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.