Astronomy: The Science of the Heavenly Bodies

by David P. Todd

How the distances of the stars are found is not difficult to explain, although the method of doing it involves a good deal of complication, interesting to the practical astronomer only. Recall the method of getting the moon's distance from the earth: it was done by measuring her displacement among the stars as seen from two widely separated observatories, as near the ends of a diameter of the earth as convenient. This is the base line, and the angle which a radius of the earth as seen from the center of the moon fills, or subtends, is the moon's parallax.

So near is the moon that this angle is almost an entire degree, and therefore not at all difficult to measure. But if we go to the distance of even Alpha Centauri, the nearest of the stars, our earth shrinks to invisibility; so that we must seek a longer base line. Fortunately there is one, but although its length is 25,000 times the earth's diameter, it is only just long enough to make the star distances measurable. We found that the sun's distance from the earth was 93 million miles; the diameter of the earth's orbit is therefore double that amount. Now conceive the diameter of the earth replaced by the diameter of the earth's orbit: by our motion round the sun we are transported from one extremity of this diameter to the opposite one in six month's time; so we may measure the displacement of a star from these two extremities, and half this displacement will be the star's parallax, often called the annual parallax because a year is consumed in traversing its period. And it is this very minute angle which Bessel and Struve were the first to measure with certainty, and which Henderson found to be in the case of Alpha Centauri the largest yet known.

Evidently the earth by its motion round the sun makes every star describe, a little parallactic ellipse; the nearer the star is the larger this ellipse will be, and the farther the star the smaller: if the star were at an infinite distance, its ellipse would become a point, that is, if we imagine ourselves occupying the position of the star, even the vast orbit of the earth, 186 million miles across, would shrink to invisibility or become a mathematical point.

Measurement of stellar parallax is one of many problems of exceeding difficulty that confront the practical astronomer. But the actual research nowadays is greatly simplified by photography, which enables the astronomer to select times when the air is not only clear, but very steady for making the exposures. Development and measurement of the plates can then be done at any time. Pritchard of Oxford, England, was among the earliest to appreciate the advantages of photography in parallax work, and Schlesinger, Mitchell, Miller, Slocum and Van Maanen, with many others in this country, have zealously prosecuted it.

How shall we intelligently express the vast distances at which the stars are removed from us? Of course we can use miles, and pile up the millions upon millions by adding on ciphers, but that fails to give much notion of the star's distance. Let us try with Alpha Centauri: its parallax of 0".75 means that it is 275,000 times farther from the sun than the earth is. Multiplying this out, we get 25 trillion miles, that is, 25 millions of million miles—an inconceivable number, and an unthinkable distance.

Suppose the entire solar system to shrink so that the orbit of Neptune, sixty times 93 million miles in diameter, would be a circle the size of the dot over this letter i. On the same scale the sun itself, although nearly a million miles in diameter, could not be seen with the most powerful microscope in existence; and on the same scale also we should have to have a circle ten feet in diameter, if the solar system were imagined at its center and Alpha Centauri in its circumference.

So astronomers do not often use the mile as a yardstick of stellar distance, any more than we state the distance from London to San Francisco in feet or inches. By convention of astronomers, the average distance between the centers of sun and earth, or 93 million miles, is the accepted unit of measure in the solar system. So the adopted unit of stellar distance is the distance traveled by a wave of light in a year's time: and this unit is technically called the light-year. This unit of distance, or stellar yardstick, as we may call it, is nearly 6 millions of million miles in length. Alpha Centauri, then, is four and one-third light-years distant, and 61 Cygni seven and one-fifth light-years away.

For convenience in their calculations most astronomers now use a longer unit called the parsec, first suggested by Turner. Its length is equal to the distance of a star whose parallax is one second of arc; that is, one parsec is equal to about three and a quarter light-years. Or the light-year is equal to 0.31 parsec. Also the parsec is equal to 206,000 astronomical units, or about 19 millions of million miles.

We have, then four distinct methods of stating the distance of a star: Sirius, for example, has a parallax of 0".38 or its distance is two and two-thirds parsecs, or eight and a half light-years, or 50 millions of million miles. It is the angle of parallax which is always found first by actual measurement and from this the three other estimates of distance are calculated.

So difficult and delicate is the determination of a stellar distance that only a few hundred parallaxes have been ascertained in the past century. The distance of the same star has been many times measured by different astronomers, with much seeming duplication of effort. Comprehensive campaigns for determining star parallaxes in large numbers have been undertaken in a few instances, particularly at the suggestion of Kapteyn, the eminent astronomer of Groningen, Holland. His catalogue of star parallaxes is the most complete and accurate yet published, and is the standard in all statistical investigations of the stars.