The Earth's Beginning

by Robert S. Ball

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.