सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

46 Comm. Clear. Verse 5. The circumferences of the orbits of the Sun, Moon and the Stars. The circumference of the Sun's orbit is 4331497½ yoja- nas, that of the Moon 324000 yojanas, of the stellar sphere 259889850 yojanas. Comm. Later, we are told by Bhaskara that the cir- cumference of the earth is 4967 yojanas and its diameter is 1581. As the method given by him in the Commentary in that context, to measure the circumference of the earth is correct, we may take it that the ancient Hindu Astronomers could estimate the same correctly. If that be so, when Bhaskara gives the circumference to be 4967 yojanas, it means 4967 yoj = (3960 × 44) / 7 miles or 1 yojana = (3960 × 44) / (7 × 4967) = 5.01 miles or what is the same 1581 yoja- nas = 7920 miles ie one yojana = 5.01 miles approximately. With this measure of a yojana, the Moon's mean distance from the earth's centre should be (as given above) (324000 × 7) / 44 × 5 miles = 257725 miles approximately. This seems to be a fair estimate and we have to find out how this estimate could be made—Indeed, there are many elementary trigonometrical methods of [finding the distance of the Moon. Which of them was used by the Hindu Astronomers, we have to discuss. Bhaskara, however takes it implicitly from Brahmagupta's version. The latter does not mention from what source he derived it but simply mentions that he has resuscitated the Brahma-Siddhānta, which grew obsolete. Either he or the author of Brahma- Siddhānta must have computed this distance using trigono- metry. The following seems to be the simplest method, by which the Moon's distance was originally estimated-Refer fig. 1. Let z be the zenith-distance of the Moon as obser-