The Story of the Heavens

surface of the earth to a height of nearly 4,000 miles, so as to be at an altitude equal to the radius of the earth. In other words, a body so situated would be twice as far from the centre of the earth as a body which lay on the surface. The law of gravitation says that the intensity of the attraction is then to be decreased to one-fourth part, so that the pull of the earth on a body 4,000 miles high is only one quarter of the pull of the earth on that body so long as it lies on the ground. We may imagine the effect of this pull to be shown in different ways. Allow the body to fall, and in the interval of one second it will only drop through four feet, a mere quarter of the distance that gravity would cause near the earth's surface. We may consider the matter in another way by supposing that the attraction of the earth is measured by one of those little weighing machines known as a spring balance. If a weight of four pounds be hung on such a contrivance, at the earth's surface, the index of course shows a weight of four pounds; but conceive this balance, still bearing the weight appended thereto, were to be carried up and up, the indicated strain would become less and less, until by the time the balance reached 4,000 miles high, where it was twice as far away from the earth's centre as at first, the indicated strain would be reduced to the fourth part, and the balance would only show one pound. If we could imagine the instrument to be carried still further into the depths of space, the indication of the scale would steadily continue to decline. By the time the apparatus had reached a distance of 8,000 miles high, being then three times as far from the earth's centre as at first, the law of gravitation tells us that the attraction must have decreased to one-ninth part. The strain[Pg 128] thus shown on the balance would be only the ninth part of four pounds, or less than half a pound. But let the voyage be once again resumed, and let not a halt be made this time until the balance and its four-pound weight have retreated to that orbit which the moon traverses in its monthly course around the earth. The distance thus attained is about sixty times the radius of the earth, and consequently the attraction of gravitation is diminished in the proportion of one to the square of sixty; the spring will then only be strained by the inappreciable fraction of 1-3,600 part of four pounds. It therefore appears that a weight which on the earth weighed a ton and a half would, if raised 240,000 miles, weigh less than a pound. But even at this vast distance we are not to halt; imagine that we retreat still further and further; the strain shown by the balance will ever decrease, but it will still exist, no matter how far we go. Astronomy appears to teach us that the attraction of gravitation can extend, with suitably enfeebled intensity, across the most profound gulfs of space. The principle of gravitation is of far wider scope than we have yet indicated. We have spoken merely of the attraction of the earth, and we have stated that this force extends throughout space. But the law of gravitation is not so limited. Not only does the earth attract every other body, and every other body attract the earth, but each of these bodies attracts the other; so that in its more complete shape the law of gravitation announces that "every body in the universe attracts every other body with a force which varies inversely as the square of the distance." It is impossible for us to over-estimate the importance of this law. It supplies the clue by which we can unravel the complicated movements of the planets. It has led to marvellous discoveries, in which the law of gravitation has enabled us to anticipate the telescope, and to feel the existence of bodies before those bodies have even been seen. An objection which may be raised at this point must first be dealt with. It seems to be, indeed, a plausible one. If the earth attracts the moon, why does not the moon tumble[Pg 129] down on the earth? If the earth is attracted by the sun, why does it not tumble into the sun? If the sun is attracted by other stars, why do they not rush together with a frightful collision? It may not unreasonably be urged that if all these bodies in the heavens are attracting each other, it would seem that they must all rush together in consequence of that attraction, and thus weld the whole material universe into a single mighty mass. We know, as a matter of fact, that these collisions do not often happen, and that there is extremely little likelihood of their taking place. We see that although our earth is said to have been attracted by the sun for countless ages, yet the earth is just as far from the sun as ever it was. Is not this in conflict with the doctrine of universal gravitation? In the early days of astronomy such objections would be regarded, and doubtless were regarded, as well-nigh insuperable; even still we occasionally hear them raised, and it is therefore the more incumbent on us to explain how it happens that the solar system has been able to escape from the catastrophe by which it seems to be threatened. There can be no doubt that if the moon and the earth had been initially placed at rest, they would have been drawn together by their mutual attraction. So, too, if the system of planets surrounding the sun had been left initially at rest they would have dashed into the sun, and the system would have been annihilated. It is the fact that the planets are moving, and that the moon is moving, which has enabled these bodies successfully to resist the attraction in so far, at least, as that they are not drawn thereby to total destruction. It is so desirable that the student should understand clearly how a central attraction is compatible with revolution in a nearly circular path, that we give an illustration to show how the moon pursues its monthly orbit under the guidance and the control of the attracting earth. [Pg 130] Fig. 36.—Illustration of the Moon's Motion. The imaginary sketch in Fig. 36 denotes a section of the earth with a high mountain thereon.[12] If a cannon were stationed on the top of the mountain at C, and if the cannonball were fired off in the direction C E with a moderate charge of powder, the ball would move down along the first curved path. If it be fired a second time with a heavier charge, the path will be along the second curved line, and the ball would again fall to the ground. But let us try next time with a charge still further increased, and, indeed, with a far stronger cannon than any piece of ordnance ever yet made. The velocity of the projectile must now be assumed to be some miles per second, but we can conceive that the speed shall be so adjusted that the ball shall move along the path C D, always at the same height above the earth, though still curving, as every projectile must curve, from the horizontal line in which it moved at the first moment. Arrived at D, the ball will still be at the same height above the surface, and its velocity must be unabated. It will therefore continue in its path and move round another quadrant of the circle without getting nearer to the surface. In this manner the projectile will travel completely round the whole globe, coming back again to C and then taking another start in the same path. If we could abolish the mountain and the cannon at[Pg 131] the top, we should have a body revolving for ever around the earth in consequence of the attraction of gravitation. Make now a bold stretch of the imagination. Conceive a terrific cannon capable of receiving a round bullet not less than 2,000 miles in diameter. Discharge this enormous bullet with a velocity of about 3,000 feet per second, which is two or three times as great as the velocity actually attainable in modern artillery. Let this notable bullet be fired horizontally from some station nearly a quarter of a million miles above the surface of the earth. That fearful missile would sweep right round the earth in a nearly circular orbit, and return to where it started in about four weeks. It would then commence another revolution, four weeks more would find it again at the starting point, and this motion would go on for ages. Do not suppose that we are entirely romancing. We cannot indeed show the cannon, but we can point to a great projectile. We see it every month; it is the beautiful moon herself. No one asserts that the moon was ever shot from such a cannon; but it must be admitted that she moves as if she had been. In a later chapter we shall enquire into the history of the moon, and show how she came to revolve in this wonderful manner. As with the moon around the earth, so with the earth around the sun. The illustration shows that a circular or nearly circular motion harmonises with the conception of the law of universal gravitation. We are accustomed to regard gravitation as a force of stupendous magnitude. Does not gravitation control the moon in its revolution around the earth? Is not even the mighty earth itself retained in its path around the sun by the surpassing power of the sun's attraction? No doubt the actual force which keeps the earth in its path, as well as that which retains the moon in our neighbourhood, is of vast intensity, but that is because gravitation is in such cases associated with bodies of enormous mass. No one can deny that all bodies accessible to our observation appear to attract each other in accordance with the law of gravitation; but[Pg 132] it must be confessed that, unless one or both of the attracting bodies is of gigantic dimensions, the intensity is almost immeasurably small. Let us attempt to illustrate how feeble is the gravitation between masses of easily manageable dimensions. Take, for instance, two iron weights, each weighing about 50lb., and separated by a distance of one foot from centre to centre. There is a certain attraction of gravitation between these weights. The two weights are drawn together, yet they do not move. The attraction between them, though it certainly exists, is an extremely minute force, not at all comparable as to intensity with magnetic attraction. Everyone knows that a magnet will draw a piece of iron with considerable vigour, but the intensity of gravitation is very much less on masses of equal amount. The attraction between these two 50lb. weights is less than the ten-millionth part of a single pound. Such a force is utterly infinitesimal in comparison with the friction between the weights and the table on which they stand, and hence there is no response to the attraction by even the slightest movement. Yet, if we can conceive each of these weights mounted on wheels absolutely devoid of friction, and running on absolutely perfect horizontal rails, then there is no doubt that the bodies would slowly commence to draw together, and in the course of time would arrive in actual contact. If we desire to conceive gravitation as a force of measurable intensity, we must employ masses immensely more ponderous than those 50lb. weights. Imagine a pair of globes, each composed of 417,000 tons of cast iron, and each, if solid, being about 53 yards in diameter. Imagine these globes placed at a