पृष्ठम्:महाभास्करीयम्.djvu/१९६

SUN'S EQUATION OF THE CENTRE Alternative rule for the determination and application of the Sun's equation of the centre (called bahuphala): 6. Or, (find the bahuphala and) subtract the bahuphala when the (Sun's mean) anomaly is in the half-orbit beginning with Aries; and add that when (the Sun's mean anomaly is) in the half-orbit beginning with Libra. This correction should always be performed by one who seeks the true longitude (of the Sun).¹ Bāhu ( due to a planet's mean anomaly) is defined in stanza 8 below. It is the arcual distance of a planet from its apogee or perigee, whichever is nearer. The Sun's bahuphala is obtained by the following formula: (Sun's tabulated epicycle) In the adjoining figure, the bigger circle UMN, centred at the Earth E, is the Sun's mean orbit called kakṣāvṛtta (deferent); the small circles are nicoccavṛttas (epicycles); and U is the Sun's ucca (apogee). Under the epicyclic theory, the mean Sun is supposed to move on the deferent, and the true Sun is supposed to move on its epicycle (centred at the mean planet) with the same angular velocity as the mean Sun has relative to the apogee but in the opposite sense. (See the arrows). Sun's bahuphala- The Sun's tabulated epicycle is 3.² The Sun's bahuphala corresponds to the Sun's equation of the centre, which is shown by means of the Hindu epicyclic theory as follows: U1 80 Rsin (bahu due to the Sun's mean anomaly) U . 111 C E N Fig. 11 2 ¹ This rule is found to occur also in SuSi, ii. 39; SiDV, I, ii. 14; Si se, iii. 26(i). 2 Vide infra, vii. 16. It must be noted that the epicycles have been tabulated after abrading them by 41.