The Siddhāntasundara of Jñānarāja: An English Translation with Commentary

12 Chapter on Mathematical Astronomy: Section 6 Solar Eclipses

12. Chapter on Mathematical Astronomy Section 6: Solar Eclipses After a careful discussion of lunar eclipses, this section turns to solar eclipses. Much of the material is the same, but solar eclipses are more complicated. During a lunar eclipse, the moon and the portion of the earth’s shadow obscuring it are at the same distance from the earth, and so it is not necessary to take parallax into account. For a solar eclipse, however, it is essential to compute parallax. (1) Two men, one on the surface of the earth, the other at its center, do not see the sun being covered by the moon at the same time. In the case of the man at the center of the earth, the moon reaches his line of sight toward the sun precisely at the time of conjunction of the sun and the moon; it is not so in the case of the man on the surface. Parallax is the phenomenon that a heavenly body (in our context only the planets), when viewed from the center of the earth (we will have to postulate an imaginary “observer” there, as Jñānarāja does), is not seen at the same position with respect to the fixed stars as when it is viewed from a position on the surface of the earth. This is illustrated in Figure 25, where the sun, S, and the moon, M , are observed from the location A on the surface of the earth, as well as from the center of the earth, C. Each luminary is seen differently with respect to the fixed stars. The parallax of a planet is the angle between the two lines formed by connecting the planet with, respectively, the center of the earth and the given location on the surface of the earth. In our example, the parallax of the sun is the angle ASC and 267 268 12. Chapter on Mathematical Astronomy, Section 6 S C A M      Figure 25: Parallax of the sun and the moon the parallax of the moon is the angle AMC. As can be readily seen in the figure, the closer a planet is to the earth, the greater its parallax; the parallax of the moon is significant, while that of the sun is minor (the magnitude of the parallax also depends on the position of the planet with respect to the zenith of the observer). When computing a lunar eclipse, it is not necessary to take parallax into account. The reason for this is that the effect of parallax is the same for the moon and the shadow of the earth, because they are seen at the same distance from the earth. However , since the sun and the moon are at different distances from the earth, the effect of parallax changes their positions not only with respect to the fixed stars, but also with respect to each other. As can be seen in Figure 25, for an observer at C, the moon is seen eclipsing the sun, whereas for an observer at A, at the same moment, no eclipse is seen. Parallax must therefore be taken into account in order to accurately compute a solar eclipse for a given locality. Note that the appearance of the sun and the moon as seen at C is not the same as that seen from most positions on the surface; if an observer is located at the point where the line CM intersects the surface of the earth, he will of course see what the “observer” at C sees. When it comes to the role of parallax in computing a solar eclipse, what we are interested in is the combined effect of parallax on the sun and the moon: in other words, how the effect of 12. Chapter on Mathematical Astronomy, Section 6 269 parallax changes the positions of the two luminaries with respect to each other. We will call this the combined parallax of the sun and the moon, or simply the combined parallax. In Figure 25, the combined parallax is the angle MAS, which, seen from A, is the angular distance between the sun and the moon measured against the backdrop of the fixed stars. It is easy to see that this angle is the difference of the angles AMC and ASC:  MAS = 180◦ −  AMS −  ASC = 180◦ − (180◦ −  AMC) −  ASC =  AMC −  ASC. (170) So, the...