Astronomy for Amateurs

by Camille Flammarion

The difficulty in exact measurements of the distance of a star consists in observing the little luminous point persistently for a whole year, to see if this star is stationary, or if it describes a minute ellipse reproducing in perspective the annual revolution of the Earth.

If it remains fixed, it is lost in such depths of space that it is impossible to gage the distance, and our 298,000,000 kilometers have no meaning in view of such an abyss. If, on the contrary, it is displaced, it will in the year describe a minute ellipse, which is only the reflection, the perspective in miniature, of the revolution of our planet round the Sun.

The annual parallax of a star is the angle under which one would see the radius, or half-diameter, of the terrestrial orbit from it. This radius of 149,000,000 kilometers (93,000,000 miles) is indeed, as previously observed, the unit, the meter of celestial measures. The angle is of course smaller in proportion as the star is more distant, and the apparent motion of the star diminishes in the same proportion. But the stars are all so distant that their annual displacement of perspective is almost imperceptible, and very exact instruments are required for its detection.

Fig. 84.—Small apparent ellipses described by the stars as a result of the annual displacement of the Earth.

The researches of the astronomers have proved that there is not one star for which the parallax is equal to that of another. The minuteness of this angle, and the extraordinary difficulties experienced in measuring the distance of the stars, will be appreciated from the fact that the value of a second is so small that the displacement of any star corresponding with it could be covered by a spider's thread.

A second of arc corresponds to the size of an object at a distance of 206,265 times its diameter; to a millimeter seen at 206 meters' distance; to a hair, 1⁄10 of a millimeter in thickness, at 20 meters' distance (more invisible to the naked eye). And yet this value is in excess of those actually obtained. In fact:—the apparent displacement of the nearest star is calculated at 75⁄100 of a second (0.75″), i.e., from this star, α of Centaur, the half-diameter of the terrestrial orbit is reduced to this infinitesimal dimension. Now in order that the length of any straight line seen from the front be reduced until it appear to subtend no more than an angle of 0.75″, it must be removed to a distance 275,000 times its length. As the radius of the terrestrial orbit is 149,000,000 kilometers (93,000,000 miles), the distance which separates α of Centaur from our world must therefore = 41,000,000,000,000 kilometers (25,000,000,000,000 miles). And that is the nearest star. We saw in [Chapter II] that it shines in the southern hemisphere. The next, and one that can be seen in our latitudes, is 61 of Cygnus, which floats in the Heavens 68,000,000,000,000 kilometers (42,000,000,000,000 miles) from here. This little star, of fifth magnitude, was the first of which the distance was determined (by Bessel, 1837–1840).

All the rest are much more remote, and the procession is extended to infinity.

We can not conceive directly of such distances, and in order to imagine them we must again measure space by time.

In order to cover the distance that separates us from our neighbor, α of Centaur, light, the most rapid of all couriers, takes 4 years, 128 days. If we would follow it, we must not jump from start to finish, for that would not give us the faintest idea of the distance: we must take the trouble to think out the direct advance of the ray of light, and associate ourselves with its progress. We must see it traverse 300,000 kilometers (186,000 miles) during the first second of the journey; then 300,000 more in the second, which makes 600,000 kilometers; then once more 300,000 kilometers during the third, and so on without stopping for four years and four months. If we take this trouble we may realize the value of the figure; otherwise, as this number surpasses all that we are in the habit of realizing, it will have no significance for us, and will be a dead letter.