138 TRUE LONGITUDE OF A PLANET We explain below the motion of the planets, Mars, Mercury, Jupiter Venus, and Saturn, according to the Hindu epicyclic theory. U Consider Fig. 14. E is the Earth. The bigger circle USM centred at E is the deferent (kakṣāvṛtta). The point U on the deferent is the planet's mandocca (apogee). M is the position of the mean planet which is supposed to move on the deferent with mean velocity from west to east (in the anticlockwise direction indicated by an arrow). The small circle centred at M is the planet's manda epicycle corresponding to the position M of the mean planet: this manda epicycle is determined as taught in stanzas 38-39(i). EC is equal to MM₁, M₂ and C are joined by a line which intersects the deferent at the point S. MM, and ES are produced to meet at the point T'. This point T' is, according to the Hindu astronomers, the position of the true-mean planet. The so called true-mean planet is assumed to move on the periphery of the true epicycle of radius MT' centred at M with the same velocity as the mean planet has relative to the apogee but in the opposite sense (i.e., clock- wise). The point S denotes the position of the true-mean planet on the deferent. C E N Fig. 14 sum or difference as the correct longitude of the planet's mandocea. There- from calculate the arc corresponding to the planet's mandakendraphala and apply that to the planet's mean longitude. Thus is obtained the planet's true-mean longitude. Then calculate the arc derived from the planet's sighrakendraphala and apply that to the true-mean longitude of the planet. Then is obtained the true longitude of the planet (Mercury or Venus). The rule stated in stanza 44 occurs also in Ā, iii. 24; LBh, ii. 37-38; and SiDV, I, li. 35. The method prescribed here for finding the true longitudes of Mercury and Venus has been prescribed for all the planets in the Karana-prakāśa (li (b). 3, 4), the Graha-läghava (ili. 10), the Ravi- siddhanta-manjart (ii. 1), and the Karana-kaustubha (iii. 19), etc., all of them being calendrical works,
