Letters on Astronomy / in which the Elements of the Science are Familiarly Explained in Connection with Biographical Sketches of the Most Eminent Astronomers

by Denison Olmsted

Beside these revolutions of the binary stars, some of the fixed stars appear to have a real motion in space. There are several apparent changes of place among the stars, arising from real changes in the earth, which, as we are not conscious of them, we refer to the stars; but there are other motions among the stars which cannot result from any changes in the earth, but must arise from changes in the stars themselves. Such motions are called the proper motions of the stars. Nearly two thousand years ago, Hipparchus and Ptolemy made the most accurate determinations in their power of the relative situations of the stars, and their observations have been transmitted to us in Ptolemy's 'Almagest;' from which it appears that the stars retain at least very nearly the same places now as they did at that period. Still, the more accurate methods of modern astronomers have brought to light minute changes in the places of certain stars, which force upon us the conclusion, either that our solar system causes an apparent displacement of certain stars, by a motion of its own in space, or that they have themselves a proper motion. Possibly, indeed, both these causes may operate.

If the sun, and of course the earth which accompanies him, is actually in motion, the fact may become manifest from the apparent approach of the stars in the region which he is leaving, and the recession of those which lie in the part of the heavens towards which he is travelling. Were two groves of trees situated on a plain at some distance apart, and we should go from one to the other, the trees before us would gradually appear further and further asunder, while those we left behind would appear to approach each other. Some years since, Sir William Herschel supposed he had detected changes of this kind among two sets of stars in opposite points of the heavens, and announced that the solar system was in motion towards a point in the constellation Hercules; but other astronomers have not found the changes in question such as would correspond to this motion, or to any motion of the sun; and, while it is a matter of general belief that the sun has a motion in space, the fact is not considered as yet entirely proved.

In most cases, where a proper motion in certain stars has been suspected, its annual amount has been so small, that many years are required to assure us, that the effect is not owing to some other cause than a real progressive motion in the stars themselves; but in a few instances the fact is too obvious to admit of any doubt. Thus, the two stars, 61 Cygni, which are nearly equal, have remained constantly at the same or nearly at the same distance of fifteen seconds, for at least fifty years past. Mean-while, they have shifted their local situation in the heavens four minutes twenty-three seconds, the annual proper motion of each star being five seconds and three tenths, by which quantity this system is every year carried along in some unknown path, by a motion which for many centuries must be regarded as uniform and rectilinear. A greater proportion of the double stars than of any other indicate proper motions, especially the binary stars, or those which have a revolution around each other. Among stars not double, and no way differing from the rest in any other obvious particular, a star in the constellation Cassiopeia, (Mu Cassiopeiæ) has the greatest proper motion of any yet ascertained, amounting to nearly four seconds annually.

You have doubtless heard much respecting the "immeasurable distances" of the fixed stars, and will desire to learn what is known to astronomers respecting this interesting subject.

We cannot ascertain the actual distance of any of the fixed stars, but we can certainly determine that the nearest star is more than twenty millions of millions of miles from the earth, (20,000,000,000,000.) For all measurements relating to the distances of the sun and planets, the radius of the earth furnishes the base line. The length of this line being known, and the horizontal parallax of the sun or any planet, we have the means of calculating the distance of the body from us, by methods explained in a previous Letter. But any star, viewed from the opposite sides of the earth, would appear from both stations to occupy precisely the same situation in the celestial sphere, and of course it would exhibit no horizontal parallax. But astronomers have endeavored to find a parallax in some of the fixed stars, by taking the diameter of the earth's orbit as a base line. Yet even a change of position amounting to one hundred and ninety millions of miles proved, until very recently, insufficient to alter the place of a single star, so far as to be capable of detection by very refined observations; from which it was concluded that the stars have not even any annual parallax; that is, the angle subtended by the semidiameter of the earth's orbit, at the nearest fixed star, is insensible. The errors to which instrumental measurements are subject, arising from the defects of instruments themselves, from refraction, and from various other sources of inaccuracy, are such, that the angular determinations of arcs of the heavens cannot be relied on to less than one second, and therefore cannot be appreciated by direct measurement. It follows, that, when viewed from the nearest star, the diameter of the earth's orbit would be insensible; the spider-line of the telescope would more than cover it. Taking, however, the annual parallax of a fixed star at one second, it can be demonstrated, that the distance of the nearest fixed star must exceed 95000000 × 200000 = 190000000 × 100000, or one hundred thousand times one hundred and ninety millions of miles. Of a distance so vast we can form no adequate conceptions, and even seek to measure it only by the time that light (which moves more than one hundred and ninety-two thousand miles per second, and passes from the sun to the earth in eight minutes and seven seconds) would take to traverse it, which is found to be more than three and a half years.

If these conclusions are drawn with respect to the largest of the fixed stars, which we suppose to be vastly nearer to us than those of the smallest magnitude, the idea of distance swells upon us when we attempt to estimate the remoteness of the latter. As it is uncertain, however, whether the difference in the apparent magnitudes of the stars is owing to a real difference, or merely to their being at various distances from the eye, more or less uncertainty must attend all efforts to determine the relative distances of the stars; but astronomers generally believe, that the lower orders of stars are vastly more distant from us than the higher. Of some stars it is said, that thousands of years would be required for their light to travel down to us.

I have said that the stars have always been held, until recently, to have no annual parallax; yet it may be observed that astronomers were not exactly agreed on this point. Dr. Brinkley, a late eminent Irish astronomer, supposed that he had detected an annual parallax in Alpha Lyræ, amounting to one second and thirteen hundreths, and in Alpha Aquilæ, of one second and forty-two hundreths. These results were controverted by Mr. Pond, of the Royal Observatory of Greenwich; and Mr. Struve, of Dorpat, has shown that, in a number of cases, the supposed parallax is in a direction opposite to that which would arise from the motion of the earth. Hence it is considered doubtful whether, in all cases of an apparent parallax, the effect is not wholly due to errors of observation.

But as if nothing was to be hidden from our times, the long sought for parallax among the fixed stars has at length been found, and consequently the distance of some of these bodies, at least, is no longer veiled in mystery. In the year 1838, Professor Bessel, of Köningsberg, announced the discovery of a parallax in one of the stars of the Swan, (61 Cygni,) amounting to about one third of a second. This seems, indeed, so small an angle, that we might have reason to suspect the reality of the determination; but the most competent judges who have thoroughly examined the process by which the discovery was made, assent to its validity. What, then, do astronomers understand, when they say that a parallax has been discovered in one of the fixed stars, amounting to one third of a second? They mean that the star in question apparently shifts its place in the heavens, to that amount, when viewed at opposite extremities of the earth's orbit, namely, at points in space distant from each other one hundred and ninety millions of miles. On calculating the distance of the star from us from these data, it is found to be six hundred and fifty-seven thousand seven hundred times ninety-five millions of miles,—a distance which it would take light more than ten years to traverse.

Indirect methods have been proposed, for ascertaining the parallax of the fixed stars, by means of observations on the double stars. If the two stars composing a double star are at different distances from us, parallax would affect them unequally, and change their relative positions with respect to each other; and since the ordinary sources of error arising from the imperfection of instruments, from precession, and from refraction, would be avoided, (as they would affect both objects alike, and therefore would not disturb their relative positions,) measurements taken with the micrometer of changes much less than one second may be relied on. Sir John Herschel proposed a method, by which changes may be determined that amount to only one fortieth of a second.

The immense distance of the fixed stars is inferred also from the fact, that the largest telescopes do not increase their apparent magnitude. They are still points, when viewed with glasses that magnify five thousand times.