The Surya Siddhanta · Chapter 6 of 8

#Eclipses

Three chapters of the Surya Siddhanta deal with eclipses: chapter IV with lunar eclipses (and the general theory), chapter V with parallax in solar eclipses, and chapter VI with drawing an eclipse.

#Sizes (IV.1–5)

The diameter of the Sun's disk is six thousand five hundred yojanas; of the Moon's, four hundred and eighty (IV.1).

These are corrected for the bodies' changing distances by their true and mean motions (IV.2–3), and the diameter of the Earth's shadow at the Moon's distance is found from the sizes of the Earth and Sun (IV.4–5).

#When an eclipse can happen (IV.6–8)

The Earth's shadow is distant half the signs from the Sun: when the longitude of the Moon's node is the same with that of the shadow, or with that of the Sun, or when it is a few degrees greater or less, there will be an eclipse (IV.6).

An eclipse needs a new or full moon near a node. The exact moment of conjunction or opposition is found from the longitudes and daily motions (IV.7–8).

#The cause (IV.9)

The Moon is the eclipser of the Sun, coming to stand underneath it, like a cloud: the Moon, moving eastward, enters the Earth's shadow, and the latter becomes its eclipser (IV.9).

A purely physical explanation, as in Aryabhata and Varahamihira.

#How much, and how long (IV.10–23)

• How much is covered: subtract the Moon's latitude from half the sum of the diameters of the eclipsed and eclipsing bodies; if the remainder exceeds the eclipsed body, the eclipse is total; if the latitude exceeds the half-sum, there is no eclipse (IV.10–11).
• How long: from the sum and difference of the two diameters and the latitude, by the right-triangle rule, the half-durations of the whole eclipse and of totality are found (IV.12–15), refined by repeated calculation.
• The moments: the middle of the eclipse, the first and last contact, and the moments of immersion into and emergence from totality (IV.16–17).
• The amount at any moment (IV.18–23).

#The deflection and the size in digits (IV.24–26)

The direction in which the eclipse appears on the disc (the "deflection") depends on the hour angle and latitude (IV.24–25); and the diameters and latitude are converted into digits (angulas) as seen, depending on the body's altitude (IV.26).

#Parallax in a solar eclipse (V)

For a solar eclipse, the Moon's position as seen from the Earth's surface differs from its position as seen from the Earth's centre — the effect of parallax, which is large for the nearby Moon. Chapter V explains when there is no parallax in longitude or latitude (V.1), its causes (V.2), and how to compute it from the "orient-sine", the "meridian-sine" and the ecliptic's zenith distance, so as to find the moment of apparent conjunction and the apparent latitude (V.3–17). This is why a solar eclipse is seen differently, or not at all, in different places.

#Drawing an eclipse (VI)

Since, without a projection, the precise differences of the two eclipses are not understood, I shall proceed to explain the exalted doctrine of the projection (VI.1).

Chapter VI teaches how to draw an eclipse on the ground or on a board: lay off the deflection and latitude for the beginning, middle and end; draw the eclipsing body's path; mark the points of contact and separation, immersion and emergence (VI.2–22). Directions are reversed in the eastern and western halves of the sky (VI.12).

#What can be seen (VI.13)

Owing to her clearness, even the twelfth part of the Moon, when eclipsed, is observable; but, owing to his piercing brilliancy, even three minutes of the Sun, when eclipsed, are not observable (VI.13).

#The colours (VI.23)

The part obscured, when less than half, will be dusky; when more than half, it will be black; when emerging, it is dark copper-colour; when the obscuration is total, it is tawny (VI.23).

#A closing caution (VI.24)

This mystery of the gods is not to be imparted indiscriminately: it is to be made known to the well-tried pupil, who remains a year under instruction (VI.24).

#Summary

• The Sun's diameter is 6,500 yojanas, the Moon's 480; the Earth's shadow at the Moon's distance is computed (IV.1–5).
• An eclipse occurs at a new or full moon near a node (IV.6); the Moon covers the Sun, the Earth's shadow covers the Moon (IV.9).
• The amount, duration and moments are found by right-triangle rules (IV.10–23); the deflection and the size in digits (IV.24–26).
• Parallax changes a solar eclipse for observers in different places (V).
• Eclipses are drawn by projection (VI); a twelfth of the Moon eclipsed is visible, three minutes of the Sun is not (VI.13); the eclipsed Moon is dusky, black, coppery or tawny (VI.23).

#Exercises

1. When can an eclipse happen, according to IV.6?
2. What causes a solar eclipse? A lunar eclipse?
3. When is an eclipse total, according to IV.11?
4. Why is a solar eclipse seen differently in different places?
5. What colours does the eclipsed Moon show?

Answers: 1. At a new or full moon, when the Moon's node is at or near the place of the Sun or the shadow (IV.6). 2. The Moon standing beneath the Sun like a cloud; the Moon entering the Earth's shadow (IV.9). 3. When half the sum of the diameters minus the latitude exceeds the eclipsed body (IV.11). 4. Because of parallax: the Moon is near, and its apparent position depends on where the observer stands (V). 5. Dusky when less than half covered, black when more, tawny when total, dark copper when emerging (VI.23).