IN STARRY SKIES

Evening Post, Volume CXX, Issue 125, 22 November 1935, Page 20

IN STARRY SKIES

STELLAR DISTANCES: THE

NEAREST STARS

(By "Omega Centauri.")

We have seen that, from the dis-

tance of the sun, a line equal to the equatorial radius of the earth, 3963.34 miles in length, would subtend' an angle of only 8.803 seconds. This tiny .angle is called the equatorial horizontal parallax of the sun, and from it the mean distance of the earth from the sun is calculated to be 92,870,000 miles. But the sun is by far the near.est of the stars. The next nearest that we know is more than 272,000 times as far away. It is quite clear, therefore, that it would be useless to attempt to detect any stellar parallax with regard to a base line measured on the earth. But what other line can we possibly use? The question is answered by the last determination. The distance of the earth from the sun is chosen as our astronomical unit, and our next attempt must be to use it as our base. The early astronomers, though they did not know the exact value of this distance, knew that it was very great. They felt certain that an annual displacement twice as large, namely, from one side of the earth's orbit to the other, should .make some perceptible change in the

apparent positions of the nearer stars with regard to the more distant stellar background. The failure to find any such apparent change was for some centuries the chief argument against the Copernican theory. Even Tycho Brahe refused to believe in the earth's motion round the sun, for this very reason. We now know that the apparent displacement exists and that it can be measured in certain cases, but that it is far too small to be detected by the methods that were then employed. Even the astronomical unit is inconveniently small, and it is only in the case of the nearer stars that the trigonometrical method of determining distances can be successfully employed. Nevertheless it is of immense importance as it furnishes a firm foundation on which the vast structure tiuilt by other methods can rest securely.

But for finding even the smallest stellar distances, the ordinary methods -of fixing positions by right ascension and declination prove inadequate. With an astronomical unit for base the greatest stellar parallax is less than one second. We must, therefore, use the more distant stars as a background and concentrate attention on relative movements. The problem is exceedingly complicated for, as far as we know, every star is in motion. There is no fixed point to measure from. Our own sun is no exception to the rule. Many researches seem to indicate that with respect to the nearer stars, our sun is moving with a velocity of nearly twelve miles per second, towards a point in the constellation Hercules, which is almost midway between Vega and Eas-al-hagua or Alpha Ophinchi. Although every star is attracting every other, stellar distances are so great that isolated stars may be considered at any moment to be moving practically in straight lines. It follows that the motion of any single star relative to our sun is also straight. In most cases we cannot tell the true direction in which a star is travelling. We may consider its actual velocity to be resolved into two components, one along the line joining the earth and the star, either directly towards us or directly from us, and the other at right angles to this line. The latter causes a cumulative apparent displacement which mounts up from year to year. Seen from the earth this displacement follows a slightly wavy line. Seen from the sun it would be straight. The apparent angular rate of motion in the latter case is called the star's "proper motion," and it is usually Measured in seconds of arc per year or per century. In most cases we have no way of translating this speed into miles per second. The radial motion causes no apparent displacement, but strange to say, its value can be determined in kilometres or miles per second by means of the spectroscope. We shall see later that in certain cases this fact is used in finding stellar distances, but at present we are concerned with proper motions. To simplify the problem let us sup-

pose first that some particular star has no proper motion, that is that it is moving at the same rate as our sun in a parallel direction^ or that a motion of that kind is combined with a radial one. Then, if we can imagine our earth to be visible from such a distance, an observer in the position of the star will see the earth describing its annual orbit round the sun. If the observer is situated in the direction of either pole of the ecliptic, the earth's path will appear as in diagram la, an ellipse which is almost circular. If, on the other hand, he were in the plane of the ecliptic, the motion would appear to be backwards and forwards in a straight line as in Ic. * From any other position the earth would appear to move in an elliptic path as shown, for example, in Ib. As we view the star from the moving platform of the earth, the direction in which it appears is always exactly opposite to that in which the earth appears from it. The star, which we have supposed to be comparatively near, will appear to move in front of the 'background of very distant stars, in a tiny orbit which is 'exactly similar to that of the earth as seen from the star.

But we do not know any stars which are moving in exactly the same way as our sun, and, in fact, in applying the trigonometrical method stars which have large proper motions are generally chosen. The reason is that apparent proper motions diminish as distances increase, so that we may infer that a star which shows an unusually large proper motion is not as distant ,as most of the others. In nearly all

cases therefore the annual orbit has to be superimposed on a straight proper motion. The result will be an apparent curved path something like that shown in diagram 111.

Of course, the comparison stars that form the background are themselves affected by parallactic displacements. But these are usually small in comparison with those of the chosen star, and due allowance can generally be made.

It is nearly a century since the first successes in the direct determination of stellar distances were attained. About 1838 results were announced by three different observers. Henderson, at the Cape of Good Hope, chose Alpha Centauri; Bessel, in Germany, studied 61 Cygni, whilst Struve, in Russia, chose Vega. Henderson adopted the old method of measuring the right ascension and declination of-the star at intervals throughout the year. This led to terrible complications, because corrections had to be applied for precession, nutation, and aberration, and these were ever as much greater than the quantity to be measured, and were in addition mingled with it since they have also a yearly period. But ha was fortunate in choosing the nearest bright star. Bessel and Struve measured the distances of their chosen stars from a number of comparison ones. Two instruments were available, the filar micrometer and the heliometer. In the former, a rectangular frame is made to slide over a larger one by turning a fine-threaded screw with a large graduated head. Across each frame is stretched a fine thread of spider web. The distance between two stars can be read by rotating the instrument according to the position angle and then setting one thread on each star.- The heliometer, devised by Fraunhofer, consists of an object glass divided along one diameter. One portion can be moved relative to the other by means of an accurate micrometer screw. Up to the beginning of the twentieth century less than a hundred trigonometrical parallaxes had been obtained. Since then the older visual methods have been superseded by photographic ones. Measurements are made' on photographs taken with long focus telescopes. By 1930 over two thousand stellar parallaxes had been determined with considerable accuracy. Only ten of these parallaxes are greater than a third of a second, and of the stars concerned the only ones visible to the naked eye are Alpha Centauri and Sirius, each of which counts as two stars. Within sixteen light years, if we take Proxima Centauri as belonging to the Alpha Centauri system, and count the sun as a star, there are 36 bodies known. Eighteen of these are solitary stars, and there are six pairs and two triplets. Of these bodies only four are intrinsically brighter than the sun namely, Altair and one component in each of the pairs Alpha Centauri, Sirius, and Procyon. It is clear that only a minute fraction of the galaxy is within the range of trigonometric measurement, but fortunately many indirect methods of finding stellar distances are available.