500 Years of Tantrasangraha: A Landmark in the History of Astronomy

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The year 2000 was the five-hundredth anniversary of the composition of the celebrated astronomical textTantrasangrahaby the renowned Kerala astronomer Nilakantha Somayaji (c. 1444-1545 AD) of Trikkantiyur. Tantrasangraharanks along with Aryabhatiya (c. 499 AD) of Aryabhata and Siddhantasiromani (c. 1150AD) of Bhaskaracharya as one of the major works which significantly influence all further work on Astronomy in India.

In Tantrasangraha, Nilakantha introduced a major revision of the traditional Indian planetary model. He arrived at a unified theory of planetary latitudes and a better formulation of the equation of centre for the interior planets (mercury and Venus) than was available, either in the earlier Indian works, or in the Islamic or European traditions of Astronomy till the work of Kepler. In his other worksGolasara, Siddhantadarpana and Aryabhatiyabhasya,Nilakantha outlined the geometrical picture of planetary motion that follows from his model. According to this picture, the five planets Mercury, Venus, Mars, Jupiter and Saturn go around the Sun which in turn goes around the Earth.

During 11-13 March, 2000, the Department of Theoretical Physics, University of Madras, organised a Conference to celebrate the 500th Anniversary of Tantrasangraha,in collaboration with the Inter-University Centre of the Indian Institute of Advanced Study, Shimla. The Conference turned out to be an important occasion for highlighting and reviewing the recent work on the achievements in Mathematics and Astronomy of the Kerala school and the new perspectives in History of Science, which are emerging from these studies. This volume is a compilation of the important papers presented at this Conference.

PROF. M. S. SRIRAM did his Ph.D. in Theoretical Physics in 1978 at IIT Kanpur. He taught in the University of Allahabad for 5 years before joining the University of Madras where he has been working for the past sixteen years. His research interests include High energy physics, Nonlinear dynamical systems and Indian Astronomy and Mathematics.

DR. K. RAMASUBRAMANIAN completed his Ph.D. in 2001 at the Department of Theoretical Physics, University of Madras where he is working as a Research Associate in an Indian National Science Academy Project on Tantrasangraha. Apart from his interests in Nonlinear dynamics and Indian Astronomy and Mathematics, he is a scholar in Advaita-Vedanta sastra.

PROF. M.D. SRINIVAS did his Ph.D. in theoretical Physics in 1976 at the University of Rochester. He has taught in the University of Madras for over 20 years. He has worked on foundations of quantum mechanics and quantum optics, and is now engaged in a study of various aspects of Indian tradition including Astronomy and Mathematics. Currently he is the Chairman of the Centre for Policy Studies, Chennai.

The year 2000 AD happens to be the five-hundredth anniversary of the composition of the celebrated astronomical text Tantrasangraha by the renowned Kerala astronomer Nilakantha Somayaji (c. 1444 - 1545 AD) of Trikkantiyur. Tantrasangraha ranks along with Aryabhatiya (c. 499 AD) of Aryabhata and Siddhantasiromani (c. 1150 AD) of Bhaskaracharya as one of the major works which significantly influenced all further work on Astronomy in India.

The Kerala School of Jyotisha, starting with Madhava of Sangamagrama (c. 1340-1425 AD), is well-known for its pioneering work on mathematical analysis, especially the discovery of infinite series for sine and cosine functions and the development of fast convergent approximations for them. Their significant contributions in Astronomy, especially in planetary theory, the computation of eclipses and spherical astronomy, are being highlighted only by some recent studies.

In Tantrasangraha, Nilakantha Somayaji introduced a major revision of the traditional Indian planetary model. He arrived at a unified theory of planetary latitudes and a better formulation of the equation of centre for the interior planets (Mercury and Venus) than was available, either in the earlier Indian works, or in the Islamic or European traditions of Astronomy till the work of Kepler, which was to come more than a hundred years later. Thus the composition of Tantrasangraha in 1500 AD is indeed a major landmark in the History of Astronomy.

In his later works, Golasara, Siddhantadarpana and the famous Aryabhatiyabhashya, Nilakantha also discussed the geometrical picture of planetary motion, implied by his computational scheme, according to which the five planets, Mercury, Venus, Mars, Jupiter and Saturn go in eccentric orbits around the mean Sun, which in turn goes around the Earth. Apart from introducing the improved planetary model, Tantrasangraha also presents a systematic exposition of all aspects of the Indian tradition of mathematical astronomy in about 432 verses. It includes several novel and more accurate results on the computation of instantaneous velocities of planets (including the well-known result for the derivative of the inverse-sine function), of eclipses, and a host of other quantities in spherical astronomy. It is clearly the most important treatise on Astronomy composed by the Kerala School of Astronomers. Sankara Variyar, in his commentary Laghuvivritti (c. 1556 AD) on