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

VII.1 VII. PAULIŚA-SIDDHĀNTA — SOLAR ECLIPSE 173 the Moon. These being given with reference to the centre of the earth, the angular distance calcu- lated is as seen by an observer at the centre of the earth. But we want the distance as seen by an observer on the surface of the earth, and a correction has got to be made for this. This is correction for parallax or simply parallax. See Fig. 1-a. Z D | / | / | / | / | / S | / / P | / / .---. / / / | \ / M / | X / | | / \ / | | / \ / | C / \ / C Earth's centre \ / / P Position of observer \ / / Z Zenith '---' M Moon S Sun Fig. VII. 1-a. (Note: The figure is only diagrammatic and does not represent actual distances). PD = a line drawn parallel to CM. The observer at C sees the Moon along CM, and for him the Moon’s zenith distance (z.d.) is ZCM (= ZPD). But the observer at P sees the Moon along PM, and its z.d. for him is ZPM. This is equal to ZPD + DPM = ZCM + PMC, and PMC is the parallax correction to ZCM. It can be seen that the parallax correction for the Sun is PSC, and less than that for the Moon. It is actually about 2/27 of the parallax of the Moon, according to the Hindu Siddhāntas, its distance being about 27/2 times that of the Moon, according to them. (It must be noted that actually the Sun’s distance is about 390 times the Moon’s, and accordingly the Sun’s parallax is about 9", and practically negligible). The amount of parallax, PMC can be calculated trigonometrically thus: Sin PMC/PC = sin CPM/CM = sin (PCM + PMC)/CM = sin PCM/CM (∵ PMC is small). Sin PMC = sin CPM × PC/CM. Arc PMC × 120/57.3 = sin CPM × PC/CM (∵ PMC is small). Parallax of Moon in minutes = sin z.d. × (PC/CM) × 60 × 57.3

120 = sin z.d. × 28.65 × Earth’s radius/Moon’s distance. Similarly, the Sun’s parallax in minutes = sin z.d. × 28.65 × Earth’s distance ÷ Sun’s distance.