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

108 INDIAN LUNI-SOLAR ASTRONOMY
Brāhmasphuṭa Siddhānta 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).
Though we take that Indian year was designed to be the
sidereal year, it approached most closely the anomalistic 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,¹
=365 da. 5 hrs. 55 min. 12 secs., which has an
error of about +6 min.
(2) Meton's sidereal year
= [ 365 + ¼ + 1/76 ] days²
=365 da. 6 hrs. 18 min. 57 secs. which has an
error of +9 min. 48 secs. nearly.
(3) The Babylonian sidereal-year was 4½ min. too long.³
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) / 100 ]
=1". 63 × [ (1900—150) / 100 ]²
=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 Siddhānta of the Pañca-siddhāntikā,
   VIII. 2, indicates the Sun's apogee to be at longitude of 75° ; this was per-
   haps a correction made by Lāṭadeva to the Greek constant.