PERIPHERIES OF EPICYCLES IN THE <italic>GRAHALĀGHAVA</italic>

Abstract

For finding the true positions of the Sun, the Moon and the five planets the Indian classical astronomical texts use the concept of the <italic>manda</italic> epicycle which accounts for the equation of the centre. In addition, in the case of the five planets (Mercury, Venus, Mars, Jupiter and Saturn) another equation called <italic>śīghraphala</italic> and the corresponding <italic>śīghra</italic> epicycle are adopted. This correction corresponds to the transformation of the true heliocentric longitude to the true geocentric longitude in modern astronomy. In some of the popularly used handbooks (<italic>karaṇa</italic>) instead of giving the mathematical expressions for the above said equations, their discrete numerical values, at intervals of 15°, are given. In the present paper using the data of discrete numerical values we build up continuous functions of periodic terms for the <italic>manda</italic> and <italic>śīghra</italic> equations. Further, we obtain the critical points and the maximum values for these two equations.