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

GRAHAYUTYADHIKĀRA Verse 1. The mean diameters of Mars, Mercury, Jupiter, Venus and Saturn are respectively 4′-45″, 6′-15″, 7′-20″, 9′, 5′-20″. Comm. Bhāskara gives us a method under verse (5) of Chandragrahaṇādhikāra, as to how the angular diameters of celestial bodies were being measured with an instrument that we may call 'protractor', describing it as follows. “यस्मिन् दिने अर्कस्य मध्यतुल्या स्फुटा गतिः स्यात् तस्मिन् दिने उदयकाले चक्रकलाव्यासार्धमितेन यष्टिद्वितयेन मूलमिलितेन तत्रस्थदृष्ट्या तदग्राभ्यां बिम्बप्रान्तौ विध्येत् “या यष्ट्यग्रयोरन्तरकलाः ता रविबिम्बकला भवन्ति मध्यमाः” ie. On the day on which the true motion of the Sun equals the mean, in the morning, observe with an instrument having two equal rods jointed at one end (and the other ends being connected by a flexible protractor marked with minutes and seconds of arc) placing the eye. at the joint of the rods, and the two rods pointing to the extremities of a diameter of the disc. The magnitude of the disc is then read on the protractor, which gives the mean diameter”. This method is alright so far as it goes. ' The measur- ing being done at the time of morning and that too with the naked eye might have been responsible for the exaggerated magnitudes of the diameters of the discs of the planets, as compared with their modern values. This kind of exaggerate estimate is due what is called the phenomenon of irradiation which increases the apparent size of a brilliant body when seen at some distance. Even Tycho Brahe, an accurate and brilliant astronomer prior to the invention of the telescope gave estimates of these angular diameters which are nearly the same as remarked by Burgess in his translation of Sūryasiddhānta under verses 13, 14 ch. VII.