liken to our piece of cardboard, the stamp will represent the spot in which the nebulous material has contracted to form the planet, and the position of the bradawl is the centre of the sun. As we have seen by our illustration, the nebulous planet is endowed with a certain movement of rotation, the period of its rotation on its axis being equal to that of its revolution around the centre; and it is important also to notice that both these movements take place in the same direction.

Thus we see from the nebular theory how the primæval nebula, in the course of its contraction, originated a planet, and how that planet was also endowed with a movement of rotation; its period of rotation being originally equal to the period of rotation of the whole nebula. This explains how the planet, or rather the materials which are to form the future planet, derived from the nebula their movement of rotation, which must have been extremely slow in the beginning. As the contraction continued, the materials of the gradually growing globe drew themselves together, and tended to become separate from the surrounding nebula. At length the time arrived when the planet became sufficiently isolated from the rest of the nebula to permit the conservation of moment of momentum to be applied to it individually. Thus, though the rotation was at first excessively slow, yet, as the contraction proceeded, and as the parts of the forming planet drew themselves closer together, in consequence of their mutual attractions, it became necessary that the speed with which these parts accomplished their revolutions should be accelerated. At last, when the planet had become consolidated, and when consequently the mutual distances of the several particles constituting the planet had been reduced to but a fraction of what those distances were originally, the speed of the planet’s rotation had become enormously increased. In this manner we learn how, from the very slow rotation which the nebulous material had at first, a solid planet may be made to rotate on its axis as rapidly as the planets in the solar system do to-day.

We thus find that the third concord, namely, the agreement in the directions of the planets’ rotations, is a further strong corroboration of the nebular theory. The unanimity of all these various movements is the dominant characteristic of the solar system.

But this third concord, derived from the rotation of the planets, may be yet further strengthened. The movements of the satellites, which accompany so many of the planets, must also find their explanation from the primæval nebula. The circumstances of the satellites are, however, different in the different cases.

As regards the moon, the theory of its evolution is now well known, mainly by the researches of Professor George Darwin. In the moon there appear to have been causes at work of a somewhat special kind. We must just refer to what is well known with regard to the history of the moon. Here, again, we observe the importance of the principles of the conservation of moment of momentum. As the moon raises tides on the ocean surrounding the earth, and as those tides flow around the globe, they cause friction, and that friction involves, as we have so often pointed out, the loss of energy to the system. Thus, the energy of the earth-moon system must be declining, while the moment of momentum remains constant. Now there are only two sources from which the energy can be derived. One of those sources is that due to the rotation of the earth on its axis. The other is due to the moon, and consists of two parts, namely, the energy arising from the velocity of the moon in its orbit, and the energy due to the distance by which the earth is separated from the moon. As the moon’s velocity depends upon its distance, we cannot view these two portions as independent. They are connected together, and we associate them into one. So that we say the total energy of the earth-moon system consists partly of that due to the rotation of the earth on its axis, and partly of that due to the revolution of the moon around the earth. It might also seem that we ought to add to this the energy due to the rotation of the moon around its own axis; but this is too inconsiderable to need attention. In the first place, the moon is so small that even if it rotated as rapidly as the earth the energy due to the rotation would not be important. Seeing, however, that the moon has for the rotation on its axis a period of between twenty-seven and twenty-eight days, its velocity of rotation is so small that, for this reason also, the energy of rotation would be inconsiderable. We are, therefore, amply justified in omitting from our present consideration the energy due to the rotation of the moon on its axis.

The energy of the earth-moon system is on the decline: the lost energy might conceivably be drawn from the rotation of the earth, or it might be drawn from the revolution of the moon, or it might be drawn from both If it were drawn from the revolution of the moon, that would imply that the moon would lose some of its speed or some of its distance, or in any case that the moon would get nearer to the earth and revolve more slowly, the speed of the earth being on this supposition unaltered. In this case, the moment of momentum of the earth would remain the same as before, while the moment of momentum of the moon would be lessened; the total moment of momentum would therefore have decreased, but this we have seen to be impossible. It therefore follows that the energy withdrawn from the earth-moon system is not to be obtained at the expense of the revolution of the moon.

The energy must therefore be obtained at the expense of the rotation of the earth on its axis. But if this be the case, the speed with which the earth rotates must be diminished; that is to say, the length of the day must be increased. And if the speed of the earth’s rotation be reduced, that means that the amount of moment of momentum contributed by the earth is lessened. But the total quantity of moment of momentum must be sustained, and this can only be done by making the moon go further away and describe a larger orbit. We thus see that in consequence of the tides the length of the day must be increasing, and the moon must be gradually retreating. Thus we find that at earlier periods the moon’s distance from the earth must have been less than it is at present, and the further we look back through remote periods the less do we find the distance between the earth and the moon. Thus we see that there must have been a time when the moon or the materials of the moon were in actual contact with the materials of the earth. In fact, it seems quite possible that the moon may have been a portion of the earth, broken off at some very early period, while the earth was still in a liquid state, if indeed it had condensed to even that extent. Thus the revolution of the moon round the earth is hardly to be used as an argument in favour of the nebular hypothesis. The moon is indeed a consequence of the earth’s rotation.

The satellites of Mars offer conditions of a very different kind, though here, again, tidal influences have been so important, that it is perhaps questions relating to tides that are illustrated by these satellites rather than the nebular theory.

A remarkable circumstance may be noted with regard to the movements of the satellites of Mars. The inner satellite has a period of about seven and a half hours, which is not a third of the period that the planet itself takes to go round on its axis. This leads to a somewhat curious consequence. The tides raised on Mars by this inner satellite would certainly tend rather to accelerate the rotation of the planet than to retard it; for these tides must course round the planet in the direction of its rotation, but with a speed in excess of that rotation. Any tidal friction, so far as this satellite is concerned, will tend to augment the velocity of the planet’s rotation, just as in the opposite case, where the moon raises tides on the earth, it is the lagging of the tides behind the movement due to the rotation that acts as a brake, and tends to check that speed. If, therefore. Mars is accelerated by this satellite, it will do more than its original share of the moment of momentum of the Martian system; it is therefore imperative that the satellite shall do less. Accordingly, we find that this satellite must go in towards the planet. No doubt this effect is much complicated by the influence of the other satellite of the same planet, but the illustration may suffice to show that if the satellites of the earth and Mars do not convey to us much direct evidence with regard to the nebular theory, this is largely because the effect of the tides has been a preponderating influence. The Martian system as we now see it has acquired its characteristic features by tidal influence, so that the more simple influences which would immediately illustrate the nebular theory have become hidden.

As to the satellites of Jupiter and Saturn, the circumstances are again quite different from those that we find in the earth and in Mars. There is little more to be said with regard to them than that everything that they present to us is consistent with the indications of the nebular theory. The evolution in each case has been a reproduction in miniature of the evolution of the solar system.

But the satellites of Uranus and Neptune present, it must be admitted, the greatest stumbling block to the acceptance of the nebular theory. Both as to the directions in which they move and as to the planes in which their orbits lie, it must be admitted that the satellites of Uranus are distinctly at variance with what the nebular theory would suggest. The consideration of this subject will be found in the next chapter.

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