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