The Story of the Heavens

Gravitation—The Falling of a Stone to the Ground—All Bodies fall equally, Sixteen Feet in a Second—Is this true at Great Heights?—Fall of a Body at a Height of a Quarter of a Million Miles—How Newton obtained an Answer from the Moon—His Great Discovery—Statement of the Law of Gravitation—Illustrations of the Law—How is it that all the Bodies in the Universe do not rush Together?—The Effect of Motion—How a Circular Path can be produced by Attraction—General Account of the Moon's Motion—Is Gravitation a Force of Great Intensity?—Two Weights of 50 lbs.—Two Iron Globes, 53 Yards in Diameter, and a Mile apart, attract with a Force of 1 lb.—Characteristics of Gravitation—Orbits of the Planets not strictly Circles—The Discoveries of Kepler—Construction of an Ellipse—Kepler's First Law—Does a Planet move Uniformly?—Law of the Changes of Velocity—Kepler's Second Law—The Relation between the Distances and the Periodic Times—Kepler's Third Law—Kepler's Laws and the Law of Gravitation—Movement in a Straight Line—A Body unacted on by Disturbing Forces would move in a Straight Line with Constant Velocity—Application to the Earth and the Planets—The Law of Gravitation deduced from Kepler's Laws—Universal Gravitation. Our description of the heavenly bodies must undergo a slight interruption, while we illustrate with appropriate detail an important principle, known as the law of gravitation, which underlies the whole of astronomy. By this law we can explain the movements of the moon around the earth, and of the planets around the sun. It is accordingly incumbent upon us to discuss this subject before we proceed to the more particular account of the separate planets. We shall find, too, that the law of gravitation sheds some much-needed light on the nature of the stars situated at the remotest distances in space. It also enables us to cast a glance through the vistas of time past, and to trace with plausibility, if not with certainty, certain early phases in the history of our system. The sun and the moon, the planets and the comets, the stars and the nebulæ, all alike are subject to this universal law, which is now to engage our attention. [Pg 123] What is more familiar than the fact that when a stone is dropped it will fall to the ground? No one at first thinks the matter even worthy of remark. People are often surprised at seeing a piece of iron drawn to a magnet. Yet the fall of a stone to the ground is the manifestation of a force quite as interesting as the force of magnetism. It is the earth which draws the stone, just as the magnet draws the iron. In each case the force is one of attraction; but while the magnetic attraction is confined to a few substances, and is of comparatively limited importance, the attraction of gravitation is significant throughout the universe. Let us commence with a few very simple experiments upon the force of gravitation. Hold in the hand a small piece of lead, and then allow it to drop upon a cushion. The lead requires a certain time to move from the fingers to the cushion, but that time is always the same when the height is the same. Take now a larger piece of lead, and hold one piece in each hand at the same height. If both are released at the same moment, they will both reach the cushion simultaneously. It might have been thought that the heavy body would fall more quickly than the light body; but when the experiment is tried, it is seen that this is not the case. Repeat the experiment with various other substances. An ordinary marble will be found to fall in the same time as the piece of lead. With a piece of cork we again try the experiment, and again obtain the same result. At first it seems to fail when we compare a feather with the piece of lead; but that is solely on account of the air, which resists the feather more than it resists the lead. If, however, the feather be placed upon the top of a penny, and the penny be horizontal when dropped, it will clear the air out of the way of the feather in its descent, and then the feather will fall as quickly as the penny, as quickly as the marble, or as quickly as the lead. If the observer were in a gallery when trying these experiments, and if the cushion were sixteen feet below his hands, then the time the marble would take to fall through the sixteen feet would be one second. The time occupied by the cork or by the lead would be the same; and even the feather[Pg 124] itself would fall through sixteen feet in one second, if it could be screened from the interference of the air. Try this experiment where we like, in London, or in any other city, in any island or continent, on board a ship at sea, at the North Pole, or the South Pole, or the equator, it will always be found that any body, of any size or any material, will fall about sixteen feet in one second of time. Lest any erroneous impression should arise, we may just mention that the distance traversed in one second does vary slightly at different parts of the earth, but from causes which need not at this moment detain us. We shall for the present regard sixteen feet as the distance through which any body, free from interference, would fall in one second at any part of the earth's surface. But now let us extend our view above the earth's surface, and enquire how far this law of sixteen feet in a second may find obedience elsewhere. Let us, for instance, ascend to the top of a mountain and try the experiment there. It would be found that at the top of the mountain a marble would take a little longer to fall through sixteen feet than the same marble would if let fall at its base. The difference would be very small; but yet it would be measurable, and would suffice to show that the power of the earth to pull the marble to the ground becomes somewhat weakened at a point high above the earth's surface. Whatever be the elevation to which we ascend, be it either the top of a high mountain, or the still greater altitudes that have been reached in balloon ascents, we shall never find that the tendency of bodies to fall to the ground ceases, though no doubt the higher we go the more is that tendency weakened. It would be of great interest to find how far this power of the earth to draw bodies towards it can really extend. We cannot attain more than about five or six miles above the earth's surface in a balloon; yet we want to know what would happen if we could ascend 500 miles, or 5,000 miles, or still further, into the regions of space. Conceive that a traveller were endowed with some means of soaring aloft for miles and thousands of miles, still up[Pg 125] and up, until at length he had attained the awful height of nearly a quarter of a million of miles above the ground. Glancing down at the surface of that earth, which is at such a stupendous depth beneath, he would be able to see a wonderful bird's-eye view. He would lose, no doubt, the details of towns and villages; the features in such a landscape would be whole continents and whole oceans, in so far as the openings between the clouds would permit the earth's surface to be exposed. At this stupendous elevation he could try one of the most interesting experiments that was ever in the power of a philosopher. He could test whether the earth's attraction was felt at such a height, and he could measure the amount of that attraction. Take for the experiment a cork, a marble, or any other object, large or small; hold it between the fingers, and let it go. Everyone knows what would happen in such a case down here; but it required Sir Isaac Newton to tell what would happen in such a case up there. Newton asserts that the power of the earth to attract bodies extends even to this great height, and that the marble would fall. This is the doctrine that we can now test. We are ready for the experiment. The marble is released, and, lo! our first exclamation is one of wonder. Instead of dropping instantly, the little object appears to remain suspended. We are on the point of exclaiming that we must have gone beyond the earth's attraction, and that Newton is wrong, when our attention is arrested; the marble is beginning to move, so slowly that at first we have to watch it carefully. But the pace gradually improves, so that the attraction is beyond all doubt, until, gradually acquiring more and more velocity, the marble speeds on its long journey of a quarter of a million of miles to the earth. But surely, it will be said, such an experiment must be entirely impossible; and no doubt it cannot be performed in the way described. The bold idea occurred to Newton of making use of the moon itself, which is almost a quarter of a million of miles above the earth, for the purpose of answering the question. Never was our satellite put to such[Pg 126] noble use before. It is actually at each moment falling in towards the earth. We can calculate how much it is deflected towards the earth in each second, and thus obtain a measure of the earth's attractive power. From such enquiries Newton was able to learn that a body released at the distance of 240,000 miles above the surface of the earth would still be attracted by the earth, that in virtue of the attraction the body would commence to move off towards the earth—not, indeed, with the velocity with which a body falls in experiments on the surface, but with a very much lesser speed. A body dropped down from the distance of the moon would commence its long journey so slowly that a minute, instead of a second, would have elapsed before the distance of sixteen feet had been accomplished.[11] It was by pondering on information thus won from the moon that Newton made his immortal discovery. The gravitation of the earth is a force which extends far and wide through space. The more distant the body, the weaker the gravitation becomes; here Newton found the means of determining the great problem as to the law according to which the intensity of the gravitation decreased. The information derived from the moon, that a body 240,000 miles away requires a minute to fall through a space equal to that through which it would fall in a second down here, was of paramount importance. In the first place, it shows that the attractive power of the earth, by which it draws all bodies earthwards, becomes weaker at a distance. This might, indeed, have been anticipated. It is as reasonable to suppose that as we retreated further and further into the depths of space the power of attraction should diminish, as that the lustre of light should diminish as we recede from it; and it is remarkable that the law according to which the attraction of gravitation decreases with the increase of distance is[Pg 127] precisely the same as the law according to which the brilliancy of a light decreases as its distance increases. The law of nature, stated in its simplest form, asserts that the intensity of gravitation varies inversely as the square of the distance. Let me endeavour to elucidate this somewhat abstract statement by one or two simple illustrations. Suppose a body were raised above the