Popular Science Monthly/Volume 5/August 1874/Distances of the Stars
SINCE the beginning of this century, our idea of the universe has undergone a complete metamorphosis, though but few persons appear to recognize this fact. Less than a century ago, the savants who admitted the earth's motion (some still rejected it) pictured to themselves the system of the universe as being bounded by the frontier of Saturn's orbit, at a distance from the central sun equal to 109,000 times the diameter of the earth, or about 860,000,000 miles. The stars were fixed, spherically distributed, at a distance but a little greater than that of Saturn. Beyond this limit a vacant space was supposed to surround the universe. The discovery of Uranus, in 1785, did away at once with this belt, consisting of Saturn's orbit, and the frontier of solar domination was pushed out to a distance of 1,900,000,000 miles from the centre of the system, that is to say, beyond the space which was vaguely supposed to be occupied by the stars. The discovery of Neptune, in 1846, again removed these limits to a distance that would have appalled our fathers; the orbit described by this planet being 2,862,000,000 miles from the sun.
But the attractive force of the sun extends farther still. Beyond the orbit of Uranus, beyond the dark route slowly traversed by Neptune, the frigid wastes of space are traveled over by the comets in their erratic courses. Of these, some, being controlled by the sun, do not leap from system to system, but move in closed curves, though at distances far greater than those of Uranus and Neptune. Thus Halley's comet recedes to a distance of over 3,200,000,000 miles from the sun; the comet of 1811, 36,000,000,000; and that of 1680, 75,000,000,000. The period of the last-named comet is 8,800 years.
Still these figures can scarcely be compared to those which represent the distances of the stars. What means have we of measuring these distances? Here the diameter of the earth will not serve as the base of the triangle, as when we measure the moon's distance; nor can we, as in the case of the sun, get any assistance from another planet. However, fortunately for us, the arrangement of our system affords us a means of measuring these distant perspectives; and this, while demonstrating over again the earth's motion round the sun, turns that motion to account for the solution of the greatest of astronomical problems.
In revolving round the sun, at the distance of 92,000,000 miles, the earth annually describes an ellipse of about 500,000,000 miles. The diameter of this orbit is 184,000,000 miles. As the earth's revolution round the sun is performed in a year, the earth, at any given instant, will be opposite to the point where it stood six months before, as also to the point where it will stand six months later. Here is a line of sufficient length to serve as base of a triangle the apex of which shall be a star.
The process, then, for measuring the distance of a star from the earth consists in minutely observing this star at an interval of six months, or better, for a whole year, noting whether it remains fixed, or whether it undergoes some little appreciable displacement of perspective, owing to the annual displacement of the earth around the sun. If it remains fixed, this is because it is at an infinite distance from us—at the horizon of the heavens, so to speak—and our baseline of 184,000,000 miles is as nothing in comparison with this remoteness. But if it is displaced, then we know that it annually describes a small ellipse, corresponding to the annual revolution of the earth. Every one has remarked, while traveling by rail, how the trees and other objects near at hand move in a direction contrary to our own, their speed being greater in proportion to their nearness; whereas distant objects on the horizon remain fixed. This same effect is produced in space, in consequence of our annual motion round the sun. But though we move incomparably swifter than an express-train, our rate being 1,632,000 miles per day, and 68,000 per hour, the stars are so distant that they scarcely budge. Our 184,000,000 miles of displacement are almost nothing as concerns even the nearest of them. The inhabitants of Jupiter, Saturn, Uranus, or Neptune, with their orbits five, nine, nineteen, and thirty times as large as ours, could determine the distance of a far greater number of stars than we.
This mode of measuring the distance of the stars by the perspective effect produced by the earth's annual displacement was anticipated by the astronomers of the eighteenth century, and in particular by Bradley, who, while attempting to measure the distances of the stars by comparing together observations made at an interval of six months, discovered—something else. Instead of finding the distance of the stars on which his observations were directed, he discovered a very important optical phenomenon, viz., the aberration of light, the effect produced by the motion of light and the motion of the earth combined. Similarly, William Herschel, while seeking the parallaxes of the stars by comparing bright stars with their nearest neighbors, discovered the systems of double stars. So, too, Fraunhofer, while seeking the limits of the colors in the solar spectrum, discovered the absorption rays, the study of which has given rise to Spectrum Analysis. The history of the sciences shows that frequently discoveries have been made in the course of investigations which had but little to do with them directly. Columbus discovered the New World while aiming to reach the eastern coast of Asia by sailing to the west. He would never have discovered it, would never have sought for it, had he known the true distance between Portugal and Kamtchatka.
It was not till 1840 that the distance of any of the stars was ascertained. This discovery is, therefore, of recent date, and we are only now beginning to form an approximate idea of the real distances which separate us from the stars. The parallax of the star 61 in the Swan, which was the first to be determined, was ascertained by Bessel, and was the result of observations made at Königsberg from 1837 to 1840. In 1812, Arago and Mathieu had made observations on this star, but without reaching any certain results. The parallax of Alpha in the Lyre was found by Struve, in the course of observations made at Dorpat between 1835 and 1838; but it was not published till after the year 1840. The same is to be said of Alpha in Centaur, observed in 1832 and in 1839 on the Cape of Good Hope by Henderson and Maclear; this is the nearest to us of all the stars.
There are two ways of determining these parallaxes. The first is, to compare together the positions observed at intervals of six months; the other, to discover an apparent motion in a star (as compared with a motionless star situated at a far greater distance than that which is studied): this apparent motion being due to the perspective produced by the annual revolution of the earth in its orbit. This is the method mostly employed now. Galileo, in his "Dialogues;" Gregory, in the "Proceedings of the Royal Society" (1675); Huyghens, in his "Cosmotheoros," published in 1695; Condorcet, in his "Éloge of Roemer," in 1773; and William Herschel, in 1781, have described both methods. Hooke, Flamstead, Cassini, Bradley, Robert Long, Herschel, Piazzi, and Brinkley, strove, from 1674 to 1820, to determine the small quantity of the apparent movement of the brightest stars, which used to be regarded as the nearest; but their efforts were fruitless, owing to the inconsiderable amount of this motion. There was need of instruments of the utmost precision, a rigid spirit of observation, and an indomitable patience, in order to get at trustworthy results.
Since 1840 the attention of astronomers has been oftentimes directed to this investigation, and thousands of calculations have been made. With great difficulty astronomers have succeeded in determining the parallaxes of a few stars. But the inevitable errors of observation often involve the results in obscurity. Let the reader only bear in mind that there is not one star that is sufficiently near to give us a parallax of one second! A second is the dimension to which would be reduced a circle one metre (3 ft. 3.37 in.) in diameter carried away to a distance of 206 kilometres (127.72 miles) from the eye. This appears to be less than nothing: it is equal to the thickness of a hair stretched at the distance from the eye of 20 metres (74 feet). The apparent annual movement of a star, whose distance can be known, is performed altogether within this infinitesimal space. For an observer on the star that is nearest to us, this hair would conceal the whole space between the earth and the sun.
As no star offers a parallax of one second, it follows that the nearest of the stars is distant from earth no less than 206,265 times 92,000,000 miles. The space which surrounds the planetary system is void of stars to that distance at least.
The star which is nearest to us, Alpha of Centaur, has a parallax of 0."91. Its distance from earth is 226,400 times the radius of the earth's orbit, or 21,000,000,000,000 miles. This is our neighbor star, and its distance is probably the minimum distance between star and star—21,000,000,000,000 miles. Each of these stars shines with its own light—is a sun like our own.
The second star, in the order of distances, is 61 Cygni. Its parallax is 0."51, and its remoteness 37,000,000,000,000 miles.
Of the thousands of stars which have been studied, we know the distances of only twenty. Among these we may signalize Sirius, a sun 2,688 times larger than our own, surrounded by a system of heavenly bodies, several of which are already known, and distant from us 82,000,000,000,000 miles; the Polar Star, which is a double star, distant 292,000,000,000,000 miles; and Capella, distant 425,000,000,000,000—a space which is traversed by light in seventy-one years and eight months; so that the luminous ray which reaches us from this fine star in 1874 must have started out in 1803! Capella might have been extinguished in 1804, but we should see it still. It might go out to-day, and yet the inhabitants of the earth would continue to admire it in their heavens until 1946. Conversely, if there existed, on the planets gravitating round Capella, minds whose transcendent vision could thence descry our little earth, lost as it is amid the sun's rays, they would now see the earth of the year 1803, and would be seventy-one years eight months behindhand in its history. These are the stars that are nearest to us. The others are incomparably more remote.
There are stars whose light cannot reach us in less than 100, 1,000, or 10,000 years, though light travels at the rate of 185,000 miles per second!
To traverse the sidereal world of which we form part (the Milky-Way), light takes 15,000 years.
To reach us from certain of the nebulæ, it must travel for 300 times that period, or 5,000,000 years.
Let the imagination, that is not appalled by these immensities, strive to conceive of them. If it does not experience the "vertigo of the infinite," let it calmly contemplate these abysses, and realize the position of the earth and of man in presence of them. Thus will it gain some conception of the discoveries made by sidereal astronomy.
Such are the dimensions actually measured in the general constitution of the universe. As yet we are only at the vestibule of the edifice, on the edge of the abyss of infinitude: and we shall never penetrate very far beyond.