INDIAN LUNI-SOLAR ASTRONOMY Brahmasphuta Siddhanta of Brahmagupta. Now the mean sidereal year =365 da. 6 hrs. 9 mins. 9.3 secs. (Lockyer). The mean anomalistic year = 365 da. 6 hrs. 13 mins. 49.3 secs. (Lockyer). The mean tropical year -365 da. 5 hrs. 48 mins. 46.054 secs. (Lockyer). 108 Though we take that Indian year was designed to be the sidereal year, it approached most closely the anomalístic year; and its excess over the sidereal year was about 3 minutes. From this consideration it appears that the Indian astronomers were justified in taking the Sun's apogee to be fixed. Against the error of+3 min. in the Indian sidereal year. we may point out that (1) The Hipparchus-Ptolemy tropical year 365 da. 14 48" in sexagesimal units. 365 da. 5 hrs. 55 min. 12 secs., which has an error of about+6 min. (2) Meton's sidereal year = [365+++6 days 76 365 da. 6 hrs. 18 min. 57 secs, which has an error of +9 min. 48 secs. nearly. (3) The Babylonian sidereal-year was 4 min. too long. Thus the Indian value of it is closer to the true value. Again in 150 A.D. the longitude of the Sun's apogee according to the Conn. des Temps was =101° 13′ 15″. 17-6189". 03 (1900-150) =1*.63 x 1900-150" 100
= 71° 16′26° 37 while Ptolemy states it to be 65° 30' which was wrong by-5° 36' 27": 1. Syntaxis, Karl Manitius's edition, Vol. I. p. 146. 2. Ibid, p. 145. 3. Encyclopaedia Britannica, History of Astronomy, 4. Syntaxis, Vol. I. p. 148. The Romaka Siddhanta of the Panca-siddhantika, VIII. 2, indicates the Sun's apogee to be at longitude of 75°; this was per- haps a correction made by Latadeva to the Greek constant.