Aryabhata’s Revolving Earth Theory

Bineesha Dilshani Wickremarachchi

 University Scholars Programme, National University of Singapore
CCSP04: Scientific Method and Strategies of Critical and Creative Thinking 
(Project - Semester II, 2000-2001)

The Indian astronomer Aryabhata is regarded as the founder of scientific astronomy in India and often called the greatest mathematician-astronomer of ancient India.  However, his name or even his contributions were not as well known as those of Varahamihira and Bhaskaracarya.  In his work, the Aryabhatiya, he mentions Kusumpura and it is believed that he lived and wrote his work there.  Kripa Shankar Shukla translates a stanza in the Aryabhatiya: “Aryabhata sets forth here the knowledge honored at Kusumpura” (xvii).  The year of his birth is known with precision.  Shukla mentions a verse in the Aryabhatiya that says, “When sixty times sixty years and three qurter-yugas had elapsed, twenty-three years had passed since my birth” (xx).  This shows that in the Kali year 3600, which corresponds to A.D. 499, Aryabhata was 23 years of age.  Thus, it follows that he was born in the year A.D. 476. 

The Aryabhatiya is a small astronomical treatise written in 118 verses giving a summary of Indian mathematics up to that time.   About two hundred years ago, modern researchers started investigating the development of mathematics and astronomy in ancient India, but at that time the Aryabhatiya was not available to them.  Gunakar Mulay states in his article that in 1864 Dr. Bhau Daji had rediscovered the Aryabhatiya and after a thorough study he had written a paper on Aryabhata.  In 1874 Dr. H. Kern published his edition of the Aryabhatiya in Holland and then in 1976 the Indian National Science Academy published four editions of this work.  “It is from that time Aryabhatiya name spread far and wide and he came to be regarded as the greatest mathematician-astronomer of ancient India” (Muley). 

The Aryabhatiya deals with both mathematics and astronomy and is divided into four parts: Gitikapada (preliminaries), Ganitapada (mathematics), Kalakriyapada (reckoning of time) and Golapada (astronomy).  Shukla describes the Gitikapada as setting forth the basic definitions and important astronomical parameters and tables.  The Ganitapada deals with mathematics such as geometrical figures, their properties and simultaneous, quadratic and linear indeterminate equations.  In the Kalakriyapada, Aryabhata deals with the various units of time, divisions of the year, determination of the true positions of the sun, moon, the planets and explains their motion by using eccentric circles and epicycles.  Finally the last section of his work, the Golapada, deals with the celestial sphere and the planetary motion.  In this section Aryabhata describes the various circles of the celestial sphere, indicates the method of automatically rotating the sphere once in twenty-four hours, and describes the motion of the celestial sphere as seen by the people on the equator and on the north and south poles.  

Mulay mentions that the belief in ancient India at that time was that the Earth was stationery and situated at the center of the universe and that all other heavenly bodies revolved around the earth.  However, Aryabhata believed that the earth rotated on its axis and the stars were fixed in space.  He goes on to say that the apparent rotation of the heavens was due to the fact that the earth revolved around its axis.  According to him the period of one rotation of the earth is 23 hours 56 mn 4.1s while the modern value is 23 hours 56 mn 4.091s.  His accuracy regarding this is amazing. 

Shukla translates the verse in the Aryabhatiya that deals with the earth’s rotation as follows:

Just as a man in a boat moving forward sees the stationery objects (on either side of the river) as moving backward, just so are the stationery stars seen by people at Lanka (on the equator), as moving exactly towards the west. 

(It so appears as if) the entire structure of the asterisms together with the planets were moving exactly towards the west of Lanka, being constantly driven by the provector wind, to cause their rising and setting (119).

The theory of the earth’s rotation was contrary to the belief held at that time by the people.  Brahmagupta and Varahamihira severely criticize Aryabhata’s view, and even his followers who were unable to refute the criticisms, misinterpreted the above verses.  One such follower was Somesvara.  In his commentary he says that there is no evidence of the earth’s motion. 

For if the Earth had a motion, the world would have been inundated by the oceans, the tops of the trees and castles would have disappeared, having been blown away by the storm caused by the velocity of the Earth, and the birds flying in the sky would never have returned to their nests (Shukla 20).

Therefore, it is his opinion that the verse in the Aryabhatiya must be interpreted to mean that the asterisms, due to their own motion, see the stationery earth lying below as if it were rotating. 

In Alberuni’s India we find a quote from the Brahmasiddhanta written by Brahmagupta:

Some people maintain that the first motion (from east to west) does not lie in the meridian, but belongs to the earth.  But Varahamihira refutes them by saying: ‘If that were the case a bird would not return to its nest as soon as it had flown away from it towards the west.’  And, in fact, it is precisely as Varahamihira says(276).

However Brahmagupta goes on to refute Varahamihira’s argument.  He says that stones and trees would not necessarily fall from the earth because according to the law of gravitation, the earth is in the center of the universe and therefore everything heavy would gravitate towards the earth. Brahmagupta goes on to say:

The wind makes all the fixed stars and the planets revolve towards the west in one and the same revolution; but the planets move also in a slow pace towards the east, like a dust atom moving on a potter’s-wheel in a direction opposite to that in which the wheel is revolving.  That motion on this atom which is visible is identical with the motion which drives the wheel round, whilst its individual motion is not perceived (Alberuni 280).

Brahmagupta and Aryabhata agree with this view that the celestial sphere, consisting of the sun, fixed stars and planets, moves as a whole and therefore the individual movements of the heavenly bodies relative to each other are not visible. However Brahmagupta doesn’t agree with Aryabhata’s theory that the heavenly bodies appear to move because of the earth’s rotation. His argument against Aryabhata’s theory is that: “On the contrary, if that were the case, the earth would not vie in keeping an even and uniform pace with the minutes of heaven, the pranas of the times” (Alberuni 277).  He says that since the earth would not keep an even, uniform pace if it were revolving on its axis, Aryabhata’s idea is not correct. 

In his commentaries Alberuni disagrees with Brahmagupta’s criticism of the revolving earth theory.  He says he cannot see what would prevent the earth from keeping an even and uniform pace with the heaven even if it’s revolving on its axis.  Alberuni believes that the revolving earth theory does not impair the value of astronomy because astronomical appearances can be explained using Aryabhata’s theory as well as the other theory.  However he believes that there are stronger arguments against Aryabhata’s theory.    Unfortunately he doesn’t elaborate on these stronger arguments against the revolving earth theory.

It is clear that many astronomers strongly opposed Aryabhata’s theory and even Aryabhata’s followers did not attempt to defend his theory.  What prompted such strong criticisms from so many astronomers?  It is clear that the commonly held belief in ancient India was that the earth was at the center of the universe and that the sun, planets and the fixed stars revolve to the west in one revolution and that this motion was caused by the wind.  Aryabhata’s theory was completely at variance with the commonly held belief.  Perhaps many of the Indian astronomers were reluctant to support such a theory.  However, this fact alone doesn’t explain the criticisms leveled against Aryabhata. 

Alberuni is of the opinion that astronomers in ancient India had a tendency to admit beliefs and notions supported in religious texts into their doctrines.  He states that many of the religious books contain ideas about the shape of the earth, which are in direct opposition to the scientific truth known by their astronomers.  But Indian astronomers accept these popular beliefs.  By means of these religious books “the great mass of the nation have been wheedled into a predilection for astronomical calculation and astrological predictions and warnings”(Alberuni 265).  As a consequence astronomers are very highly regarded by the people.  Alberuni believes that for this reason astronomers accept popular beliefs however far they may be from the actual truth.  “This is the reason why the doctrines of astronomers have become confused, in particular the doctrines of those authors who take the bases of their science from tradition and do not make them the objects of independent scientific research” (Alberuni 265). 

This could explain why so many Indian astronomers strongly criticized Aryabhata’s theory.  Aryabhata’s theory would have violated the sacred religious texts.  Opposition from religious priests would have created great difficulty for the astronomers and it would have constituted political opposition.  This problem with the religious clerics would have been similar to the problem faced by Copernicus and Galileo when they violated sacred religious scriptures in modern Europe.  It would explain why even his followers attempted to misinterpret his theory rather than look at it from a critical point of view.  Prthudaka, a supporter of Aryabhata’s revolving Earth theory, believed that Aryabhata’s followers misinterpreted his verse because they were afraid of public opinion, which was strongly against this theory. 

Another opposition that Aryabhata faced was the opposition based on the physical theories accepted in India at that time.  The astronomers believed that if the earth was revolving on its axis then the trees and stones would fall off the earth and birds would not be able to return to its nest as soon as it flies away towards the west.  Both Varahamihira and Someswara use this argument in their commentaries.  This was a difficult argument to refute.  Unable to refute it many of Aryabhata’s followers instead misinterpreted Aryabhata’s theory and said he doesn’t say the earth is revolving on its axis.  Somesvara was one such follower.

The argument that if the earth was revolving then trees and stones would fall off the earth can be refuted by the law of gravitation which was accepted in ancient India. 

As Brahmagupta argues, since the earth is at the center of the universe all heavy objects would be attracted to the earth and therefore trees and stones would not fall from it.  The other opposition comes from the common beliefs and the experiences of the common people.  It can be observed that it is the heavenly bodies which are moving, and not the earth.  There are no observations to prove the earth is revolving on its axis.  Therefore the earth cannot be moving.  This argument can be refuted by saying that the observations could be an illusion and that it could actually be the earth which is moving, while the heavenly bodies remain stationery. 

The opposition from the religious clerics was probably the strongest criticism against Aryabhata.  Religious texts and religious priests played a dominant role in the Indian society.  In fact, as Alberuni comments, Indian astronomers accepted popular beliefs and theories given in religious texts even though they may be in direct opposition to scientific truths.  It would have been extremely difficult for an astronomer to oppose the religious text and the religious priests.  Thus the religious opposition to Aryabhata’s theory would have been the main and strongest opposition. 

The theory widely accepted during Aryabhata’s time was able to explain successfully the movements of the celestial sphere and all appearances of an astronomic character.  Aryabhata’s theory too could explain the celestial observations quite well, as Alberuni pointed out.  Yet, Aryabhata’s theory was not accepted.  Oppositions from religious clerics, opposition by the commonly held beliefs and criticisms based on the physical theories accepted at that time caused this paradox to emerge. 

Even though Aryabhata faced great opposition because of his theories, his contributions to Indian mathematics and astronomy are unparalleled.  Bhaskara I who wrote a commentary about 100 years later says:  “Aryabhata is the master who, after reaching the furthest shores and plumbing the inmost depths of the sea of ultimate knowledge of mathematics, kinematics and spherics, handed over the three sciences to the learned world” (Aryabhata the Elder). 

Works Cited 

WWW References

1.                  Department of Mathematics and Statistics, Simon Fraser University.  Aryabhata.  July 2000.  Department of Mathematics and Statistics, Simon Fraser University.  1^st February 2001.  <http://www.math.sfu.ca/histmath/India/5thCenturyAD/Aryabhata.html>. 

2.                  Indira Gandhi National Centre for the Arts.  Indian Cosmology, Reflections in Religion and Metaphysics.  2^nd February 2001.  Indira Gandhi National Centre for the Arts.  1^st February 2001.  <http://www.ignca.nic.in/ps_04016.htm>. 

3.                  Muley, Gunakar.  “Aryabhata”.  Vigyan Prasar News.  August 2000.  5^th February 2001.  <http://vigyanprasar.com/dream/August2000/VPnews.htm>. 

4.                  University of St. Andrews, Scotland.  Aryabhata, the Elder.  November 2000.  University of St. Andrews, Scotland.  28^th January 2001.  <http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Aryabhata_I.html>.

Print References: 

1.                  Aryabhata.  Aryabhatiya of Aryabhata.  Ed.  Kripa Shankar Shukla.  New Delhi : The Indian National Science Academy, 1976. 

2.                  Biruni, Muhammad ibn Ahmed.  Alberuni’s India.  Trans. Edward C. Sachau.  New York, Norton, 1971. 

Arun Bala (Email: phibalas@nus.edu.sg) 
Last updated: Sunday, October 03, 2004
Website created: 1 January 2001

Rajeev Srinivasan

Millennium Fuss

In the midst of all the fuss about the new millennium in the Gregorian calendar, most of us missed another centenarian event: the beginning of the 52nd century of the Kali Yuga in the Hindu calendar, on March 18. This is Yugabda 5101. So why should anyone care? Isn't this just another somewhat eccentric calendar like the Saka Era followed by the Indian government?

On the contrary, Indians or at least Hindus should care. The widespread popularity of the Gregorian calendar is a vestigial side-effect of European colonialism, and the fact that Anglo-American business practices have more or less become the default option in much of the world. Although we tend to take these European-derived practices as somehow rational and even pre-ordained, there is nothing inherently scientific about them.

For example, millions of Muslims get along just fine on the Islamic calendar, even given the fact that being a lunar calendar, the length of their year doesn't quite match the 365 or so days in the solar year. They also get by just fine with an Islamic system of banking that doesn't allow for interest payments. Other non-Gregorian calendars and non-Euro-centric practices are used elsewhere.

Therefore the Gregorian calendar is just a convenient device. Although it is supposed to be related to the life of Jesus Christ, it is not quite in sync -- nobody quite knows when the historic Jesus lived, except that it was probably somewhere between 6 BCE and 40 CE. However, this calendar is definitely ethno-centric and religio-centric.

For instance, people ask me why I refer to dates in the Gregorian calendar as CE/BCE (i e Common Era/Before Common Era) as opposed to AD/BC. This is because AD/BC has certain religious connotations -- AD stands for Anno Domini or The Year of Our Lord, which is meaningless unless you are Christian. It was Jewish historians in the US who initially started the use of CE/BCE, which is a non-committal term with no assumptions about religion.

Interestingly, Jews have a rather ancient calendar, wherein this year is 5759. Since Judaism has been around for some time, this calendar must date back to some significant early event in the history of the Jewish people. Similarly, one would assume, the length of the Hindu calendar signifies some early event in the history of Hindus.

However, the earliest known Hindu text is the Rg Veda, dated to about 1500 BCE. Thus the Hindu calendar should date back only about 3,500 years. Therefore, the business about the Kali Yuga and 5,000 years must be some convenient fiction made up by medieval Hindu scholars, right? This is certainly what we have been led to believe by the Macaulayite educational system in India.

According to conventional wisdom, the Hindu texts that state that the Kali Yuga began in 3102 BCE, and that there was some spectacular celestial configuration of planets to mark that event, are merely fanciful mythical accounts. For after all, in 3102 BCE, Hindus were still far from writing the earliest Vedic texts -- and they were not a civilisation until around the 1500 BCE date of the Rg Veda.

But wait, where did the estimate of 1500 BCE come from? Why, it came from Max Mueller, the eminent German Indologist, who dated the Vedas after considerable study in the 19th century CE. And how exactly did Max Mueller come upon this date? It turns out that he just made it up, based on certain cyclical logic!

You see, Max Mueller, being a Christian fundamentalist/missionary, took it as an axiom that the world was created in 4004 BCE, as some British bishop had deduced from a study of the Bible and related texts. Therefore, argued Mueller, after Adam and Eve, it would have taken a 1,000 years or so to populate Europe (with pure Aryans, of course).

Thereafter, given the Aryan Invasion Theory, it would have taken the Aryans a thousand years to migrate from Central Europe to India, bringing the Vedas with them. So add 2,000 years or so to 4004 BCE, put in a little swag factor of 500 years, and hey presto, you have the Rg Veda dated to 1500 BCE! Impeccable logic, surely.

I exaggerate slightly above, but in substance, this is the ethno-centric and Christian-centric view that has illuminated, so to speak, Indian understanding of its own pre-history. And this has been the state of affairs until scholars such as Dr Koenraad Elst, Dr Subhash Kak, Dr David Frawley, et al began to question both the Aryan Invasion Theory and the dating of Indian pre-history.

I will not get into the wretched Aryan Invasion Theory controversy, but it is surely interesting to look at ancient Indian astronomy. It has long been assumed that Indian astronomy was derived from the Greek -- after all, Euro-centrics pre-supposed that Greek civilisation was the fount of all classical knowledge; the curious fact that the Indian and Greek astrological signs were identical was attributed to Indian borrowing from the Greeks.

It turns out, however, that Hindu texts do fairly accurately describe historical celestial events -- for instance the singular planetary configuration that is supposed to have taken place in 3102 BCE to mark the beginning of the Kali Yuga did in fact take place. This leads to two possibilities: one, that the astronomical events were actually observed then; two, that someone, after the laws of astrophysics became known (say Newton's time) back-caculated and inserted them into texts.

There is a problem with the first hypothesis: ancient Indians were not known to be astronomers, unlike, say the Chinese, who left detailed records of supernovae they observed, for instance in the Crab Nebula in 1054 CE. Second, if Indians were accurate astronomers 5,000 years ago, that presupposes an advanced civilisation by that time, which makes India the oldest of all known civilisations. This does not fit in with conventional wisdom.

But consider the other hypothesis. Given the notorious state of the authenticity of Indian texts, tampering is not out of the question. So let\rquote s say some clever 18th century Hindu mathematician manufactured the evidence and inserted it into allegedly ancient texts.

But there is a flaw in this argument. It turns out that Indian astronomy (and astrology) over the centuries has had an error in it: it does not take into account the precession of the axis of the earth as it rotates around the sun. This is the tendency of the axis itself not to be oriented in space in fixed fashion, but to describe a cone -- it spins like the axis of a top does.

This error has accumulated over time. So for instance, Hindus celebrate the Winter Solstice on Makara Sankranti day, January 14th; however the real Winter Solstice is on December 22nd. Similarly, the Indian astrological months are offset by a couple of weeks from the real dates on which the sun enters those constellations.

Therefore, if an Indian mathematician were to recognise this error in Indian astronomy, take it into account, correct it, and backtrack to 3102 BCE, it would take a prodigious amount of computing power, that was not available until the recent creation of supercomputers. Therefore, the second hypothesis is impossible -- it was not back-calculated. The event was in fact observed in 3102 BCE.

We are left with the possibility then that Indian civilisation was already well-established in 3102 BCE. Which is interesting in and of itself. Furthermore, the Hindu calendar does speak in cosmic terms -- and it establishes the age of the universe as some 8.64 billion years, which fits in with modern, scientific cosmology (see Carl Sagan at

http://www.rediff.com/news/jan/29sagan.htm).

I understand that the Indian government has denoted this year of the Hindu calendar as the Year of Sanskrit. Maybe in some of those crumbling palm-leaf manuscripts rotting away unsung, unwept, and unhonored, there are other ancient treasures like the astronomical observations from 5,000 years ago.

Rajeev Srinivasan