Astronomy in Ancient India- with special reference to Arya Bhatiyam
By Prof. S Balachandra Rao

Jyotisha in common parlance today is used to mean 'predictive astrology; but, in ancient India it was used as a synonym for Astronomy, of which Mathematics was a part. 

Why did ancient Indians study celestial objects?That part of the Vedas, called Purva Mimamsa, deals mainly with the performance of yagnas (sacrifices).  The time of the sacrifice always had to be precisely fixed, and days in the Vedic period were reckoned in terms of the nakshatras (stars). To perform sacrifices knowledgeably, it was important to be conversant with time and direction. It was imperative, therefore, that Jyotisha, or the study of the motion of celestial objects, was properly understood.  

For us, today, it is important to know about astronomy in ancient India so as to appreciate the Indian approach to Science and the remarkable achievements of our astronomers of yore, whose efforts, unfortunately, were not followed up.

Vedanga Jyotisha is the earliest available Indian text on astronomy.  Based on the astronomical observations in the text, the book has been dated to the 14th century BC, or the last part of the Vedic Age.   It is written in a language that is comparable to Kalidasa, rather than the Vedic Sanskrit.  

After Vedanga Jyotisha, there are no complete texts on astronomy available up to the date of the Aryabhatiyam, that is the 5th century AD, except the Siddhantas, which, though compiled by Varahamihira as the Panchasiddhantika in the 6th century AD, actually evolved in the beginning of the Christian era and were originally 18 in number.    


Aryabhatiyam has 121 sutras, which are very difficult to understand by themselves, though they are very brief.  Bhaskara's commentary explained these aphorisms  of

Aryabhatta I.  In 1976, to commemorate the 1500th birth anniversary of Aryabhatta, INSA published English and Hindi translations of Aryabhatiyam and Bhaskara's commentary as well.  But, you'd be lucky if you could find an Aryabhatiyam now in any language - Sanskrit, English or Hindi! 

As Aryabhatiyam is written in the form of shlokas, the author uses a standardised, innovative method of substituting letters from the Sanskrit lexicon for representing numbers, so that the chandas, or metrics, are maintained, making the text easy to memorize.  For example, the first line of the stanza in which Aryabhatta gives the rule for the formation of the sine table reads:

Makhi bhakhi phakhi dhakhi Nakhi Gnakhi…..,

to indicate that (the R sine differences in the minutes of an arc are)

225, 224, 222, 219, 215, 210…….. 

Some of the important findings of Arybhatta, which had application in Astronomy, are listed here: 

¨       He gave the value of P correct to four decimal places, but more importantly, mentioned that this value could only be 'asanna', or approximate!  It was only a 1000+ years after Aryabhatta that the western world came to recognise this feature of P!

¨      In just one stanza (the first line of which you would have read in the previous para), he gives the rule for drawing up the sine table for values of angles from 0 degrees to 90 degrees, at intervals of 3º45'.

¨       Disagreeing with the majority of his time, he stated that the earth is circular in all directions - "Bugolah sarvato vruttah", he said.

¨      He was the first Indian astronomer to recognise that the earth and other planets are not self-luminous: "Halves of the globes of the earth and the planets are dark due to their own shadows; the other halves facing the sun are bright," he said.

¨    He explicitly mentions that the luminous heavenly bodies, despite being stationary appear to move from east to west - "Achalani bhani samapashchimagani", he said.

¨      He gave a remarkably accurate measure of the period of one rotation of the earth with reference to the fixed stars in the sky, as 23hours, 56minutes, 4.1seconds.  The corresponding modern value is 23hours, 56minutes, 4.091seconds!

¨       He has computed the number of revolutions likely to be made by the planets in one mahayuga, the traditional duration of which time period is considered as being 43,20,000 years. 

The scientific temperament of ancient Indian astronomers

A serious criticism against ancient Indian astronomers is that they were not scientific observers but only mathematical manipulators.  However, a detailed study of the original texts of the earliest works on astronomy and an appraisal of the observation methodology and attitude of the astronomers reveals their strong scientific basis. 

¨       The Yajurveda recognised that a year comprised 12 solar months and 6 seasons (rtus) (See box for Vedic nomenclature of seasons and corresponding months) 



vedic Solar Months

Julian calendar months(Approx.)



Madhu, Madhava

February 19 - April 19



Shukra, Suchi

April 20 - June 20



Nabhas, Nabhasya

June 21 - August 22



Sahas, Sahasya

August 23 - October 23


Dewy/ Snowy

Isa, Urja

October 24 - December 21



Tapas, Tapasya

December 22 - February 18

¨       The Vedic astronomers also noted that the shortest day was at the winter solstice when the seasonal year, Sisira began, with Uttarayana and rose to the maximum at the summer solstice.

¨       The Vedangajyotisa gives the duration of the longest and the shortest days and a number of other astronomical computations such as the time taken by the Sun and Moon to transit through a nakshatra, which were required for practical application by the people of that age, in their day to day lives.

¨       The Kerala astronomer, Paramesvara (1360-1455), a prolific writer, made astronomical observations for 55 long years and recorded many of his findings in his works.  Besides revising existing parameters to be more exact, he also said that his computations had to be periodically revised in keeping with the time period.

¨       Aryabhatta boldly differed from the puranic theory of creation and destruction of the universe and maintained that time is anadi, or continuous - without beginning or end.

¨       Bhaskara, speaking against those who blindly believed in tradition, asserted, "It will be impossible to believe in whatever is said earlier unless every erroneous statement is criticised and condemned."

¨       Ganesha Daivajna (1507 AD) whose computations are used to this day to draw up panchangas in North India, and even north Karnataka, reasoned that shastras, which are accurate in one era, become inaccurate over time, and therefore need periodical correction. 

The Hindu calendar (panchanga), which began as a simple compilation of celestial observations relevant to the contemporary needs of the Vedic times is an abiding symbol of the unbroken continuity of Indian astronomy. The knowledge of astronomy, which was once common throughout India, was lost due to the vagaries of history, though it was prevalent in Kerala till the 15th and 16th centuries.  In fact, the astronomers of Kerala made discoveries that were often corroborated by the discoveries of western mathematicians and astronomers only in the 18th or 19th centuries!

Dr S Balachandra Rao is the Director,  BHAVAN's Gandhi Centre of Science and Human Values, and the author of several acclaimed books on Indian Mathematics and Astronomy.  This essay is based on a talk delivered by him at the invitation of Sri Tirunarayana Trust, at the Indian Institute of World Culture, on August 29, 2004