Popular Science Monthly/Volume 17/September 1880/The Solar System and its Neighbors
ASTRONOMERS say that this world of ours, which seems to us so large, is in fact so small in comparison with the sun and stars, that its presence or absence is, to the universe, a matter of inconceivably small importance; and that, even in its own system, it would hardly be noticed by an eye capable of taking in at one view the sun and its attendant planets.
Sir John Herschel gives the following illustration of the size and distance of these bodies: "Choose," he says, "any well-leveled field. On it place a globe two feet in diameter; this will represent the sun; Mercury will be represented by a grain of mustard-seed on the circumference of a circle 164 feet in diameter for its orbit; Venus, a pea in a circle of 284 feet in diameter; the earth, also, a pea on a circle of 430 feet; Mars, a rather large pin's head in a circle of 654 feet; Jupiter, a moderate-sized orange in a circle nearly half a mile across; Saturn, a smaller orange on a circle of four fifths of a mile; Uranus, a full-sized cherry upon the circumference of a circle more than a mile and a half; and Neptune, a good-sized plum on a circle two and a half miles in diameter."
If our earth were struck out of existence, it would hardly be missed from such a system. But this is far from the extreme measure of our littleness. The evening sky is studded with stars. Between us and them is empty space. As we look across it, the distance does not seem so very great, and even astronomers were long in learning how great it is, and how utterly isolated the sun with its train of planets is from even the nearest star. Keeping the same scale as before, in which our inconceivable distance from the sun, 923 millions of miles, was reduced to a dozen rods or so, and then setting out to visit our neighbors, if we are lucky enough to turn our steps to the nearest, we find before us a journey of nearly 9,000 miles. Had we directed our course to any other of the stars, our road would have been many thousand miles longer. There are stars from which light requires 6,000 years to reach our globe!
Had we gone toward one of them, our journey on the same infinitely reduced scale would have taken us nearly 18,000,000 miles before reaching our goal.
Even this scale gives distances too vast. Let it be changed. Let the sun shrink to a point 100 of an inch in diameter. The distance to the sun, 923 millions of miles, would be reduced to nearly one inch. The earth would be only 1000 of an inch in diameter, requiring 1,000,000,000,000 times its bulk to make a globe one inch in diameter. On such a scale our world would be equaled in minuteness only by the animalcules which the microscope reveals. Even then, on this inconceivably reduced scale, the line that would reach our nearest neighbor would need to be something more than three miles long.
Yet that sun, which in this estimate we have mentally reduced to a point 100 of an inch in diameter, is in reality a body so vast that, were it hollow, and our earth placed at its center, the moon would not only revolve freely around our planet, just as it now does, but on every side the sun would extend more than 200,000 miles beyond the lunar orbit. We have heard so often of the distance from here to the sun, 92⅓ millions of miles, that we begin to think we have some idea of its inconceivable greatness. Yet, so large is the sun that only 107 such bodies, laid so as to touch each other, would be needed to form a continuous bridge from the earth to that luminary. In the sky it appears so small that we find it difficult to realize that scarcely more than 100 times its diameter would reach so far.
However many of us may have sought, by these or by other illustrations, to form some conception of the vastness of the universe, but few have attempted to grasp the measure of that power which compels the planets to move in elliptical orbits instead of flying off in tangents, as, if left to themselves, they would inevitably do; and still fewer have thought of the force with which these bodies tend to pull one another out of their courses. Of these influences astronomers have given no illustrations, yet their contemplation will lead to results that will enlarge our views of the universe, and help us to rise at least a little toward a conception of Omnipotence.
We must work out our conclusions ourselves. The data are all at our hand. We need only to know the distances and masses; the rest is a matter of easy computation. But that our results may not be meaningless from their very greatness, it will be wise to follow the method which we pursue when trying to get an idea of great distances. We take first some unit with which we are familiar—for instance, a mile—and think how many miles it is to some place familiar to us. Then we extend that measure, or some multiple of it, to another place more remote, and then to one still more distant; and thus by degrees we become able to grasp distances whose statement in figures had previously conveyed little or no meaning to our minds. So, in measuring a force, we get a better idea of its greatness if we work up to it in a similar manner.
Of all known substances steel is the most tenacious. If the interplanetary forces can be represented by steel bars of known size, it will at least help to bring them within the limits of our comprehension.
Philosophers have found that a steel wire one tenth of an inch in diameter will support nearly half a ton, while a bar one inch square will not be pulled asunder by less than sixty tons. If two inches square, it will require 240 tons; if three inches square, it will scarcely break with 540 tons. Bars of steel are not often made larger than this, although Krupp, in his colossal works, doubtless makes some whose section equals 144 square inches. To pull apart such a bar would require a strain equal to the weight of 8,640 tons. It requires an effort to grasp the meaning of such a load. A stout team will haul two tons over a good road for a moderate distance; that number of tons would require more than 4,000 such teams to move it. If put upon a railroad it would need 864 cars and twenty-three locomotives to draw it. It would equal in weight one of the largest ocean-steamers with its complement of freight.
But we shall need a much larger unit than this. Could a bar of steel three feet square be forged—and, judging from the size of his steel cannon, Krupp might do this also—it would be able to lift nine times that great amount. Probably no furnace can much exceed this, but we may imagine a monster bar measuring one rod—162 feet—square, and by easy multiplication we find its strength great enough to lift 304 times as much as the last, or in figures 2,352,240 tons, three times the weight of the cotton crop of the United States when it equaled 4,000,000 bales.
To get a fit unit for our purpose we shall need to go far beyond this, but first pause to contemplate a bar of steel 16½ feet square. As it lay stretched upon the ground, we would need a ladder to get upon its upper side. Few rooms in private dwellings are 162 feet high, and 162 feet wide makes a spacious parlor.
Endeavor to get some idea of its tenacity, and how many million horses it would require to pull it asunder, and then, after getting somewhat accustomed to the greatness and strength of a bar of solid steel 162 feet square, imagine one which is one mile square—5,280 feet wide, and as many thick. If it lay on the ground near the Catskill Mountains, its upper surface would overtop their highest summit by more than 1,000 feet. It would be equal to 102,400 such monster bars as the last. Its lifting power would be nearly 240,869,000,000 tons. The mind is utterly unable to grasp such figures. The whole globe contains 1,200,000,000 inhabitants. If each man, woman, and child, could pull with a force of 100 pounds—a large estimate—to move such a weight would require the united efforts of the inhabitants of two thousand such worlds as this.
As I shall have frequent occasion to speak of the load which such a bar could sustain, I shall, for convenience, call it in round numbers 240,000,000,000 tons, neglecting the other figures, because the number is so inconceivably great that taking from it a billion or so of tons will alter the result less than one half of one per cent. This bar is to be the unit of measure which I shall for the present employ, and with its help I shall attempt to give some idea of the influence of the sun in holding the system together, and of the attraction exerted by the planets upon our earth, and by the earth upon the moon; and, lastly, by the fixed stars upon the sun and upon each other.
We begin with the moon because it is nearest to us, and, with the exception of the sun, is to us the most important of all the heavenly bodies.
If a half-dozen persons were asked how large the moon appears, they would give as many different replies: "The size of a cart-wheel"; "Twelve inches across"; "The size of a dining-plate "; "As big as a man's head," etc. Probably no one would mention a smaller measure, yet a cherry held at arm's length much more than covers its disk. It is difficult to believe that so small a body exerts any considerable influence on the earth which seems so immensely larger. It is easy enough to admit that the earth holds the moon in its orbit; but, that to do this, to bend its course into a nearly circular orbit, requires any great outlay of force, is not so clear. Our credulity would be taxed were we asked to believe that the moon in its efforts to move in a straight line would break away, although held by a bar of steel one foot square, for that means a force able to lift nearly 9,000 tons. An astronomer would grant it, making first a mental calculation to see if he were justified in doing so; but even he would hesitate, and perhaps would deny that it was possible the moon could pull asunder one of those great unit-bars one mile square, and equal to more than 27,000,000 bars each one foot square.
But he would have no hesitation in saying, "Impossible!" if told that, rather than change its course from a straight line to its present curve, our willful little satellite would snap like pack-thread not one, nor two, nor three of those unit-bars, but the united strength of 10,000 or, in other words, one gigantic bar whose section is 100 miles square. Yet, more than eight such bars, or, more precisely, 87,500 unit-bars, would but barely deflect the moon into its present path.
You will say, "This is too much no one will believe it!" Let us see. A few astronomical facts, with a very small amount of mathematics, will suffice to show that there is no exaggeration here. One need know only the weight of the earth and moon, and their distance apart, and the law that gravitation grows less as the square of the distance increases, and he has all the elements required for the calculation.
The weight of the earth is found by an experiment described in almost every school philosophy. It consists in comparing the attraction exerted by a ball of lead of known weight with that exerted by the earth. In this way the earth's weight has been ascertained to be in round numbers 6,000,000,000,000,000,000,000 tons, or, as it is more conveniently written, 6X1021, where the 21, of course, denotes the number of ciphers after the 6. The moon's mass is nearly one eightieth (81) as great, or, in other words, if it lay upon the surface of the earth, it would weigh 75,000,000,000,000,000,000 tons (75xl018). This, however, must be diminished because the moon is, in fact, sixty times farther off, measuring in both cases from the center of the earth. Dividing, then, the moon's weight by the square of 60, or 3,600, we have for the weight at its actual distance something more than 21x1015 (21,000,000,000,000,000) tons after adding one eightieth for the attractive power of the moon itself, for there is a mutual attraction.
To get, then, the number of unit-bars necessary to equal this effect, we have only to divide the weight of the latter by the amount which one of these bars will sustain. That is, we divide 21X1015, by 24X1010, and find the quotient to be 87,500, which agrees with our statement.
It will be interesting to stop here, and endeavor to get some faint idea of what these enormous numbers mean. A bar of steel whose section is 87,500 square miles would include within its four sides a territory as large as that of New York State, and still leave enough to cover the State of Ohio, with a surplus of 536 square miles for good measure. We read in a certain book of a traveler who, coming into Lilliput, was held immovable by thousands of tiny threads. If a web of steel were stretched from the earth to the moon to hold our satellite from flying off into space, each tiny thread being represented by a bar of steel one fourth of an inch square no trifle, for each could hold 7,500 pounds—they would cover our globe on the side toward the moon with a network whose threads would be only six inches apart, and through which none but the smallest animals could pass.
It may aid us, while seeking to grasp such a force, if we reflect that the very small difference between the moon's pull upon the ocean and that upon the earth's center suffices to lift the tides; how vast, then, must be the whole pull upon the earth!
All this inconceivably great force is needed to bend our satellite's course from the straight line in which it would move if left to itself. This force is exerted, not once for all, as in case of the original impulse that sent the moon forward in its path, but afresh every second; for otherwise, after such an indrawing, it would move thenceforth in a straight line. To give a circular orbit, the direction of the moon needs to be changed every moment, and this requires a series of impulses.
Thus much for our earth's satellite. We may extend our reasoning to more distant bodies. The earth is 81 times the mass of the moon; the sun is 315,000 times the mass of the earth, and something more than 381 times as far from it as we are from the moon. Combining these in an easy calculation, we find that the sun puts forth upon our earth a coercive force to bend its path into an ellipse, a force to be measured by 15,000,000 of our unit-bars, together making a bar of solid steel whose section would cover 15,000,000 square miles, more than four times the area of the United States. The wires, such as we supposed to hold the moon, would, in the case of the earth and sun, be almost as close as the blades of grass on a lawn.
Without going any further into calculations, it is enough to say of the other planets, that Mercury is held to its duty by 6,590,000 of our unit-bars; while Venus, being nearly as large as the earth, and so much nearer the sun, requires the united strength of nearly 23,000,000. Mars is smaller, and more remote, and therefore needs only some 811,500 such bands to hold it to its course; for, strange as it may appear, and however unlike other sovereigns, the sun holds its subjects in obedience the more easily, the greater their distance from the center of the system, provided, of course, that their importance otherwise is the same. But still, distant as it is, Jupiter's immense mass demands incomparably the strongest measures to keep it in check; nothing less than 170,000,000 of those bands of steel will overcome its wandering tendencies. Saturn, being a lighter weight, is more easily guided —15,000,000 suffice for that. Uranus and Neptune are of little account as compared with Jupiter; 588,000 for the one and 282,000 for the other are all that are needed to restrain their vagaries.
If, now, we turn to the planets, and study their influence, we shall find them pulling and tugging at each other with forces that, but for compensations planted in the system itself, would tear it to pieces; but, like the armed men of Cadmus, these forces destroy each other.
However difficult it may be to conceive of such an amount of power as the sun puts forth, we are so accustomed to regard that body as the governing center of our part of the universe, and have heard so much of its vast size, that we are prepared to accept almost any statement in regard to it. But as to the planets we do not realize their size, and we seldom think of their exerting any influence on the earth or on one another. That they do exert such an influence we know, for astronomers have told us of perturbations thus produced; but, then, very few of us connect such statements with the tiny specks which we see in the heavens. Yet their influence is no trifle. Mercury, which is too small and too near the sun for most of us to have seen, draws the earth when in mean perigee with a force small indeed when compared with those which we have been considering, but large enough to break 232,390,000 bars one foot square; Venus pulls with a force of 11,175,000,000; Mars pulls enough to overcome the united strength of 590,680,000; while Jupiter draws away with a steady tug of nearly 23,000,000,000; and even Neptune, 2,700,000,000 miles away, and utterly invisible to the naked eye, still has sufficient energy to drag our earth toward it with force able to snap 27,000,000 such bars. Besides these, which are only the interplay of forces between our globe and its sister planets, a similar action is constantly going on between each planet and all the others. The mind is lost in such a labyrinth of forces, and almost refuses to proceed. But we have only entered upon the vestibule of the mysteries of the universe. Across that gulf which separates our system from the stars, unseen hands with sinews strong as steel are extended to bind all into one great whole. From each star reaches out to our sun a force, small as compared with those which hold our system together, yet of a size that will amaze us. To the nearest of these far-off suns the distance is so great that light, which travels almost 200,000 miles in a second, requires three years to traverse it! Yet gravity reaches across that gulf with a speed which, if not absolutely instantaneous, is, according to Laplace, 50,000,000 times greater than that of light. Such a distance reduces proportionably the attraction; yet our sun with its attendant planets is drawn by mutual attraction toward the nearest star, supposing them to be of the same size, with a force great enough to break a cable, each of whose strands, 236 in number, should be a solid bar of steel one mile square; or, if we change our scale, and employ such bars as those used when speaking of the interplanetary forces, bars of steel one foot square, then the attraction between the nearest tiny speck of light and our sun would be equal to the united strength of 6,500,000,000 such bars.
When we remember that each star, however remote, adds its quota of force, and that a star whose light requires 6,000 years to reach the earth is linked to our system by a band able to lift more than 14,000,000 tons, we may well believe that our system is being hurried through space in a path which is the resultant of innumerable forces.
The force which thus impels our sun reacts on other suns, and they on each other, and thus all are in movement. This is not a conclusion drawn from mere theorizing; the measurements of astronomers have established the fact that the "fixed" stars are moving with enormous velocities, not, as has often been said, about a common center, but in directions which cross each other at all angles. Millions of years hence these movements will result in the destruction of the present universe, unless He who called the stars into existence shall lay his hand upon them. If, as revelation and science both teach, not a sparrow falls to the ground without his knowledge, surely suns and worlds shall not perish without his consent. He who in the beginning created the heavens and the earth will guide them to the end.
- Read, January 13, 1880, before the Poughkeepsie Society of Natural Science.
- The non-astronomical reader may, perhaps, need to be reminded that the moon does not move easily and naturally in a circle—or ellipse—but that its path, if left to itself, would be a straight line a tangent to its orbit. Consequently, the moon requires to be forced into a curve.