Astronomy and Cosmology

Author(s): L C Jain
Publisher: Rajasthan Prakrit Bharti Sansthan Jaipur

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neglect in the precision of the motion of the sun against the background of stars led them to inconsistant and incompatible results, in course of time. They took 1830 days in their yuga of five years whereas it ought to have been 1826.2819 civil days, leading to a deficit of about a tithi in course of five years, 129 From Ganitānuyoga, pp. 303-305, the hours passed after 365 th day of the year is 5.81 hours, when the next year starts.
4. EVOLUTION OF EPICYCLES
The motion of the moon or the sun as described in Parkrit texts comprises of two motions : the rotation of the earth, which in turn, relatively gives a kinematic view of them; the other is their motion along the fixed stars. Both these, unified as one, were manipulated by the ancient school, through motion in circles for each day, with a constant radius, varying from day to day. Actually, due to the continuity of the motion, the geometrical figure of the path comes out to be an spiro-elliptic one, winding and
ft go unwinding. Its equation may be written in the form r=;
h+k Cos A, where
r is the radial distance of the sun from the earth, 0 is the angle through which it turns and f, g, h are constants. The dynamical laws found from the above are those of Newton, Einstein and one more, of attraction. 130
It is not known exactly, how this system further contributed or did not contribute to the development of the theory of eccentric and epicycles in Greece. If the Greek came to know about independent rotation of the earth, they must have tried to analyse the motion in two parts or through two types of circles. Or, if they wanted to trace the spiro-elliptic path through two circles, they must have planned to trace the path which had approximated simply as a circle for the specific day. As their geometry had become perfect by that time, it was not difficult for them to analyse the unified motion into two parts. Such attempts could also not be denied for India, but the records appear to start from the period of Āryabhaţa-I. Yet the yuga system was given, perhaps a priority, in which again, there were cycles, of periodic character, based on the following siddhāntas; as found by A. N Singh, 131
129 Cf. Dixit, op. cit., pp. 129-131. Cf. also, Petri, W., op. cit., for colours
of lunar eclipses. 130 Cf. Jain, L. C., [17], op. cit. 131 Cf. Radhakrishan, S., op. cit., article by Singh on Mathematics and
Astronomy, pp. 444 et seq., in History of Philosophy, Eastern and Western, London, 1957.
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