CHAPTER III.

THE DISTANCES AND MOTIONS OF THE STARS.

The determination of the distances of the stars from the earth has always formed a subject of great interest to astronomers. The earlier observers appear to have thought that the problem was an insoluble one. The famous Kepler, judging from what he called the “harmony of relations,” came to the conclusion that the distance of the fixed stars should be about 2,000 times the distance of Saturn from the sun. Saturn was then the outermost planet of the solar system. The distance of even the nearest star, as now known, is about 14 times greater than that supposed by Kepler. Huygens thought the determination of stellar distance by observation to be impossible, but made an attempt at a solution of the problem by a photometric comparison between Sirius and the sun. By this method, he found that Sirius is probably about 28,000 times the sun’s distance from the earth, but modern measures show that this estimate is far too small, the distance of Sirius being probably over 500,000 times the sun’s distance, or about 18 times greater than Huygens made it.

When the Copernican theory of the earth’s motion round the sun was first advanced, it was objected that, if the earth moved in a large orbit, its real change of place should produce an _apparent_ change of position in the stars nearest to the earth, causing them to shift their relative position with reference to more distant stars. Copernicus replied to this objection—and we now know that his reply was correct—by saying that the distance of even the nearest stars was so great that the earth’s motion would have no perceptible effect in changing their apparent position in the heavens; in other words, the diameter of the earth’s orbit round the sun would be almost a vanishing point if viewed from the distance of the nearest stars. This explanation of Copernicus was at first ridiculed, and even the famous astronomer, Tycho Brahé, could not accept such a startling conclusion. This celebrated observer failed indeed to detect by his own observations any annual change of place in the stars, but he fancied that the brightest stars showed a perceptible disc, like the planets, a fact which, if true, would imply that, if the distance of the stars was so great as Copernicus supposed, their real diameter must be enormous. The invention of the telescope, however, dispelled this delusion of Tycho Brahé, and showed that even the brightest stars showed no perceptible disc. This was proved by Horrocks and Crabtree, who noticed that, in occultations of stars by the moon, the stars disappeared instantaneously, a fact which proved that the apparent diameter of the stars must be a very small fraction of a second of arc.

Galileo suggested that possibly the distance of the nearer stars might be determined by careful measures of double stars, on the assumption that the brighter star of the pair—if the difference in brilliancy is considerable—is nearer the earth than the fainter star. He says (in his “_Opere di Galileo Galilei_”), “I do not believe that all the stars are scattered over a spherical superficies _at equal distances from a common centre_, but I am of opinion that their distances from us are so various that some of them may be two or three times as remote as others, so that when some minute star is discovered by the telescope close to one of the larger, and yet the former is highest, it may be that some sensible change might take place among them.” Acting on this idea, Sir William Herschel, at the close of the eighteenth century, made a careful series of measures of certain double stars. He did not, however, succeed in his attempt, as his instruments were not sufficiently accurate for such an investigation, but his labours were rewarded by the great discovery of binary or revolving double stars, most interesting objects, which will be considered in the next chapter.

Numerous but unsuccessful attempts were made by Hooke, Flamsteed, Cassini, Molyneux, and Bradley, to find the distance of some of the stars. Hooke, in the year 1669, thought he had detected a parallax of 27 to 30 seconds arc in the star Gamma Draconis, but we now know that no star in the heavens has anything like so large a parallax. It must be here explained that to find the distance of any star from the earth, we must first measure its “parallax,” which is the apparent change in its place due to the earth’s motion round the sun. As the earth makes half a revolution in six months, and as the earth’s mean distance from the sun—or the radius of the earth’s orbit—is about 93 millions of miles, the earth is, at any given time, about 186 millions of miles distant from the point in its orbit which it occupied six months previously. The apparent change of position in a star’s place, known as parallax, is _one-half_ the total displacement of the star as seen from opposite points of the earth’s orbit. In other words, it is the angle subtended at the star by the sun’s mean distance from the earth. The measured parallax of a star may be either “absolute” or “relative.” An “absolute parallax” is the actual parallax. A “relative parallax” is the parallax with reference to a faint star situated near a brighter star, the faint star being assumed to lie, as suggested by Galileo, at a much greater distance from the earth. As, however, the faint star may have a small parallax of its own, the “relative parallax” is the difference between the parallaxes of the two stars. Indeed, in some cases a “negative parallax” has been found, which, if not due to errors of observation, would imply that the faint star is actually the nearer of the two. From the observed parallax, the star’s distance in miles may be found by simply multiplying 93 millions of miles by 206,265 and dividing the result by the parallax. To find the time that light would take to reach us from the star—the light journey as it is called—it is only necessary to divide the number 3·258 by the parallax.

In attempting to verify the result found by Hooke for the parallax of Gamma Draconis, Molyneux and Bradley found an apparent parallax of about 20 seconds of arc, thus apparently confirming Hooke’s result, but observations of other stars showing a similar result, Bradley came to the conclusion that the apparent change of position was not really due to parallax, but was caused by a phenomenon now known as the “aberration of light,” an apparent displacement in the positions of the stars, due to the effect of the earth’s motion in its orbit round the sun combined with the progressive motion of light. The result is that “a star is displaced by aberration along a great circle, joining its true place to the point on the celestial sphere towards which the earth is moving.” The amount of aberration is a maximum for stars lying in a direction at right angles to that of the earth’s motion. The existence of aberration is an absolute proof that the earth does revolve round the sun, for were the earth at rest—as some paradoxes contend—there would be no aberration of the stars. This effect of aberration must, of course, be carefully allowed for in all measures of stellar parallax. To show that “aberration” could not possibly be due to “parallax,” it may be stated that aberration shifts the apparent place of a star in one direction, while parallax shifts it in the opposite direction.

From photometric comparisons, the Rev. John Mitchell, in the year 1767, concluded that the parallax of Sirius is less than a second of arc; a result which has been fully confirmed by modern measures. He considered that stars of the sixth magnitude are probably 20 to 30 times the distance of Sirius, and judging from their relative brilliancy alone, this result would also be nearly correct. But recent measures have shown that some of the fainter stars are actually nearer to us than some of the brighter, and that the brightness of a star is no criterion of its distance.

The first stars on which observations seem to have been made with a view to a determination of their distance seem to have been Aldebaran and Sirius. From observations made in the years 1792 to 1804 with a vertical circle and telescope of 3 inches aperture, Piazzi found for Aldebaran an “absolute” parallax of about 1½ seconds of arc. O. Struve and Shdanow, in 1857, using a refractor of 15 inches aperture, found a “relative” parallax of about half a second. This was further reduced by Hall with the 26-inch refractor of the Washington Observatory to about one-tenth of a second, and Elkin, with a heliometer of 6 inches aperture, finds a relative parallax of 0″·116, or about 30 years’ journey for light For Sirius, Piazzi found, in 1792–1804, an absolute parallax of four seconds, but this was certainly much too large. All subsequent observers find a much smaller parallax, recent measures giving a relative parallax of 0·370″ by Gill, and 0·407″ by Elkin. In the years 1802–1804, Piazzi and Cacciatori found an absolute parallax of 1′·31 for the Pole Star; but this has been much reduced by other observers. Pritchard, by means of photography, found a relative parallax of only 0·073″, which agrees closely with some other previous results, and indicates a “light journey” of about 44 years!

For the bright star Procyon, Piazzi found a parallax of about three seconds, but this is also much too large, a recent determination by Elkin giving 0·266″, a figure in fair agreement with results found by Auwers and Wagner. For the bright star Vega, Calandrelli, in the years 1805–6, found an absolute parallax of nearly four seconds, but this has also been much reduced by modern measures; Elkin, from observations in the years 1887–88, finding a relative parallax of only 0·034″. Brinkley found a parallax of over one second for Arcturus, but Elkin’s result is only 0·018″. If this minute parallax can be relied on, Arcturus must be a sun of vast size.

Owing to the large “proper motion” of the star known as 61 Cygni, its comparative proximity to the earth was suspected, and in 1812, Arago and Mathieu found, from measures made with a repeating circle, a parallax of over half a second. Various measures of its parallax have since been made, ranging from about 0·27″ to 0·566″. Sir Robert Ball, at Dunsink, Ireland, found 0·468″, and Pritchard, by means of photography with a 13-inch reflector, found 0·437″. We may, therefore, safely assume that the parallax of 61 Cygni is about 0·45″. This implies a distance of 458,366 times the sun’s distance from the earth, or about 42 billions of miles, and a “light journey” of about 7¼ years.

It is usually stated that 61 Cygni is the nearest star to the earth in the Northern Hemisphere, but for the star known as Lalande 21,185, Winnecke found 0·511″, and afterwards 0·501″. This has, however, been reduced by Kapteyn (1885–1887) to 0·434″; and recently a parallax of 0·465″ has been found by the photographic method for the binary star, Eta Cassiopeiæ. 61 Cygni is a wide double star, but it seems doubtful whether the components are physically connected, although several orbits have been provisionally computed.

Nearer to us than 61 Cygni is the bright southern star Alpha Centauri, which, so far as is known at present, is the nearest of all the fixed stars to the earth. The first attempt to find its distance was made by Henderson in the years 1832–33, using a mural circle of 4 inches aperture and a transit of 5 inches. He found an “absolute” parallax of about one second of arc, which subsequent measures have shown to be rather too large. Measures in recent years range from 0·512″ to 0·976″, but probably the most reliable are those made with a heliometer of 4½ inches aperture by Dr. Gill (1881–82), who found a “relative” parallax of 0·76″, and by Dr. Elkin, using the same instrument, 0·671″. Gill’s result would place the star at a distance of 271,400 times the sun’s distance from the earth, or about 25 billions of miles, a distance which light, with its great velocity of 186,300 miles a second, would take over 4¼ years to traverse.

It will be understood that the parallaxes found for even the nearest fixed stars are so small that their exact determination taxes the powers of the most perfect instruments and the skill of the most experienced observers. One thing, however, seems certain, that the brightest stars are not necessarily the nearest, and that comparatively faint stars may be actually nearer to the earth than some of the brightest gems which deck our midnight sky. Indeed, from a discussion of the observed parallaxes and “proper motions” of 11 stars, Gylden finds a mean parallax of only 0·083″ for stars of the first magnitude. This agrees closely with the value 0·089″ found by Dr. Elkin.

In old times the stars were supposed to be absolutely fixed in the celestial vault, that is to say, that their relative positions did not change. This was a very natural conclusion, for before the invention of the telescope it would have been impossible to detect any “proper motion”—as it is called—by naked eye observations. Hence the term “fixed stars,” used to distinguish the stars from the planets, which are always shifting their positions in the heavens. The existence of proper motion, in some at least of the stars, seems to have been discovered by Halley, who found from his observations in 1715 that the bright stars, Sirius, Arcturus, and Aldebaran, had apparently shifted their positions since the date of the earliest observations. This discovery was confirmed by James Cassini in 1738. He found that Arcturus had apparently moved through some five minutes of arc in 152 years, or about two seconds a year, a result which agrees fairly well with more exact modern measures.

This interesting discovery of stellar motion has been fully confirmed by modern observations, and we now know that, far from the stars being “fixed,” most of them have an apparent motion on the celestial vault. These motions are, however, very slow, and can only be detected by accurate measurements and a careful comparison of their positions after the lapse of a number of years. The largest proper motion hitherto detected is that of a star known as 1830 of Groombridge’s catalogue, a small star of about 6½ magnitude, which lies in the constellation Ursa Major. This star has an apparent motion of seven seconds per annum, which, though relatively large, is of course absolutely small, as the observed motion would only suffice to carry it through a space equal to the moon’s apparent diameter in about 266 years. Assuming a parallax of about one-sixth of a second found by Kapteyn, this apparent motion would indicate a real motion of about 128 miles a second at right angles to the line of sight. As, however, there may be also motion _in_ the line of sight, the above velocity would be a minimum—if the parallax can be relied upon—and the actual motion may be considerably more. From its rapidity, 1830 Groombridge has been called by Prof. Newcomb “the runaway star.”

Next in order of rapidity of motion comes the southern star known as Lacaille 9352, which lies in the constellation Piscis Australis, a little south of Fomalhaut. This seventh magnitude star has an apparent motion of 6·9 seconds, which, with a parallax of 0·285″ found by Gill, indicates a velocity of 71 miles per second. Next comes 61 Cygni, with a velocity of 30 miles, and Epsilon Indi—another southern star—with a velocity of nearly 68 miles a second. These velocities are, however, exceeded by other stars if the measured parallaxes are correct. Thus the star Mu Cassiopeiæ, with a proper motion of 3·7 seconds, has, according to Pritchard’s photographic measures, a parallax of only 0·036″, which would indicate a velocity of no less than 302 miles a second! and the small parallax found by Elkin for Arcturus would imply the startling velocity of 376 miles a second!

It is a remarkable fact that the eight stars with the largest proper motions are all below the fourth magnitude in brightness, and as a large proper motion probably indicates proximity to the earth, the conclusion seems evident that the brightest stars are not as a rule the nearest. Of twenty-five stars, with proper motions greater than two seconds of arc, there are only two—Arcturus and Alpha Centauri—whose magnitude exceeds the third. Indeed, more than half the stars with motions greater than one second are invisible to the naked eye!

Many stars have proper motions of less than a second of arc per annum. Very small proper motions have also been detected, which only reveal themselves after the lapse of a great number of years, and it seems probable that there are no really “fixed stars” in the heavens. For stars of the sixth magnitude, M. Ludwig Struve finds an average motion of only eight seconds in a hundred years, or about one-twelfth of a second per annum. If we assume that stars of the sixth magnitude are, on the average, of the same size and brightness as stars of the first magnitude, their distance from the earth would be ten times greater. Consequently, stars of the first magnitude should have an average proper motion of about eighty seconds in one hundred years. This, however, is not the case. The twenty brightest stars show an average motion of only sixty seconds in a hundred years. And the motion of stars of the second magnitude is relatively still slower. Instead of an average motion of fifty seconds in a hundred years—which they should have if the brightness were inversely proportional to the distance—it has been found that twenty-two stars of the second magnitude show an average motion of only seventeen seconds. This result seems to show that the brighter stars are not so near us as their brilliancy would lead us to suppose, a conclusion which has been already proved by actual measures of their distance.

From a consideration of the results found for stellar parallax, Mr. Thomas Lewis, F.R.A.S., of the Greenwich Observatory, comes to the following conclusions[108]:—

“(1) Leaving out a few of the brightest stars, the parallaxes are constant down to 2·70 magnitude.

“(2) After 2·70 mag. is reached, the parallaxes are doubled, and remain practically constant to 8·40 mag.

“(3) Up to the 3rd mag. the velocities are very small, averaging about 9 miles per second, while after the 3rd mag. the velocity is 38 miles per second.

“Hence we may fairly deduce—

“(1) That there are a few stars (about 8) of exceptional brilliancy in our immediate neighbourhood, and scattered about amongst these a number of small stars (at present about 40 are known).

“(2) Stars of mag. 1·0 to 3·0 are, as a class, far outside this inner space, and have very small velocities.

“(3) The small stars here dealt with have apparently large velocities across the line of sight.

“These results show that the generally received idea that parallaxes are to be sought for in stars with large proper motion is correct, and we may add that this holds good, no matter what may be the star’s magnitude.”

The “proper motion” of a star only indicates its motion at right angles to the line of sight—that is, its motion on the surface of the celestial vault—and gives us no information as to whether the star is approaching to or receding from the earth. This motion “in the line of sight” cannot be detected by micrometrical measures with an ordinary telescope, and would probably have remained for ever unknown had the spectroscope not been invented. Dr. Huggins was the first to show that motions in the line of sight could be determined by measuring the displacement of the spectral lines caused by the approach or recession of the source of light, the lines being slightly shifted towards the blue end of the spectrum when the star is approaching the earth, and towards the red end when it is receding from us. The effect would, of course, be exactly the same if the star were at rest and the earth in motion. By carefully measuring this observed displacement of the spectral lines, the velocity in the line of sight can be easily computed. Dr. Huggins’ observations were fully confirmed by Dr. Vogel.

The earlier determinations of motion in the line of sight were made by eye measurements with a micrometer, and owing to the difficulty and delicacy of these measures, the results were very discordant. The method has recently been much improved by photographing the spectra and measuring the positions of the lines on the photograph. Both methods agree in showing that the following stars, among others, are certainly _approaching_ the earth: Arcturus, Vega, Procyon, Pollux, Altair, Spica, Alpha Cephei, Alpha Persei, Alpha Arietis, 61 Cygni, and the Pole Star; and the following are certainly _receding_: Capella, Rigel, Betelgeuse, Aldebaran, and Regulus.

Measures of photographic stellar spectra have yielded much more accurate results than the old method. Some of the velocities found in this way by Dr. Vogel—who has given especial attention to this subject—are very considerable. For the bright star Rigel he finds a velocity of recession of about 39 miles a second, for Aldebaran 30 miles, and for Capella 15 miles. He finds that the Pole Star is approaching the earth at the rate of 16 miles a second, and Procyon about 7 miles.

Dr. Bélopolsky has recently investigated the _absolute_ velocity in space of the brighter component of 61 Cygni—that is, the motion across the line of sight combined with the motion _in_ the line of sight. Assuming a parallax of half a second and a proper motion of 5·2 seconds, he finds that the motion across the line of sight, corrected for the sun’s motion in space, is about 22½ miles per second. The motion _in_ the line of sight, also corrected for the sun’s motion, he finds, from photographs taken at Pulkova, to be about 27 miles a second towards the earth. Combining these motions, he finds the absolute velocity of the star in space to be about 35 miles a second, or nearly double the velocity of the earth in its orbit

This method of measuring velocities in the line of sight has also been applied to the nebulæ. Mr. Keeler has observed and measured a displacement of the line known as the chief nebular line in several planetary nebulæ, and finds considerable motion in the line of sight. For example, in the nebula numbered 6790 in the “New General Catalogue,” he finds a motion of recession of about 38 miles a second. Some of these motions may possibly be due, in part at least, to the sun’s motion in space, carrying the earth with it, a motion which will now be considered. The method has also led to the discovery of the so-called “spectroscopic binary stars,” a most interesting class of objects, which will be considered in the next chapter.

The proper motions of the stars long since suggested the idea that possibly the observed motion may be—to some extent, at least—merely apparent, and due to the real motion of the sun and solar system through space. The first investigation of this interesting question was made by Sir William Herschel in 1783, and he came to the conclusion that the sun is moving towards a point near Lambda Herculis, a result not differing widely from modern determinations. The reality of Herschel’s result has been fully confirmed by subsequent investigations, and Argelander placed it beyond doubt by a comparison of the positions of a large number of stars determined at Abo with those found by Bradley in 1752. The accuracy of Argelander’s result was confirmed by Otto Struve. According to the elder Struve, the results arrived at by Argelander, O. Struve, and Peters, is to place the point towards which the sun is moving, between the stars Pi and Mu Herculis, “at a quarter of the apparent distance of these stars from Pi Herculis,” and they estimated the annual motion at about 33½ million miles geographical. The general accuracy of this conclusion has been verified by modern researches, although the results found by different astronomers vary to some extent. The accompanying diagram shows some of the different positions found by various computers. The later determinations seem to place the “apex of the solar motion,” as it is termed, not far from the bright star Vega, or further to the east than Herschel placed it. The velocity of the sun’s motion in space has not been so well determined as its direction. L. Struve’s computations would indicate a velocity of about 14 miles a second; but other results give a much smaller velocity.

[Illustration:

FIG. 3.—_Diagram showing “Solar Apex,” and the different Positions found by various Computers._

(From “Visible Universe.”) ]

From a recent investigation of the nature of the sun’s motion in space by Mr. G. C. Bompas,[109] he considers that the various positions of the sun’s “apex” show a tendency to a drift along the edge of the Milky Way, and that this drift “seems to point to a plane of motion of the sun nearly coinciding with the plane of the Milky Way, or, perhaps, more nearly with the plane of that great circle of bright stars first described by Sir Wm. Herschel as inclined about 20° to the galaxy, and which passes through Lyra, in or near which constellation the solar apex lies,” and he concludes, from the motion of the nearer stars, “that the sun moves in a retrograde orbit from east to west, and in a plane inclined a few degrees to that of the Milky Way.” With reference to this very interesting conclusion, which may, perhaps, be confirmed by further observations, Mr. Bompas quotes the following passage from “The Visible Universe,” p. 197, by the present writer:—“With reference to a possible motion of the stars in some general system, M. Rancken has found, from an examination of 106 stars, a tendency to drift along the course of the Milky Way from Aquila towards Cygnus and Cassiopeia, and past Capella through Orion to Argo. The _larger_ motions, shown in Proctor’s map of ‘proper motions,’ exhibit this tendency in a marked degree between Cygnus and Capella, and less clearly on the Sirius, but the smaller motions not so well,” and Mr. Bompas points out that this apparent drift of the stars in the Milky Way, from west to east, “is just such as would be occasioned by a real motion of the sun in that plane, in a contrary direction from east to west.”