Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s3.88

v2.c12.s3.88

Mars and Jupiter are concerned, have given values nearer to the modern ones than those of Ptolemy. The values given in Brahma Siddhānta and Second Ārya Siddhānta are almost equal to the modern ones. The value for Saturn is wrong by a few minutes only. As regards the Vikṣepa values of Mercury and Venus, it was found that if Mercury occupies at present a position of maximum heliocentric latitude, then, at one position its radius vector attains the value of 3382 and at the other, 4114*, and if in addition to this, its distance from the earth has attained the mean value, its true latitude respectively becomes 2°23'' and 2°53.' The mean of these values comes to 2°38' and it agrees very closely with that given in our works. The radius vector of Venus at its position of maximum heliocentric latitude attains the values of 7193 and 7293. If at both these positions its distance from the earth attains the mean value, its true latitude would be about 2°28'. This also agrees with the value given in our works. The values given in the table in the column for "modern" values, were calculated by the author from the data in the English Nautical Almanacs for the six years 1883 to 1888. It was only on two or three dates during these six years that when Mercury attained maximum value for its heliocentric latitude, its distance from the earth was also equal to or very nearly equal to its mean value ; and in the case of Venus no such dates could be found. It shows that these values cannot be accurately found unless observations are taken for several years ; and for this reason our astronomers deserve praise for having found out very accurate values. The nodes of planetary orbits have got some slight motion. Hence, if the maximum values of the latitudes of planets at the time of Brahmagupta and Āryabhaṭa be calculated in the light of modern mathematics' the above Siddhānta values may perhaps prove to be nearer to the true values** than what we found in this comparison. The above verses will show that the values given by the two Āryabhaṭas are different from those given by Brahmagupta and this shows that the values have been found by them independently. It cannot be argued that the figures are different in the three cases because they have been set down at random. If no other proofs be forthcoming, even the Vikṣepa values given in the above table would be enough to show that our astronomers determined the values for inclusion in their works, actually after taking observations.