On the Accuracy of some Ancient Indian Astronomical Instruments

Abstract

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°.