Mathematics for the Million by Lancelot Hogben

Author:Lancelot Hogben
Language: eng
Format: epub
Publisher: W. W. Norton & Company

Fig. 105. Small Circles of Latitude on the Terrestrial and of Declination on the Celestial Sphere

Thus each star can be given a position in a great imaginary sphere of the heavens, fixed by the crossing of two circles (Fig. 104), a great circle of Right Ascension (comparable to our meridian of longitude) cutting all other similar circles at the celestial poles, and a small circle of Declination (comparable to our parallels of latitude), all lying on planes at right angles to the polar axis. A circle of declination is numbered in the same way as circles of latitude by the angle which the two points where it and the celestial equator are cut by its RA meridian make at the center of the, earth (Fig. 105). What we call the earth’s polar axis is only the axis about which the stars appear to rotate, and what we call the plane of the earth’s equator is therefore only the slab of the earth where it is cut by the plane of the heavenly equator. The line which joins an observer to the center of the earth (see Fig. 59) goes through his zenith, cutting his parallel of latitude and a corresponding declination circle in the heavens. Any star on such a declination circle will pass directly above an observer anywhere on the corresponding circle of latitude once in twenty-four hours. Once the stars had been mapped out in this way to act as landmarks in navigation, it was therefore an easy step to map out the globe in a similar way.

It is important to bear in mind that mapping stars in this manner is merely a way of telling us in what direction we have to look or to point a telescope in order to see them. The position of a star as shown on the star map has nothing to do with how far it is away from us. If you dug straight down following the plumbline, you would eventually reach the center of the earth; and the bottom of a straight well, as viewed from the center of the earth, if that were possible, would therefore be exactly in line with the top. It has the same latitude and longitude as the latter, though it is not so far away from the earth’s center. The latitude or longitude of the bottom of a mine is the latitude and longitude of the spot where the line joining it with the center of the earth continued upwards cuts the earth’s surface. So the declination and right ascension of a star measure the place where the line joining the earth’s center and the star cuts an imaginary globe whose radius extends to the furthermost stars. In a total eclipse, the sun and the moon have the same declination and RA just as the top and bottom of a mine have the same latitude and longitude. This means that the sun and moon are directly in line with the center of the earth like the top and the bottom of a mine.

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