पृष्ठम्:महाभास्करीयम्.djvu/१९८

SUN'S EQUATION OF THE CENTRE But T₁B₁=SB-arc SM approx. Hence it follows that the Sun's bahuphala is the same as the Sun's equation of the centre. Sun If 0 dénote the bahu due to the Sun's mean anomaly, then according to Aryabhata I and Bháskara I Sun's bahuphala p 3x3438'xsin ( 80 128'-9 sin 0 = '0375 sin 0 radians. = 3x Rsin 0 80 = (1) According to Ptolemy, the greatest equation of the centre for the 2° 23'. Therefore, according to him, Sun's equation of the centre = = According to modern astronomy, Sun's equation of the centre - 113: 2°23' sin 143' sin 0 143 sin 0 3438 0416 sin radians radians. 2e sin , where e= .0167 0334 sin 0. 9 (2) (3) neglecting e and higher powers of e. Comparison of the results (1), (2), and (3) shows that the Hindu approximation for the Sun's equation of the centre in good enough and much better than that of Ptolemy. Addition and subtraction of the bahuphala. When the Sun's mean anomaly is less than 180°, the true Sun is behind the mean Sun; and when the Sun's mean anomaly is greater than 180⁰, the true Sun is in advance of the mean Sun. Hence the Sun's bahuphala is subtractive or additive according as the Sun's mean anomaly is in the half-orbit beginning with Aries or in the half-orbit beginning with Libra. The Sun's bahuphala correction is applied to the Sun's mean longi- tude as corrected for the longitude-correction (i.e., to the Sun's mean longitude for mean sunrise at the svanirakṣa place). And after the bahuphala correction has been made, we obtain the Sun's true longitude for mean sunrise at the svanirakṣa place,