104. Height of the lunar mountains.—Attention has already been called to the detached mountain peaks, which in [Fig. 55] prolong the range of Apennines into the lunar night. These are the beginnings of the Caucasus mountains, and from the photograph we may measure as follows the height to which they rise above the surrounding level of the moon: [Fig. 62] represents a part of the lunar surface along the boundary line between night and day, the horizontal line at the top of the figure representing a level ray of sunlight which just touches the moon at T and barely illuminates the top of the mountain, M, whose height, h, is to be determined. If we let R stand for the radius of the moon and s for the distance, T M, we shall have in the right-angled triangle M T C,
R2 + s2 = (R + h)2,
and we need only to measure s—that is, the distance from the terminator to the detached mountain peak—to make this equation determine h, since R is already known, being half the diameter of the moon—1,081 miles. Practically it is more convenient to use instead of this equation another form, which the student who is expert in algebra may show to be very nearly equivalent to it:
| h (miles) | = | s2 / 2163, |
| or h (feet) | = | 2.44 s2. |
Fig. 61.—Occultations and the moon's atmosphere.
The distance s must be expressed in miles in all of these equations. In [Fig. 55] the distance from the terminator to the first detached peak of the Caucasus mountains is 1.7 millimeters = 52 miles, from which we find the height of the mountain to be 1.25 miles, or 6,600 feet.