Astronomy for Everybody/Part 6/Chapter 4

The principles on which distances in the heavens are determined was set forth in our chapter explaining how the heavens are measured. For distances of the moon and nearer planets, we use, as a base line for measurement, the radius of the earth, or the line joining two points of observation on its surface. But this is entirely too short to serve for measuring a distance so great as that even of the nearest star. For this purpose we take as a base line the whole diameter of the earth's orbit. As the earth moves from one side of the orbit to the other, the stars must seem to have a slight motion in the opposite direction. But this motion is found to be almost immeasurably small. It can be made out with sufficient precision only by comparing the stars among themselves in the following way:

Let the little circle on the left of the following figure represent the orbit of the earth. Let S be the star, supposed to be near us, of which we wish to measure the distance. Let the dotted lines almost parallel to each other show the direction of a star T many times farther away. When the earth is at one side of its orbit, say at P, we measure the small angle SPT, which seems to us to separate these two stars. When the earth goes to the opposite side, it is readily seen that the corresponding angle SQT will be greater. We again measure it. The difference ​between these two angles will furnish a basis for computing, by trigonometric methods, the distance of the nearest star when that of the farthest is known. Practically we have to assume that the star T is at an infinite distance, so that the dotted lines are parallel. Then the measured difference between the angles will enable us to calculate the angle subtended by the radius of the earth's orbit, as seen from the star S. This angle is what astrono-

mers habitually use in their computations, not the distance of the star. It is called the Parallax of the star. If we wish to obtain the distance of the star, we have to divide the number 206,265 by the parallax of the star expressed as a fraction of a second. This will give its distance in terms of the radius of the earth's orbit as a unit of measure. One second is the angle subtended by an object one inch in diameter at a distance of 206,265 inches, or more than three miles. It is, of course, completely invisible to the naked eye.

It will be seen that this method of measurement implies that we know which of the two stars is the nearer; in fact, that we know the farther star to be at an almost infinite distance. The question may be asked how this knowledge is obtained, and how a star is selected as being near to us. The most careful measures that can be made with the finest instruments show that the great mass of small ​telescopic stars do not have the slightest change in their relative positions, but remain as if fixed on the celestial sphere from year to year. Now and then, however, an exception is found. A very bright star is probably nearer to us than the fainter ones, and if a star shows any change in its position, the astronomer may proceed to measure and determine its parallax.

So far as has yet been determined, the nearest star to us is Alpha Centauri, a star of nearly the first magnitude, in the southern hemisphere. The parallax of this star is 0.75". By the rule we have given, its distance will be nearly 275,000 times that of the sun. Such a distance transcends all our power of conception over and over again. A crude idea of it may be obtained by reflecting that light itself, the speed of which we have already described, would require more than four years to reach us from this star. We see the latter, not as it is now, but as it was more than four years ago. At such a distance not only does the earth's orbit itself vanish away to a point, but a ball as large as the whole body of Neptune would be barely visible to the naked eye as the minutest possible point.

The next star in the order of distance is supposed to be about one half as far again as Alpha Centauri, and there are some half dozen others, within three or four times its distance. In all, the parallaxes of about one hundred stars have been determined with more or less exactness; but even in these cases the parallax is sometimes so small that we cannot be sure it is real. It seems likely that only about fifty stars are within seven times the distance of ​Alpha Centauri. The distance of the stars whose parallaxes are too small to be measured is a matter of judgment rather than calculation. The probability seems to be that at least the brighter stars are scattered through space with some approach to uniformity. If this is the case, many of the fainter telescopic stars, perhaps the large majority of the smallest ones found on photographs of the heavens, must be more than one thousand times the distance of Alpha Centauri. The light by which their presence is made known to us must have been on its way to our system during the whole period of human history.