New Theories in Astronomy

by William Stirling

(6) In the "Story of the Heavens," Sir Robert S. Ball informs us, in the fifteenth thousand, 1890, page 530, "That the moon should bend the same face to the earth depends immediately on the condition that the moon should rotate on its axis in precisely the same period as that which it requires to revolve around the earth. The tides are a regulating power of the most unremitting efficiency to ensure that this condition should be observed."

(7) And finally we have what follows from Messrs. Newcomb and Holden, at page 164 of their work already referred to at page 27, "The moon rotates on her axis in the same time and in the same direction in which she moves around the earth. In consequence, she always presents very nearly the same face to the earth." And in a footnote to this consequence, add: "This conclusion is often a pons asinorum to some who conceive that, if the same face of the moon is always presented to the earth, she cannot rotate at all. The difficulty arises from a misunderstanding of the difference between a relative and an absolute rotation. It is true that she does not rotate relatively to a line drawn from the earth to her centre, but she must rotate relative to a fixed line, or a line drawn to a fixed star."

In six of the above cases it is distinctly maintained that the moon rotates once on its axis in the same time that it makes one revolution round the earth, and that it is in consequence of this rotation that it always presents the same side to the earth. Thus we feel authorised to conclude that their authors did either believe that it does so rotate, or that they entertained some confused idea on the subject, which they did not take the trouble to examine properly, but accepted as a dogma, because some predecessor, with a great name, had stated that such rotation was necessary in order that its same side should be always turned towards the earth. In the seventh case the authors, while actually making the same assertion, try to persuade those who they acknowledge can see that the moon does not rotate on its axis in any sense, that their difficulty in comprehending what is meant by rotation, arises from the misunderstanding of the difference between an absolute rotation and one relative to a line drawn to a fixed star. But they do not attempt to show how this relative rotation has anything to do with or has any effect in causing the moon to present always the same side to the earth; and leave the story in the same confused state, out of which nobody can draw any satisfactory conclusion. Also, though they distinctly recognise that it does not rotate relatively to a line drawn from the surface of the earth to its centre, they do not include in their general description of the moon anything in any way connected with what would be the consequences of its not really rotating on its axis relatively to the earth. So they leave us the problem in much the same state as they found it, and it is still necessary to show that there can be no actual rotation of any kind on its axis; and the worst of it is that it is a thing that will have to be done in such very plain language that it will compel people to think of the absurdity of the idea so generally accepted.

To begin, it is very difficult to comprehend what the authors, above alluded to, meant by saying that the moon "must rotate relative to a fixed line, or a line drawn to a fixed star." It may mean relative to the line itself or to the star to which it is drawn. If it is to the line itself we cannot form any notion of what direction the rotation will have, direct, retrograde, or otherwise; and if it is relative to the star itself, then we can see that the relative rotation must depend on what is the position of the star. Should it be placed in the "milky way," we can understand how the moon could show every side it has—almost, not quite—to the star during every revolution it makes round the earth, and how they may look upon it as a relative rotation. But if we draw the line to the pole star we cannot see how the moon can show every side it has to it in every revolution round the earth, so there can be no relative rotation in that case—and the "almost, not quite," applies to every star between the pole and the ecliptic. The moon shows only the northern hemisphere, or a little more due to libration of its own kind, to that star, and would have to remove its poles to the equator, and make a new departure, in order to show the whole of its surface to that star in every revolution round the earth. Thus it is clear that the explanation given us of the relative rotation, is evidently one of the kind not properly thought out to the end.

No one has ever said, or perhaps even thought, that a gin-horse makes one rotation on his vertical axis, in the same time as he makes a circuit round his ring, but, all the same, he keeps his same side always towards the gin, or mill, he is giving motion to. The proof that he does not make any such rotation is easy—no proof is really required. But, suppose he is giving motion to a whim for raising ores from a mine, and that his motion is what is called direct. When the cage containing the ore is brought to bank, is emptied, and has to be lowered into the mine again, the horse has then to reverse his motion to retrograde, in doing which he has to make a half rotation on his vertical axis, and turn his other side to the whim. When again the cage has to be raised to bank, he has to resume his direct motion, for which he has to make another half rotation on his vertical axis, but it is this time in the opposite direction. Thus it is shown that he can only make half rotations, under any circumstances, on his axis, and these in opposite directions, when he changes his motion from direct to retrograde, or vice versâ; and that, when he moves in only one direction he cannot make even one rotation on his vertical axis, however long he may travel round the mill. In the same manner the moon which never turns back in its orbit can never make even one half rotation on its axis, which is all that we have had to prove. It is hardly necessary to observe that its axis is nearly parallel to the earth's, just the same as the horse's is to that of the whim. Neither could any one say that the relative rotation of the horse to a star, or tower, or, say, a bridge, outside of his ring, could have any effect on his revolution round the mill, or his always keeping his same side to it, there being no mechanical connection between them, nor any law of attraction; and the same is the case between the moon and a fixed star.

Now, we may begin to consider what effects must be produced by the moon not rotating on its axis, and we can do so most easily by continuing to work with our gin horse, or some equivalent substitute. It would not cost a great deal of ingenuity to plant a steam engine in the centre of the mill he is supposed to be driving, and to drive with it not only the mill but the horse also at the end of his lever. There might be some dissipation—Professor Tate would call it degradation—of energy in such an experiment, but we could get over that by making divina Palladis arte a wooden horse. We might arrange the steam-engine so as to cause the mill to make 27-1/3 revolutions for one made by our wooden horse, and so have a sort of a model of the earth and moon performing their most important relative motions. Then, having got our model ready for action, instead of filling it armato milite we might fill it half full of water. We fill it only half full, because the armed soldiers could not lie on the top of each other in the other horse, and there would be a vacant space above them for air, thus making the resemblance between the two the more similar; and also because it suits our purpose better, as will soon be seen. We have still to propose that a lot of holes should be supposed to be made in the sides of our horse all round, just a little higher than between wind and water. Pallas did not order any holes to be made in hers as far as we know, even for ventilation, though we think it would have been an advantage; but that will not spoil the experiment we are now prepared for. Let the steam-engine be started now and we shall soon see what will happen to the water. As the speed increases it will not be long till it begins to be thrown out, not from the side turned towards the mill but from the one furthest from it; and if it is increased sufficiently the whole of it will be very soon thrown out. If we could now close up the holes on the side of the horse turned towards the mill, it would so happen that a good deal of the air would be expelled also; and if the speed of the horse were brought up so as to equal that of the moon in its orbit, there would be nothing more, at the most, than traces of air left even in it. The expelling agent in this experiment would, of course, be centrifugal force, and we do not need to exercise our mental faculties very greatly, to comprehend that it is the same force that has driven both air and water away from the side of the moon always turned towards the earth. All the difficulty we have to contend with will be to make sure that the orbital velocity of the moon is sufficient to produce the force required. That the force is exceedingly greater than what is required is proved by the fact, that the velocity with which the moon travels in its orbit is a little more than 38 miles per minute, whereas the velocity of the circumference of a centrifugal machine, used for clarifying sugar, drying clothes, or any other similar industrial purpose, does not require a greater velocity than about one mile per minute, in order to throw everything in the form of water out of the material to be dried, and out of the centrifugal machine itself; and we know that air would be expelled more easily than water, were none re-admitted to supply the place of what was expelled.

Here the idea very naturally occurs to any one, that so great a velocity would drive both air and water away, even from the far off side of the moon, into space, but in order to do so the velocity would have to be 120, not 38, miles per minute. Our authority for this statement will be found in "The Nineteenth Century," for August 1896, in an article written by Prince Kropotkin, in which he says: "But it appears from Dr. Johnstone Stoney's investigations that even if the moon was surrounded at some time of its existence with a gaseous envelope consisting of oxygen, nitrogen and water vapour, it would not have retained much of it. The gases, as is known, consist of molecules rushing in all directions at immense speeds; and the moment that the speed of a molecule which moves near the outer boundary of the atmosphere exceeds a certain limit (which would be about 10,600 feet in a second for the moon) it can escape from the sphere of attraction of the planet. Molecule by molecule the gas must wander off into interplanetary space; and the smaller the mass of the molecule of a given gas, the feebler the planet's attraction, and this is why no free hydrogen could be retained in the earth's atmosphere, and why the moon could retain no air or water vapour."

A velocity of 10,600 feet per second is as near 120 miles per minute as there is any use for, which is more than three times as great as the velocity of the moon in its orbit, so there is no possibility whatever of air and water having been swept away from the far off side of it by centrifugal force; more especially as it ought to be well known that that force is always counteracted by the attractive force of the satellite for these or any other elements.

We do not want to discuss the point of whether the mutual collisions of the molecules of a gas could get up such a velocity as would enable them to free themselves from the attraction of the moon, for it looks to us too much like one of those notions that are got up to account for something that does not exist; but we do want to state our dissent to the conclusion—evidently jumped at—that because there are hardly any signs of there being air or water on our side of the moon, there can be none on the other. No astronomer, physicist, scientist of any kind, can prove that there is none, simply because he has never been round there to see or make experiments to prove it; and if there is any one bold enough to make such an assertion, it is only an example of how stupendous a jump to a conclusion can be made.