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

300 BRAHMAGUPTA'S ASTRONOMY : ITS HIGHLIGHTS +13 (Sun's mean longitude) This expression may be rearranged to get the mean longitude of the Sun from the mean longitude of the Moon¹. Mean longitude of the Sun = 1/13 [mean longitude of the Moon

• ((intercalary months in a yuga) × ahargaṇa / civil days in a yuga) revolutions] Calculating the Mean Longitudes of the Sun and the Moon without using Ahargaṇa Bhāskara I follows the method of Āryabhaṭa I and the same method more or less has been adopted by Brahmagupta in calculating the mean longitudes of the Moon and the Sun without the use of ahargaṇa. The method may be described thus : Reduce the years elapsed since the beginning of kali- yuga to months and add to them elapsed months of the current year. Then multiply the sum by 30 and add the product to the number of lunar days elapsed since the beginning of the current month. Multiply that sum by the number of intercalary months in a yuga and divide by the number of solar months in a yuga reduced to days; the quotient denotes the number of intercalary months elapsed. The remainder is the adhimāsaśeṣa. Multiply the complete intercalary months thus obtained by 30 and to the product add the number of solar days elapsed since the beginning of kaliyuga² : then multiply that sum by the number of omitted lunar days in a yuga and divide by the number of lunar days in a yuga ; the remainder obtained is the avamaśeṣa called āhnika. Then multiply the avamaśeṣa

1. कुमुदतीनां सुहृदोऽधवाऽऽगतं विशोध्य शेषस्य लवस्त्रयोदशः । स मध्यमार्को गणकैर्निरूप्यते गुरुप्रसादात्प्रति बुद्ध बुद्धिभिः ॥ MBh. I. 11-12
2. By the number of solar days here is meant the number obtained above by reducing the years elapsed since the beginning of kaliyuga to months, then adding to them the number of months elapsed since the beginning of the current year, then multiplying the sum by 30, and then adding to the product thus obtained the number of lunar days elapsed of the current month.