पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

VI.4 VI. VĀS.-PAUL. SIDDHĀNTA -,LUNAR ECLIPSE 157 iii. Corrected time of duration = uncorrected time ± 5 × degrees of Moon ~ Rāhu in vināḍis (If Rāhu is greater use the upper sign, if less use the lower sign. Moon ~ Rāhu is what we get in verse 2, in this section). Example 1. On a day, at sunset, the longitude of the Sun is rā. 10-10-12, longitude of the Moon rā. 4-8-57, Sun's daily motion 60' and Moon's daily motion 810'. (From these the end of the full moon tithi falls at 6 nāḍis after sunset). The Tail of Rāhu at full moon is rā. 4-7-42. Examine whether a lunar eclipse will occur, and if so, find the duration. As a preliminary, the Moon at full moon should be found by verse 1, thus: The time to elapse after sunset, for full moon, is 6 nāḍis. Adding 6' to the Sun at sunset, the Sun at full moon is rā. 10- 10-12 + 6' = rā. 10-10-18. Therefore the Moon is rā. 4-10-18. Now, examine whether there will be an eclipse. Rāhu at full moon = rā. 4-7-42 (given). Corrected Rāhu = rā. 4-7-42 − 1° 36′ = rā. 4-6-6. Moon ~ corrected Rāhu = 4° 12′. As this is less than 13°, there is eclipse. Now for the work of getting the duration: i. The Moon's latitude (supposed known already) = 380′ × (rā. 4-10-18 −rā. 4-7-42 in degrees) ÷ 90° = 11′. ii. Uncorrected duration in nāḍis = √(3025 − 11²) × 120 ÷ (810 − 60) = √2904 × 120 ÷ 750 = nā. 8-37. iii. Corrected duration = nā. 8-37 − 5 × 4.2 vināḍis = nā. 8-16. (subtraction because Rāhu is less than the Moon). The following is the rationale of the procedure: We have said that, according to the Siddhānta, when the distance between the centres of the Shadow and the Moon is 55′, the eclipse begins or ends, because at these times the distances are equal to the sum of the semi-diameters. [चित्रम्: Moon's orbit, Ecliptic, M1, M, M2, A, S, B] Fig. VI. 2 See SM₁ and SM₂ in Fig 2, where S is the Shadow and M₁, M₂ are the Moon. At full moon, the latitude is the distance between the centres, at that time. (SM), because at full moon the centre of the shadow is at S, because it is always 6 rāśis distant from the Sun. Since the inclination of the orbit to the ecliptic is small, the siddhānta takes it that the orbit and the ecliptic are practically parallel, and that the latitudes of the Moon at first contact (AM₁) at full moon (SM), and at last contact (BM₂) are