Fig. 81.—Division of the Circumference into 360 degrees.
This problem has been solved, as follows:
Two observers go as far as possible from each other, and observe the Moon simultaneously, from two stations situated on the same meridian, but having a wide difference of latitude. The distance that separates the two points of observation forms the base of a triangle, of which the two long sides come together on the Moon.
Fig. 82.—Measurement of the distance of the Moon.
It is by this proceeding that the distance of our satellite was finally 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).