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

X.2 X. SAURA-SIDDHĀNTA — LUNAR ECLIPSE 229 Or, (since the arc is small, multiplying this by 3438 and dividing by 120), the angular diameter of the Shadow in minutes = 1,23,768 ÷ Moon's true distance − 3,93,307 ÷ Sun's true distance. Example 1. On a certain day at the time of full moon (T) the true Sun is rā. 10-0-0, the true Moon is rā. 4-0-0, Rāhu Head is rā. 3-25-0, the Sun's motion per day for the time is 60′, and the Moon's 780′. Compute the lunar eclipse. The Sun's true dist. = 9,48,558 ÷ 60 = 15,809 (by IX.15). The Moon's true dist. = 9,48,680 ÷ 780 = 1216.3 (by IX.15). The Moon's angular dia. = 38,640 ÷ 1216.3 = 31′.77 (by IX.16). The Moon's lat. at T = 9 × sine (rā. 4-0-0 − rā. 3-25-0) ÷ 4 = 23′.5, north. From the true distances got above, the angular diameter of the Shadow = 1,23,768 ÷ 1216.3 − 3,93,307 ÷ 15,809 = 101′.76 − 24′.88 = 76′.9. The following is the explanation of the method for finding the Moon's angular diameter: The actual diameter of the Shadow is the diameter of the circular section of the Shadow-cone (formed by the earth intercepting the Sun's light,) at the Moon's orbit, at the time of full moon. This is represented in fig. 1, below by U′U″. Fig. X. 1 The angle subtended by this at the centre of the earth, E, is the angular diameter desired to be computed here. In the figure, S is the centre of the Sun, E, that of the Earth, and U that of the Shadow section. SS′ is the Sun's radius, EE′ is the Earth's, and UU′ is that of the Shadow. SE is the true distance of the earth from the Sun, and EU, that of the Moon from the earth. S′E′U′ is the direct common tangent to the orbs of the Sun and the Moon. As the distance are very great when compared with the radii, EE′, SS′, and UU′ are practically parallel. Draw ES″ parallel to E′S′, and U′E″ parallel to U′E′. The triangles, ES″S and UE″E, are similar. Therefore, E″E/EU = S″S/SE.