The Story of the Heavens

by Robert S. Ball

No attempt to solve the problem of the absolute distances of the stars was successful until many years after Herschel's labours were closed. Fresh generations of astronomers, armed with fresh appliances, have for many years pursued the subject with unremitting diligence, but for a long time the effort seemed hopeless. The distances of the stars were so great that they could not be ascertained until the utmost refinements of mechanical skill and the most elaborate methods of mathematical calculation were brought to converge on the difficulty. At last it was found that the problem was beginning to yield. A few stars have been induced to disclose the secret of their distance. We are able to give some answer to the question—How far are the stars? though it must be confessed that our reply up to the present moment is both hesitating and imperfect. Even the little knowledge which has been gained possesses interest and importance. As often happens in similar cases, the discovery of the distance of a star was made independently about the same time by two or three astronomers. The name of Bessel stands out conspicuously in this memorable chapter of astronomy. Bessel proved (1840) that the distance of the star known as 61 Cygni was a measurable quantity. His demonstration possessed such unanswerable logic that universal assent could not be withheld. Almost simultaneously with the classical labours of Bessel we have Struve's measurement of the distance of Vega, and Henderson's determination of the distance of the southern star α Centauri. Great interest was excited in the astronomical world by these discoveries, and the Royal Astronomical Society awarded its gold medal to Bessel. It appropriately devolved on Sir John Herschel to deliver the address on the occasion of the presentation of the medal: that address is a most eloquent tribute to the labours of the three astronomers. We cannot resist quoting the few lines in which Sir John said:—

"Gentlemen of the Royal Astronomical Society,—I congratulate you and myself that we have lived to see the great and hitherto impassable barrier to our excursion into the sidereal universe, that barrier against which we have chafed so long and so vainly—æstuantes angusto limite mundi—almost simultaneously overleaped at three different points. It is the greatest and most glorious triumph which practical astronomy has ever witnessed. Perhaps I ought not to speak so strongly; perhaps I should hold some reserve in favour of the bare possibility that it may be all an illusion, and that future researches, as they have repeatedly before, so may now fail to substantiate this noble result. But I confess myself unequal to such prudence under such excitement. Let us rather accept the joyful omens of the time, and trust that, as the barrier has begun to yield, it will speedily be effectually prostrated."

Before proceeding further, it will be convenient to explain briefly how the distance of a star can be measured. The problem is one of a wholly different character from that of the sun's distance, which we have already discussed in these pages. The observations for the determination of stellar parallax are founded on the familiar truth that the earth revolves around the sun. We may for our present purpose assume that the earth revolves in a circular path. The centre of that path is at the centre of the sun, and the radius of the path is 92,900,000 miles. Owing to our position on the earth, we observe the stars from a point of view which is constantly changing. In summer the earth is 185,800,000 miles distant from the position which it occupied in winter. It follows that the apparent positions of the stars, as projected on the background of the sky, must present corresponding changes. We do not now mean that the actual positions of the stars are really displaced. The changes are only apparent, and while oblivious of our own motion, which produces the displacements, we attribute the changes to the stars.

On the diagram in Fig. 93 is an ellipse with certain months—viz., January, April, July, October—marked upon its circumference. This ellipse may be regarded as a miniature picture of the earth's orbit around the sun. In January the earth is at the spot so marked; in April it has moved a quarter of the whole journey; and so on round the whole circle, returning to its original position in the course of one year. When we look from the position of the earth in January, we see the star A projected against the point of the sky marked 1. Three months later the observer with his telescope is carried round to April; but he now sees the star projected to the position marked 2. Thus, as the observer moves around the whole orbit in the annual revolution of the earth, so the star appears to move round in an ellipse on the background of the sky. In the technical language of astronomers, we speak of this as the parallactic ellipse, and it is by measuring the major axis of this ellipse that we determine the distance of the star from the sun. Half of this major axis, or, what comes to the same thing, the angle which the radius of the earth's orbit subtends as seen from the star, is called the star's "annual parallax."

Fig. 93.—The Parallactic Ellipse.

The figure shows another star, B, more distant from the earth and the solar system generally than the star previously considered. This star also describes an elliptic path. We cannot, however, fail to notice that the parallactic ellipse belonging to B is much smaller than that of A. The difference in the sizes of the ellipses arises from the different distances of the stars from the earth. The nearer the star is to the earth the greater is the ellipse, so that the nearest star in the heavens will describe the largest ellipse, while the most distant star will describe the smallest ellipse. We thus see that the distance of the star is inversely proportional to the size of the ellipse, and if we measure the angular value of the major axis of the ellipse, then, by an exceedingly simple mathematical manipulation, the distance of the star can be expressed as a multiple of a radius of the earth's orbit. Assuming that radius to be 92,900,000 miles, the distance of the star is obtained by simple arithmetic. The difficulty in the process arises from the fact that these ellipses are so small that our micrometers often fail to detect them.

How shall we adequately describe the extreme minuteness of the parallactic ellipses in the case of even the nearest stars? In the technical language of astronomers, we may state that the longest diameter of the ellipse never subtends an angle of more than one and a half seconds. In a somewhat more popular manner, we would say that one thousand times the major axis of the very largest parallactic ellipse would not be as great as the diameter of the full moon. For a still more simple illustration, let us endeavour to think of a penny-piece placed at a distance of two miles. If looked at edgeways it will be linear, if tilted a little it would be elliptic; but the ellipse would, even at that distance, be greater than the greatest parallactic ellipse of any star in the sky. Suppose a sphere described around an observer, with a radius of two miles. If a penny-piece were placed on this sphere, in front of each of the stars, every parallactic ellipse would be totally concealed.

The star in the Swan known as 61 Cygni is not remarkable either for its size or for its brightness. It is barely visible to the unaided eye, and there are some thousands of stars which are apparently larger and brighter. It is, however, a very interesting example of that remarkable class of objects known as double stars. It consists of two nearly equal stars close together, and evidently connected by a bond of mutual attraction. The attention of astronomers is also specially directed towards the star by its large proper motion. In virtue of that proper motion, the two components are carried together over the sky at the rate of five seconds annually. A proper motion of this magnitude is extremely rare, yet we do not say it is unparalleled, for there are some few stars which have a proper motion even more rapid; but the remarkable duplex character of 61 Cygni, combined with the large proper motion, render it an unique object, at all events, in the northern hemisphere.