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

INFERIOR PLANETS 151 AM=arc A'M₁; MM₁ is parallel and equal to EC. As used be- fore, both the concentric and the eccentric are of the same radius. Here the mean planet M in the concentric is taken to be, deflected to M₁ due to the true motion in the eccentric circle. Join EM₁ cutting the concentric at M₂. Now let ES be joined and let S' be taken along ES, such that ES' / ES = (Śīghra periphery of the planet in degrees) / 360 = (Sun's mean distance from the Earth) / (Planets mean distance from the Sun or the Earth); ES' thus determined is called the radius of the śīghra epicycle of the superior planet. With S' as the centre and the radius equal to ES or EA describe another circle which is called the śīghra eccentric cutting ES produced at S''. Now measure the arc S''M₃ in the concen- tric=SM₂ in the concentric. The apparent superior planet is seen in the direction EM₃ from the Earth. This is the construc- tion used in Hindu astronomy calculating the geocentric longitude of any star planet. It is evident in the case of a superior planet that the eccen- tric having S' for the centre and whose radius=EA=R the standard radius for any circular orbit, is the mean orbit of the planet and S' the mean position of the Sun. In other words, in the case of a superior planet, the śīghra eccentric represents the mean orbit round the Sun. If the parallelogram CES'C' be constructed, then an equal circle described with C' as the centre is the apparent eccentric orbit of the superior planet. In the actual method of calculating the geocentric longitude of a “star planet” there are four operations given, the first two of which have the effect of changing the arc MA or rather the point A. The last two operations relate to the two displacements MM₁ and M₂M₃. We have here followed solely the construction of the eccentric circles; the same geocentric position of a superior planet could be equally well obtained by the epicyclic cons- truction. In describing the constructions for finding the position, of an inferior planet we shall follow the epicyclic construction only Inferior Planets Let E be the centre of the Earth (Fig. 18), AMS the orbit of