Aryabhatiya: an Introduction

This is the first article on Aryabhatiya. It is quite a broad one, so it is impossible to cover the whole topic in one article. I will post more articles in the coming days.

Aryabhata I, author of Aryabhatiya

An Indian astronomer-mathematician. His notable work is Aryabhatiya. As mentioned by himself in his work – Aryabhatiya – “Aryabhata sets forth the knowledge honored at Kusumpura”. This tells us that he gathered his knowledge of astronomy at Kusumpura (an older name for Patliputra). Nalanda University in Pataliputra had an astronomical observatory. Scholars mentioned him as Acharya (professor) and Kulpa (head of the university). All this indicates that – He was a professor of astronomy at Nalanda University (Pataliputra) and was head of the university.


His work Aryabhatiya was widely used in households in India, to find the right date and time for various rituals. Even though his work was on astronomical calculations and mathematics, it was mainly used for astrology. For almost 1000 years after Aryabhata I, many Indian astronomers wrote their commentary on Aryabhatiya. His work influenced Persian astronomy, when his translated work reached there, and further influenced European astronomy. Aryabhatiya also reached China along with Buddhism. The first Indian satellite ‘Aryabhata’ was put into orbit on April 19, 1975.

Aryabhatiya, an introduction

Divided into 4 sections – the first section contains only basic astronomical and mathematical constants and definitions. The second section has mathematical formulae. The third have units of time and the fourth section is all about astronomical motions. Here the first section was intended for freshers in astronomy. And second, third, and fourth was for those who have mastered the basics.

Key features of Aryabhatiya

Method for writing large numbers

The first thing to notice is, Aryabhata gave a method for writing large numbers using Sanskrit (or Hindi) letters. Using vowels for place notation (like units, tenths etc.) and consonants for numbers (from 1 to 25 and 30,40,50,60,70,80,90,100). To write them in stanzas like words. For example – nm = y, i.e. 5+25 = 30.

The week system

He mentioned days of the week in various places in his work. This shows us that the week system was well established before his period. Here is a separate article on origin of week system.

Length of a day

He gave the theory of the rotation of the earth and calculated the day as – 23hr56m4.1s (modern value – 23hr56m4.091s). The accuracy of this value is remarkable for that time.

Time and division of time

He doesn’t believe in the creation and annihilation of the world. He said time is without beginning and end. During Aryabhata’s time, the following were the values for various units of time-

1 Kalpa = 14 Manu

1 Manu = 71 Yug

1 Yug = 43,20,000 years

And 1 Yug was further divided into 4 smaller Yugs in the ratio of 4:3:2:1. . This method was very complex and needed an error correction. Aryabhata rejected this pattern of units and created his system as- 

1 Kalpa = 14 manus

1 manu = 72 yugs

1 yug = 43,20,000 years

Here Yug was further divided into 4 smaller yugs but of the same duration. This gives us 1008 yugs in 1 Kalpa, and we no longer needed the error correction.

Model of the solar system

For calculations, Aryabhata assumed a heliocentric model of the solar system (though not explicitly mentioned). In which the Earth is rotating on its axis. According to him, the sky was a hollow sphere or without boundary. All 12 asterisms were fixed points in the sky and all were at the same distance from Earth.


It is seen that debunking old theories for a better one was quite common practice in India. Aryabhata gave his version of many previously known theories and mathematical formulae for better results and rejected many old beliefs. Not only this, if you read commentary on Aryabhatiya by other Indian astronomers you will witness many would disagree with him on his pattern of division of time. Brahmagupta (AD 598 – 668) even rejected the Aryabhata theory of the rotation of the earth. In AD 1500 Kerala astronomers updated the earlier geocentric model of the solar system to the pseudo-heliocentric model. Aryabhata’s formula for finding the volume of the sphere was way off than the true value, and mathematicians after Aryabhata gave their new formula for better results.

In the following articles, we will be discussing Aryabhatiya in more detail. Till then, clear skies!



Published by Anand Krishna

Amateur astronomer and astrophotographer. Interested in astrophoto processing, astrostatistics, comet hunting, visual and radio astronomy.

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