iCHSTM 2013 Programme • Version 5.3.6, 27 July 2013 • ONLINE (includes late changes)
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The implication of Asakrt-karma on planetary orbit
Ramasubramanian K. | Indian Institute of Technology Bombay, India

The Indian astronomers have been employing a certain mathematical technique called asakrt-karma in order to deal with the problem of interdependence among the variables involved in planetary computations. This technique is essentially an iterative procedure that may also be conceived as the method of successive approximation that converges to a limiting value. The term asakrt-karma---literally meaning `doing more than once'---is also called avisesa-karma in the sense that this iterative process is to be carried out till we get consecutive values that are very close to each other. That is, the successive values do not differ from each other (avisesa), upto a specified degree of accuracy.
Among the astronomical works that are extant today, the earliest one that provides a systematic exposition of the method of asakrt-karma, is Maha-bhaskariya of Bhaskara (c.~7th century). During the talk we will provide a clear exposition of this procedure as described by Bhaskara in the context of computing the manda-sphuta-graha (the longitude of the planet corrected for the eccentricity of its orbit) and also study the convergence of the iterative process. We will also discuss the physical significance of doing asakrt-karma in terms of the geometry of the planetary orbit.