On the Accuracy of some Ancient Indian Astronomical Instruments
There are references to astronomical instruments in various Indian works, from the Kātyāyana Śulbasūtra dated earlier than 350 BCE, to the later Siddhānta (mathematical astronomy) texts from the fifth century CE onwards. The simplest of these instruments is the gnomon (sañku) which initially was used for fixing the east-west direction and finding the time, and later for finding the latitude of a location, the Sun’s declination on any day, and other astronomical quantities. More advanced instruments would follow. Bhāskara-II (twelfth century) devised a board-instrument called phalakayantra to measure the hour angle of the Sun.
While these instruments have been described in the literature on history of astronomy in recent times, we are not aware of any study assessing the feasibility of construction, and the accuracy of these instruments. This paper is a very preliminary attempt in that direction. Here, we present our measurements relating to the determination of the east-west direction, and the declination of the Sun, using simple gnomons. The accuracy can be of the order of 1°, even with simple versions of them. We also report our findings on the measurement of the hour angle of the Sun, using a simple variant of the board-instrument of Bhāskara-II. At least with this version, the maximum error was of the order of 5°.
MSS is grateful to A.V. Ramani of Bengaluru for helping with the design of the ‘plumb-line gnomon’, and taking measurements with it. SV acknowledges the generous support (including but not limited to funding) from Amrita Vishwa Vidyapeetham (Amrita University), Coimbatore, in carrying out this work, and travel support for collaboration. He also acknowledges the support of Bharat K Sharma, Nandakumar, Iyappan and Yashmita of Amrita University who helped with the instrumentation and measurements. The support of Aditya of Coimbatore towards computer design of the charts and image processing is duly acknowledged.
- BāpūdevaŚāstri (ed.), and GanapatiŚāstri (revised), 2005. Siddhāntaśiromaṇi of Bhāskarācārya with his Vāsanābhāṣya. Fourth Edition. Varanasi. Chaukhambha Sanskrit Sansthan.Google Scholar
- Datta, B., 1932. The Science of the Śulba. Calcutta, Calcutta University (reprint: Cosmo Pub, 1993).Google Scholar
- Equation of time table, 2016. https://en.wikipedia.org/wiki/Equation_oftime.
- Ohashi, Y., 1993. Development of astronomical observation in Vedic and Post-Vedic India. Indian Journal of History of Science, 28, 185–251.Google Scholar
- Ohashi, Y., 1994. Astronomical instruments in classical sidhhāntas. Indian Journal of History of Science, 29, 155–313.Google Scholar
- Sen, S.N., and Bag, A.K. (eds., with English translation and commentary), 1983. Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana, and Mānava. New Delhi, Indian National Science Academy (revised edition, 2000).Google Scholar
- Sriram, M.S., 2016. Bhāskarācārya’s astronomy. In Ramasubramanian, K., Sule, A., and Vahia, M. (eds.). History of Indian Astronomy: A Handbook. Mumbai, Indian Institute of Technology, and Tata Institute of Fundamental Research. Pp. 349–378.Google Scholar
- Table of Declination of the Sun, 2016. www.sci.ccny.cuny.edu/~luo/EAS488/Table_Declination_of_the_Sun.pdf