Peripheries of epicycles in the Grahalāghava

For finding the true positions of the Sun, the Moon and the five planets the Indian classical astronomical texts use the concept of the manda 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 śīghraphala and the corresponding śīghra 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 (karaṇa) instead of giving the mathematical expressions for the above said equations, their discrete numerical values, at intervals of 15 degrees, are given. In the present paper using the data of discrete numerical values we build up continuous functions of periodic terms for the manda and śīghra equations. Further, we obtain the critical points and the maximum values for these two equations.