Astronomy for Amateurs, Camille Flammarion [best free ebook reader txt] 📗

established, in 1751 and 1752, by two French astronomers, Lalande and Lacaille; the former observing at Berlin, the latter at the Cape of Good Hope. The result of their combined observations showed that the angle formed at the center of the lunar disk by the half-diameter of the Earth is 57 minutes of arc (a little less than a degree). This is known as the parallax of the Moon.

Here is a more or less alarming word; yet it is one that we can not dispense with in discussing the distance of the stars. This astronomical term will soon become familiar in the course of the present lesson, where it will frequently recur, and always in connection with the measurement of celestial distances. "Do not let us fear," wrote Lalande in his Astronomie des Dames, "do not let us fear to use the term parallax, despite its scientific aspect; it is convenient, and this term explains a very simple and very familiar effect."

"If one is at the play," he continues, "behind a woman whose hat is too large, and prevents one from seeing the stage [written a hundred years ago!], one leans to the left or right, one rises or stoops: all this is a parallax, a diversity of aspect, in virtue of which the hat appears to correspond with another part of the theater from that in which are the actors." "It is thus," he adds, "that there may be an eclipse of the Sun in Africa and none for us, and that we see the Sun perfectly, because we are high enough to prevent the Moon's hiding it from us."

See how simple it is. This parallax of 57 minutes proves that the Earth is removed from the Moon at a distance of about 60 times its half-diameter (precisely, 60.27). From this to the distance of the Moon in kilometers is only a step, because it suffices to multiply the half-diameter of the Earth, which is 6,371 kilometers (3,950 miles) by this number. The distance of our satellite, accordingly, is 6,371 kilometers, multiplied by 60.27—that is, 384,000 kilometers (238,000 miles). The parallax of the Moon not only tells us definitely the distance of our planet, but also permits us to calculate its real volume by the measure of its apparent volume. As the diameter of the Moon seen from the Earth subtends an angle of 31′, while that of the Earth seen from the Moon is 114′, the real diameter of the orb of night must be to that of the terrestrial globe in the relation of 273 to 1,000. That is a little more than a quarter, or 3,480 kilometers (2,157 miles), the diameter of our planet being 12,742 kilometers (7,900 miles).

This distance, calculated thus by geometry, is positively determined with greater precision than that employed in the ordinary measurements of terrestrial distances, such as the length of a road, or of a railway. This statement may seem to be a romance to many, but it is undeniable that the distance separating the Earth from the Moon is measured with greater care than, for instance, the length of the road from Paris to Marseilles, or the weight of a pound of sugar at the grocer's. (And we may add without comment, that the astronomers are incomparably more conscientious in their measurements than the most scrupulous shop-keepers.)

Had we conveyed ourselves to the Moon in order to determine its distance and its diameter directly, we should have arrived at no greater precision, and we should, moreover, have had to plan out a journey which in itself is the most insurmountable of all the problems.

The Moon is at the frontier of our little terrestrial province: one might say that it traces the limits of our domain in space. And yet, a distance of 384,000 kilometers (238,000 miles) separates the planet from the satellite. This space is insignificant in the immeasurable distances of Heaven: for the Saturnians (if such exist!) the Earth and the Moon are confounded in one tiny star; but for the inhabitants of our globe, the distance is beyond all to which we are accustomed. Let us try, however, to span it in thought.

A cannon-ball at constant speed of 500 meters (547 yards) per second would travel 8 days, 5 hours to reach the Moon. A train started at a speed of one kilometer per minute, would arrive at the end of an uninterrupted journey in 384,000 minutes, or 6,400 hours, or 266 days, 16 hours. And in less than the time it takes to write the name of the Queen of Night, a telegraphic message would convey our news to the Moon in one and a quarter seconds.

Long-distance travelers who have been round the world some dozen times have journeyed a greater distance.

The other stars (beginning with the Sun) are incomparably farther from us. Yet it has been found possible to determine their distances, and the same method has been employed.

But it will at once be seen that different measures are required in calculating the distance of the Sun, 388 times farther from us than the Moon, for from here to the orb of day is 12,000 times the breadth of our planet. Here we must not think of erecting a triangle with the diameter of the Earth for its base: the two ideal lines drawn from the extremities of this diameter would come together between the Earth and the Sun; there would be no triangle, and the measurement would be absurd.

In order to measure the distance which separates the Earth from the Sun, we have recourse to the fine planet Venus, whose orbit is situated inside the terrestrial orbit. Owing to the combination of the Earth's motion with that of the Star of the Morning and Evening, the capricious Venus passes in front of the Sun at the curious intervals of 8 years, 1131⁄2 years less 8 years, 8 years, 1131⁄2 years plus 8 years.

Thus there was a transit in June, 1761, then another 8 years after, in June, 1769. The next occurred 1131⁄2 years less 8 years, i.e., 1051⁄2 years after the preceding, in December, 1874; the next in December, 1882. The next will be in June, 2004, and June, 2012. At these eagerly anticipated epochs, astronomers watch the transit of Venus across the Sun at two terrestrial stations as far as possible removed from each other, marking the two points at which the planet, seen from their respective stations, appears to be projected at the same moment on the solar disk. This measure gives the width of an angle formed by two lines, which starting from two diametrically opposite points of the Earth, cross upon Venus, and form an identical angle upon the Sun. Venus is thus at the apex of two equal triangles, the bases of which rest, respectively, upon the Earth and on the Sun. The measurement of this angle gives what is called the parallax of the Sun—that is, the angular dimension at which the Earth would be seen at the distance of the Sun.