ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

LUNAR ASTRONOMY 109 In 500 A. D (Āryabhaṭa's time) the longitude of the Sun's apogee by the same rule works out to be=77°19'19.44". Āryabhaṭa states this to be 78° in the Āryabhaṭīya, Brahmagupta in the Uttarādhyāya of the Khaṇḍakhādyaka states the same to be 77°, while the Khaṇḍakhādyaka gives it as=80°. Hence the Indian findings of the longitude of the Sun's apogee were more accurate. Again as to the Sun's equations of the centre we find that the Āryabhaṭīya states the periphery of the Sun's epicycle to be 13°30', The Khaṇḍakhādyaka gives it as 14° ; while according to the Indian form, Ptolemy's value of the same is 15°. Hence according to these writers, the Sun's equations at 90° of the mean anomaly are :— According to the Āryabhaṭīya =2° 8' 54". ” ” Khaṇḍakhādyaka=2° 1' 40". ” ” Brahmagupta=2° 7' 20". ” ” Ptolemy=2° 23' 3". The modern value =1° 55' 97". Thus the Indian equations of the Sun are in general by more correct than the Greek ones. The Indian constants in solar astronomy are thus, generally, more accurate than the Greek ones. We now turn to the Indian Lunar astronomy. Lunar Astronomy Before discussing the constants in Indian lunar astronomy it is necessary to state something as to the time when the Moon was observed by our ancient astronomers and the astronomers from Āryabhaṭa I (499 A.D. to Pṛthūdaka Svāmī (864 A.D.). The months were reckoned from the first visibility of the crescent at the time of the Mahābhārata (1400 B. C.). We have a pass- age in the Bhīṣmaparva where Vyāsa speaks of the evil omens on the eve of the Kurukṣetra war thus— चन्द्रसूर्य्यावुभौ ग्रस्तावेकामासीं त्रयोदशीम् । "That the Moon and the Sun have been both eclipsed on the 13th days of the light and dark halves of the same month." The eclipses could not take place on the 13th days of the month unless the months were reckoned from the first visibility of the crescent. This was the custom in Babylonia and it has still survived in the Mahomedan world. Even in the Pañca siddhāntikā of Varāhamihira ( 540 A. D. ), there is a special