Longitude Zero

Continued in: Medieval Navigation in the Arabian Sea

One of the early achievements of Indian Mathematical Astronomy (jyotisha) was the system of latitude (aksha-amsa) and Longitude (rekha-amsa). The prime meridian passed through Ujjaini, the capital of the country of Avanti. It is identified as the modern city of Ujjain at co-ordinates 23.182778, 75.777222 . Just as we use Greenwich mean time as a standard measure of time today, in those days, Ujjaini time would have been the standard.


The classical work on the subject is the Aryabhatiya . This is a long Sanskrit poem in the Arya1 meter divided into four chapters-literally, pada means quarter. The Gitika-pada (the Introduction), the Ganika-pada (Mathematics) Kala-kriya-pada (The Measurement of Time) and the Gola-pada ( The Sphere) . Very little is known about the author, except that his name was Aryabhata-hence the name of the work. Also, his birthday : he says in the book that he is 23 years old in the year 3600 of the Kali yuga, which is 499 AD. He lived in a place called Kusumapura which may or may not be Pataliputra, todays Patna in Bihar. He was born in Asmaka-desa, which could be almost any place; everyone in India finds some reason to claim Aryabhata as one of their own2 .

It was the tradition in India to describe extensions and later developments related to a classical work in commentaries to it. Thus, all the important Indian astronomer mathematicians wrote commentaries on the Aryabhatiya as a way to publish their own work: Brahmagupta (b. 598 AD), Bhaskara (629 AD), Suryadeva (b. 1191 AD), Parameswara(1408 AD) , Nilakanta Somayaji (b. 1444AD) and many more. Their refinements and extensions and occasional alterations of the text are the place to learn about the Indian theory of the sphere3. The text and translation I will use is that of K.S. Shukla and K. V. Sharma4.

The Idealized Earth of the Aryabhatiya

I will skip over the mathematics and the measurement of time to get to the last part on the sphere-more precisely, the Earthly sphere Khagola, skipping also the celestial sphere Bhagola.

The Gola-pada gives a simplified or idealized model of the Earth. Then establishes a co-ordinate system on it with which astronomical calculations can be performed. Much the same way a physicist might today model the Universe as a homogenous space, ignoring such real things as clusters of galaxies, Aryabhata’s Earth is a mathematical construct that resembles-but does not reproduce exactly- the real Earth.

A point on the equator is the most natural one from which to imagine the motion of the stars. For example, Aryabhatta says that someone at such a point (Lanka) would see the stars moving exactly East-West, just as a person on a boat would see objects ashore move backwards.

AB_4.9a/ anuloma-gatis nau-sthas @paśyati acalam viloma-gam yad-vat/
AB_4.9c/ acalāni bhāni tad-vat sama-paścima-gāni laṅkāyām//

The implication is that the stars are fixed and it is the earth that is moving. This would be hard to explain from any other latitude, as the axis of rotation would not be exactly horizontal.

The North Pole (Meru) is at the center of the Land and the South Pole (Naraka or Badavamukha) at the center of the Ocean. To first approximation, most of the Land is in the North Hemisphere and the South is mostly Ocean.

AB_4.13a/ udayas yas laṅkāyām sas astamayas savitur eva siddha-pure/
AB_4.13c/ madhya-ahnas yama-koṭyām romaka-viṣaye %ardha-rātras @syāt//

When the Sun rises at Lanka it sets in Siddha-pura, it is Noon at Yama-koti and midnight at Romaka. This does not mean literally that Rome (12° 30′ E) is at 90W with respect to Ujjaini. Romaka is at best a general reference to Europe. Siddha-pura which is antipodal to Lanka is clearly a mythical place as is Yama-kodi. Still this description of the time at the cardinal points of direction give the method for computation of lcoal time from longitude, as a fraction of the circle (aksha-amsa).

The next verse establishes the location of the idealized Lanka on the equator (establishing the prime meridian)

AB_4.14a/ sthala-jala-madhyāt laṅkā bhū-kakṣyāyās @bhavet %catur-bhāge/
AB_4.14c/ ujjayinī laṅkāyās tad-%catur-aṃśe sama-uttaratas//

From the center of land and ocean (the poles), at a distance of one-quarter of the Earth’s circumference, lies Lanka; and from Lanka, at a distance one-quarter thereof, exactly Northwards likes Ujjaini.

Thus Lanka is equidistant from the poles, a quarter circle away from them; and Ujjaini is one-sixteenth of a circle directly North of Lanka.

There is a problem here if we identify Lanka to mean the island of Sri Lanka and Ujjaini to be Ujjain, the historical capital of Avanti. The Southern most point of the island of Lanka is 5 degrees north of the Equator and its Western most point is 3 degrees east of Ujjaini’s meridian. The Lanka of Aryabhatta is a mathematical abstraction, a point where two great circles meet, somewhere in the general vicinity of the actual island of Lanka.

If Aryabhata’s Lanka is an abstraction, are we safe in identifying his Ujjaini with the real city of Ujjaini? This seems more likely as Aryabhata while not a sailor, would have direct knowledge of a well known city in the middle of India. The verse says that Ujjaini is one sixteenth of a circle North of the equator or, at 22deg 30’N latitude. The actual city of Ujjiani is at 23deg 10’N which is only off by only 40′ or about fortyfive miles. So it seems reasonable that Ujjaini really is the actual city. The ideal point one sixteenth of a circle from the equator could have been within the region of which it was the capital. Or may be it was thought of close enough to Ujjaini to get the name of the city.

By the way, there is another reading of the above verse preferred by some Indian commentators (Brahmagupta most importantly) tat-catur-amse above be replaced by pancha-dasamse; i.e., one-fifteenth. This would put Ujjaini at 24deg N which apparently was the latitude of the place where Brahmagupta lived in Avanti. None of the commentators seem bothered by the much greater error in assuming that Lanka is directly South of Ujjaini. Perhaps , they were not aware of the exact boundaries of the island.

In addition to verses that can pass a scientific scrutiny, Aryabhata’s text also contains many fantastic passages that say things like: the Gods live at the Meru mountain (North Pole) and the demons at the South Pole. The Meru mountain at the North Pole is one yojana high (not sure sure how high that is) and it glows in the dark. Earth expands and shrinks by one yojana every yuga ( a very long Hindu unit of time). I thought it best to ignore these poetic fantasies.

What is Special About Ujjaini?

There is also something special about the latitude of Ujjaini. The plane of the ecliptic (the plane of the orbit of the Earth) intersects the earth at 23deg 26’N latitude, the Tropic of Cancer.
This is because the axis of earth’s rotation is not perpendicular to the plane of its orbit around the Sun. Or, because the celestial equator is inclined with respect to the Earth’s equator. This is what causes seasons in the Earth’s climate: the days are shorter in winter and longer in the summer.

Thus above the Tropic of Cancer, the Sun will never be directly overhead. Below this latitude, the Sun will be directly overhead at noon on the day when its north declination becomes equal to the latitude. On the equator this happens twice, on the equinoxes. On the Tropic of Cancer it happens on the summer solstice (June 21). Ujjaini is almost right on the Tropic of Cancer, only a quarter of a degree away while Pataliputra for example, is two degrees North of this latitude. This point is noted by commentators.

Prime Meridian

Once the Aryabhatiya became popular among Arabs one imagines that at least some of them would have used this Prime Meridan. Throughout the middle ages, Arab sailors had a monopoly on the spice trade with India. Is there any harbor of interest on this zero longitude? The city of Calicut (Kozhikode) 11°16’38″N 75°42’48″E is the unique point where the old prime meridian meets the coast of India. Moreover, it is exactly half the distance to Ujjaini from the idealized Lanka ( 11deg 15’N), one eighth the distance to the Pole! Easy co-ordinates to
remember indeed. Arab sailors memorized the positions of their destinations, often as poems.

Kalikut (as it is also spelled) has been for a long time an important port. It is where Vasco da Gama arrived in 1492 when he discovered the Sea route to India. It is no coincidence that he ended up at Kalikut: the navigator he had hired (or kidnapped- it is hard to tell, da Gama was a rough customer) followed a standard Arab trade route from the African port of Malindi to Kalikut.

Could it be just a coincidence that Kalikut happens to at Longitude zero? Did its easily remembered position give it any special advantage over the competing Sea ports in the lucrative Arab-Indian trade in medieval times? We need to look into how the Arabs navigated in medieval times to understand this. The answer is not what I had hoped for when I started this quest, but along the way I discovered interesting information about the navigational methods used by Arab sailors.

Read on: Medieval Navigation in the Arabian Sea

1. Did the author choose the Arya vrtta because his name was Arya? Or did he adopt the pseudonym Arya because his main work was in the Arya meter? The word Arya means noble in the Indian context. It was appropriated in the twentieth century by certain evil Germans to mean a race that does not exist. Sadly, the word association they created continues in the mind of Western readers.

2. I have excellent reasons to place his birth at the village of Veiloor in Kerala. My reasons are as good as those who place him at Ponnani, Sri Lanka, Gujerat, Ujjaini etc. Such uncertainties are not unusual in classical Sanskrit literature: there are just as many controversies about Kalidasa, the most important dramatic poet. We don’t even know for sure which century Kalidasa lived; at least in the case of astronomers we can determine their time because they give some clues. The situation improves in medieval times, as the historical records are more complete.

3. There are also additional commentaries in local Indian languages. The Aryabhatiya was translated into Arabic and his work was quite influential in the Middle East as well.

4. Aryabhatiya, Critically Edited with Translation K. S. Shukla and K. V. Sharma, Indian National Science Academy New Delhi (1976). Where I cannot rely on my own knowledge of Sanskrit I have used this translation. There is an online version of the text in Roman transliteration (but not a translation) available at

4 Responses to “Longitude Zero”

  1. jose goncalves says:

    I’m interested to know how the arabian sailors manage to
    determine the longitude before XVth century.

    Can anybody can help me?


    Pereira Goncalves

  2. S. G. Rajeev says:

    I would like to know also. What I could find out about it is in a related post http://www.sgrajeev.com/medieval-navigation

    As far as I can make out, it was some combination of dead reckoning and celestial navigation. If you can sight a fixed star and a planet within a short time (about ten minutes) you can get longitude. I suspect that some version of this is what they did, and corrected the estimate by their knowledge of the ships speed and currents. The trouble is that on a moving ship, it is hard to take sightings accurately.

    If you do find out more, please let me know.

  3. Viswa Sharma says:

    I see the comment
    “In addition to verses that can pass a scientific scrutiny, Aryabhata’s text also contains many fantastic passages that say things like: the Gods live at the Meru mountain (North Pole) and the demons at the South Pole. The Meru mountain at the North Pole is one yojana high (not sure sure how high that is) and it glows in the dark. Earth expands and shrinks by one yojana every yuga ( a very long Hindu unit of time). I thought it best to ignore these poetic fantasies. ”

    Well one way to look at this is the Back bone – If you are familiar with Yoga this makes sense! because As above (skies) so below(body),

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