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Chaya Ganita In Hinduism – Calculations Based On Shadow

Chaya Ganita, calculations based on shadow in Hinduism, has its roots in man’s observation of the changes in his own shadow during daytime. Starting from the gnomon, this science grew to the extent of using sophisticated astronomical instruments.

In Atharva Jyotisha, muhurtas (time divisions) are defined in terms of the shadow of gnomon of twelve angula (finger) size.

Details of chayaganita for determining accurately the cardinal points, time, seasons, length of year, obliquity, ascendant etc., have been given in all the texts of mathematical astronomy, which appeared around 4th century AD or even earlier.

For instance, when the sun is at the equinox, its meridional zenith distance is equal to the latitude of the observer. This can be obtained by measuring the equinoctial shadow cast by a gnomon, from which declination of the sun can be calculated. Following this, the obliquity of the ecliptic with the equator could be calculated to be 24 degrees. These methods are further elaborated in medieval astronomical works.

Ganesha Daivajna (1522 AD) constructed the Pratodayantra, essentially a horizontal gnomon, for geometrical calculations based on the shadows cast by it.

Later, triangular gnomons, in the form of sundials with slanting styles, were also developed, which formed a significant constituent of the Samratyantra of Jai Singh (1724 AD).

Another application of chayaganita lies in understanding the eclipses. Varahamihira (535 AD) explains that the real cause of lunar eclipse is the entry of the moon into the earth’s shadow, and likewise  at the solar eclipse the moon enters between the sun and the earth.
Aryabhata I has described the formulae for calculating the length and diameter of the shadows cast, conditions and the duration of eclipses.

Notes taken from
  • Sen, S.N. 1971 ‘Astronomy’ In A Concise History of Science in India (ed.) D. M. Bose, S. N. Sen, and B. V. Subbarayappa. New Delhi: Indian National Science Academy.
  • Encyclopedia of Hinduism Volume III page 157-58 – IHRF




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