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Notes on Indian Astronomy

Here is a neat little essay on Tithi, Nakshatra and raashi

[url=]Tithi, Nakshatra, Raashi …[/url]
M. R. Dwarakanath

THE UNIVERSE: Our Universe consists of billions of galaxies; each galaxy comprising billions of stars. Our galaxy is called the Milky Way and all the stars we see in the night sky are in our galaxy. Stars in other galaxies are too far to be discerned as individual stars by the naked eye. Our Sun is a star in the Milky Way galaxy and has 9 known planets. Most of the planets have satellites or moons. Our Earth is the 3rd inner planet to the sun and the moon orbits the earth. All the objects in this universe are moving relative to each other at great speeds. Although all the astronomical objects are really moving at great speeds, the more distant objects appear to move more slowly and the stars are sufficiently far away that in terms of our time frames, the star field looks fixed in the firmament.

THE SUN and the EARTH: The Earth revolves once around the Sun in 365.256 days. Because the sun is also moving around the center of the galaxy, the earth does not return to the exact same spot in space after 365.256 days. The "fixed" background of stars is used as a reference when we say the earth completes one orbit around the sun in 365.256 days. At the end of one year the relative positions of the sun, the earth and the background stars will be the same as at the beginning of the year.

We can look at the sun during a total solar eclipse and find a star that is closest to the sun (better yet, one eclipsed by it) and declare the sun to be located in the direction of that star at that time. We can do this directly only during a total solar eclipse (assuming the sky is clear etc.) but at other times we can infer the location of the sun relative to the background stars. As the sun and earth move, the sun appears to move relative to the fixed stars. The sun traces an apparent path against this backdrop. This path is divided into 12 equal segments called the Zodiac or the Rashis. The brighter stars in the segment form a constellation. The constellations are given names based on their appearance and the imagination of people who named them. On any given day, the sun is in a specific Rashi. Actually, the sun spends one month in a Rashi as there are 12 Rashis and 12 months in a year.

THE MOON: The moon is revolving around the earth, the earth revolving around the sun and the sun revolving around the center of the galaxy. We could ignore the motion of the sun in looking at the motion of the earth. However, when we want to look at the motion of the moon, we cannot ignore the motion of the earth because these objects are much closer together. As before, we can look at the moon and pick the star closest to it. About a month a later, the moon will once again be very to close to the same star. The period of time for one such revolution is called a sidereal month and is 27.322 days long. At the end of a month, the moon will not return to the exact spot against the stars because of details having to do with the orbital planes of the earth and the moon.

The moon now makes a complete loop against the stellar backdrop in one sidereal month. This path is divided into 27 equal segments and each segment is associated with a Nakshatra. Each Nakshatra is further subdivided into 4 Padas. The location of the moon at the time of a person’s birth determines that person’s Janma Nakshatra and the pada. A Nakshatra is 4 padas and 27x4 padas are equally distributed among the 12 Rashis. Thus each Rashi includes 9 Padas.

[color=red][size=7]A sidereal month is the time taken by the moon to make one revolution against the stellar backdrop. A second kind of month is the time taken by the moon to make a complete loop with reference to the sun. The sun, earth and moon fall in a line once every fortnight or a Paksha. However, they fall in a line and in the same order once every synodic or lunar month. These bodies will not be in exact alignment every month. When the alignment is close enough, we have eclipses of either the sun or the moon and we know it does not happen every fortnight! The synodic month (Masa) is 29.531 days and has 2 Pakshas – Sukla and Krishna. Each Paksha has 15 days called Tithis. The Tithi is not related to the background stars but instead to the phases of the moon. The Tithis are numbered one through fourteen and the fifteenth day of the fortnight is called Poornima (full moon) or Amavasya (new moon). [/size][/color]
During mid Amavasya, the sun and the moon are both generally in the same direction as viewed from the earth and therefore they will be in the same Rashi.

TIME: The day we have been referring to is the mean solar day. This is the interval of time taken by the earth to make one rotation on its axis relative to the sun. This time is slightly variable and the average time is the mean solar day. Time can be universal but we are used to local time. Local time attempts to place the sun overhead at noon. The sun rises at different universal times at different points on the earth and at different times of the year. Some events such as Rahukala are related to sunrise and therefore to local time. However, at any given instant (not local time) the Nakshatra is the same independent of where you are! This is because the location of the earth and the moon relative to the stars is nearly the same irrespective of where you are on the earth.

How to figure your birth star? Let us say you do not know your birth star and you want to find out. You may consult the almanac of the year of your birth. This may be hard to find. However, if you have any almanac (most likely the current one) you can easily figure it out. Here is how:

Let us say, your date of birth is June 1, 1950 and time of birth – noon. We can calculate the number of days between June 1, 1950 and June 1, 1999. There are 49 years intervening of which 12 are leap years (actually, you have to count the number of February 29s between the two dates). The total number of days = 365x49 + 12 = 17897 days.

Divide this number (17897) by the number of days in a sidereal month (27.322).

17897/27.322 = 655.0399.

The significance of this division is that from June 1, 1950 to June 1, 1999 the moon has completed 655 revolutions. The moon has also made an extra 0.0399 revolutions. The time for this extra fraction of a revolution is 0.0399x27.322 = 1.09 days or 1 day and 2 hours. We have to go back 1 day and 2 hours from June 1, 1999 – noon, to find the exact same alignment of the earth, moon and your Nakshatra. It would be May 31 - 10 a.m. You may now look up the almanac for the Nakshatra at 10 a.m. on May 31, 1999!

Determination of Tithi is analogous. Simply use 29.531 in place of 27.322 in the above calculations. The answer is the Tithi at 7 a.m. on May 31, 1999. During this time the moon would have completed 606 lunar months. The fact, these two dates are relatively close is no accident. It can be explained with a simple sketch. This explains why Krishna Janmastami and Rohini Nakshatra either fall on the same day or just a few days apart. However, not all Krishna Paksha Astamis are close to Rohini Nakshatra. They are close in August!

Dr. Dwarakanath is a physicist working at Bell Labs. in New Jersey. He teaches sanskrit during his free time and interested in vedic learning and vedanta.

From one of the earlier links provided in the first post in this thread, we have the folllowing(one will forgive the references to an Aryan race, since the author is Western) ;

[quote]The basis of Hindu calendar calculation is Vedic. This calendar has been modified and elaborated, but because it is based on the stars (nakshatras) visible to the naked eye, and on the visible Lunar phases, it is more accurate than any others of the past. The actual moments when Lunar months begin can easily be checked by the regular appearances of Solar eclipses, and the middle moment of a Lunar month -- Purnima or full moon -- can similarly be verified by the more frequent Lunar eclipses. Hence the Hindu calendar, not requiring special instruments for its rectification, has maintained great accuracy for thousands of years.

The oldest Aryan calendar is probably the Vedic; at first lunar, later with solar elements added to it. The sister Avesta calendar is similarly first Lunar, but later only Solar. Both these calendars (the oldest in the Aryan Race) are influenced by the prehistoric calendars of the first and second root races at the North Pole and its surroundings, as they reckon with days and nights lasting six months. (The Inca Zodiac, the Dendra Egyptian Zodiac, and the Chinese lunar mansions are possibly Atlantean or Atlanto-Aryan; though much has been added to both the Egyptian and the Chinese systems which is purely Aryan and post Vedic.)

For untold ages, the Hindus have observed the motion of the moon, the sun and the seven planets along a definite path that circles our sky and is marked by fixed clusters of stars. The moon afforded the simplest example. These early astronomers observed that the moon, moving among these fixed star constellations which they called nakshatras, returned to the same nakshatra in 27.32166 days, thus completing one nakshatra month. They found it convenient to divide these groups of stars into 27 almost equal sections, or the 27 nakshatras. By this method of reckoning, instead of giving the date of a month, as Western calendars do, the Hindus gave the name of the nakshatra in which the moon was to be seen. (The moon is in each of these nakshatras for approximately one day plus eighteen minutes.)

This scheme fitted nicely with the sun's cycle, for the Hindus noted that the sun traversed the same circle through the sky, but that it returned to its starting place only after 365.258756481 days, or what we call a Solar Sidereal Year. (Modern figures based on this Hindu figure quote 365.2596296 days -- a distinction without a difference, for ordinary purposes.) Now, having already divided the month into the 27 nakshatras for the convenience of reckoning the moon's voyage through the heavens, what more natural than that these same nakshatras should serve for the study of the Sun's course? Being in a circle of 360 degrees, each nakshatra takes up 131/3 degrees of that circle. The Sun, moving about 1 degree in a day, is seen for 131/3 days in each nakshatra. The system of reckoning according to the moon nakshatras is current today, that of the sun's being uncommon.

At present, the nakshatra reckoning, both Solar and Lunar, is begun from ASVINI, which is also the beginning of the first Zodiacal Rasi or sign Mesha. (Aswins, according to the Theosophical Glossary, are twin deities, "the Kumara-Egos, the reincarnating 'Principles' in this Manvantara.") This method obtains only at present, because, due to the precession of the equinoxes, not only will the English date change (after 1975) for the starting of the first Solar nakshatra, but in the course of a longer time, the sun's entry on any particular nakshatra will regress and occur during all the four seasons of the year. The Maitriopanishad (6.14) shows how, since the writing of that record, this regress has been taking place.

In brief, then, the earliest method, the Vedic, of counting, was to name the moon through the various nakshatras -- the circle or cycle repeating itself each Sidereal-Star-Month. Later the sun's place in the same nakshatras was noted, the year ending when the Sun returned to the same nakshatra. Then came the noting of the Solar and Lunar eclipses, and the observance of the New and Full Moons divided the month into the two phases of waxing and waning Moon, the month beginning at the moment of New Moon. This is how the Hindus reckon today, the month taking its name from the nakshatra in which the Full Moon is seen each month. The Full Moon being exactly opposite the Sun, the Solar nakshatra bears the same name as the Lunar month six months ahead, while each Lunar month bears the same name as the 14th Solar nakshatra ahead.

The Western student faced with these unfamiliar calculations may echo the old Persian proverb, "Why count big numbers and small fractions, when they are all amassed in 1?" But the Hindu looks on these figures from another point of view -- he lives with them, and among them, and by them, much of the time. Consider a Sanscrit sloka (verse) about the Savati or pearl nakshatra, which marks the new season after the monsoon is over. The sloka says, "If in the Swati a rain drop falls into the sea, that drop becomes a pearl." This may sound foolish, for the peasant, though he live in the depth of the interior of India, knows that pearls come from the sea -- even if he does not necessarily understand that these pearls grow inside the oyster. He does know, however, that if it rains at this period of the year, his crops will yield great wealth. And the pearl is synonymous with wealth among people who, if they have any money, invest it in jewelry, especially gold and pearls, rather than in the banks. (Poetically, rice, their staple food,

is referred to as pearls.) Thus another apparently meaningless sloka which stumps the dry and intellectually bound translators, is found to contain "pearls of wisdom"!


The following is also a useful beginner essay on Jyotish (one of the links above)

[url=]For Beginners in Jyotish-1[/url]

History has not yet caught up with the investigation of the works done by the scholars of Ancient India. In this article, I would like to give you a brief idea of the work of some of the great astronomers of ancient India. Before beginning, let me tell you that these men were mostly into several fields at the same time. So, the same person may have dealt in varied subjects like astronomy,mathematics, philosophy etc. at the same time.

byPradeep Nair (

      We begin this journey covering the works of ancient astronomers with Aryabhata.

      Aryabhata was one of the revolutionaries in science whose work, the Aryabhatiya was almost forgotten. Aryabhata is regarded as the greatest mathematician-astronomer of India. It was with this honour that India's first satellite was named after him. 

     Aryabhatta was born in 476 A.D. He wrote his first work, Aryabhatiya in 499 A.D. at the age of 23. 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).

     Aryabhata (476 - 550 A.D.) 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. To justify this point, he stated:

        "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."

     Aryabhata was among the first astronomers to make an attempt at measuring the Earth's circumference. Aryabhata accurately calculated the Earth's circumference as 24,835 miles, which was only 0.2% smaller than the actual value of 24,902 miles.      

    Another of Aryabhatta's work, Aryabhatiya-Siddhanta, is only known through references to it another books.Among his most notable contributions to modern astronomy are: the explanation and computation of solar and lunar eclipses, the expounding of the heliocentric model of the solar system and the computation of the length of earth's revolution around the sun.

     We now go ahead in chronological order to the other great astronomers of ancient India beginning with Varahmihira (505 - 587 AD). He worked as one of the Navratnas or nine gems in the court of Chandragupta Vikramaditya. His book Panchasiddhantika (The Five Astronomical Canons), written in 575 AD gives us information about older Indian texts which are now lost. The work is a treatise on mathematical astronomy.

    Next,we come to, Brahmagupta (598-668 AD). He wrote two texts - Brahmasphutasiddhanta in 628 and the Khandakhadyaka in 665. Some of his important contributions are: methods for calculations of the motions and places of various planets, their rising and setting, conjunctions, and the calculations of eclipses of the sun and the moon.    

    Sripati(1019 - 1066 AD) was an Indian astronomer and mathematician, author of Dhikotidakarana (written in 1039 AD) a work on solar and lunar eclipses. He also wrote the Druvamanasa in 1056 AD for calculating planetary longitudes, eclipses and planetary transits. He also wrote a major work on astronomy titled Siddhantasekhara and an incomplete mathematical treatise Ganitatilaka.
     Next, we take a look at Bhaskara (1114 - 1185). His main works are Lilavati, Bijaganti and Siddhanta Shiromani. He worked on the following subjects: mean longigtudes of the planets, true longitudes of the planets, the three problems of diurnal rotation, syzygies, lunar and solar eclipses,latitudes of the planets, risings and settings, the moon's crescent, conjunctions of planets with each other and the conjunctions of planets with the fixed stars, the paths of the sun and the moon. He is also credited with the near accurate calculation of the sidereal earth as 365.2588 days. The modern accepted measurement is 365.2596 days, an error of just one minute. He also wrote about the first visibilities of the planets,astronomical instruments, problems of astronomical calculations and the seasons.

     Here we end the great journey that began with Aryabhatta and ended with Bhaskara. I hope you can respect that the work that these great astronomers have done at so early a time. Their work was lost before being found. Theories are being discussed that the Arabs translated this work in Kerala and then made it available to the Europeans in the 15th century which introduced them to the works of calculus. This is only a theory and has not yet been proved.Studies on this matter continues till this date. There is also work on the translation of some of the major works into English and Hindi. But, the true beauty of these works can be recognized only when read in the language in which they were written -  Sanskrit.

Ancient Indians' interest in astronomy was an extension of their religious preoccupations and inasmuch, astronomy and mathematics ran parallel. Both were faithful to the needs of objectivity and subjectivity. Astronomy began as mere wonder at what was observed in the heavens above, grew into a systematic observation and speculation, hence forward into scientific inquiry and interpretation, finally emerging as a sophisticated discipline. Mystical interpretations of the movement of stars and planets developed into astrological science, and astronomy grew into a major factor in the intellectual pursuits of different cultural periods.
The chief sources of astronomy-related information are the Vedic texts, Jain literature, and the siddhantas (texts), as also the endeavours in Kerala. Some seals of the Indus Valley period are believed to yield information of the knowledge available to those early settlers, as also the orientation of certain constructions clearly governed by such considerations. An interesting aspect is the Jantar Mantar observatories built by Sawai Jai Singh of Jaipur. There are 5 such structures for measuring time and for astronomy-related calculations, at New Delhi, Varanasi, Jaipur, Mathura and Ujjain. These eighteenth century astrolabes are important for both scientific and architectural reasons.

Sawai Jai Singh, in his determination to provide accurate astrological tables, ordered these gigantic structures of stone. The Jaipur observatory includes the largest sundial in the world with a 90 feet high projecting arm (the gnomon). The measurements achieved by these Jantar Mantars were particularly impressive for their time - the astronomical table was very accurate and in some instances, better than contemporary western ones. This table was published in Persian and Sanskrit as the Zij Muhammad Shahi. The time was and is calculated by a study of the shadows cast by the central straight walls on to the curved walls beyond. The weather forecasts and other information provided by these sundials are very much in use at present, for religious and practical purposes.


The four Vedas comprise the Samhitas - texts of prayers and hymns, charms, invocations and sacrificial formulae. The Rig Veda is the Book of Devotional Verse, the Yajur Veda is the Book of Sacrificial Formulae, the Sama Veda is the Book of Chants, and the Atharva Veda is the book of Mystico-therapeutic Priestcraft. Their composition precedes their arrangement into the four Samhitas by a long period of oral transmission.

Rig Veda and Atharva Veda hymns point to the observance of a lunar year. The Moon itself was regarded as the 'maker of months' - masakrt. Many indications are present as to the awareness of the autumn equinox - references to Aditi (this corresponds to Pollux, longitude 113°). Daksha (Vega longitude 284°), Rudra (Betelgeuse, longitude 88°) and Rohini (Aedebaran, longitude 69°). The changing longitudes mentioned are a consequence of the precession of the equinoxes. These details are useful for another reason: they reveal the date of composition. Thus, allowing for 72 years per degree (plus, allowance for error) the years should be 6200 BC, 5400 BC, 4350 BC and 3070 BC respectively. Hymn 1.164 of the Rig Veda composed by the sage Dirghatamas refers to a wheel of time with a year 0f 360 lunar days and twelve lunar months. The year mentioned in the hymn begins with the Autumn star Agni (Alcyon, longitude 59°5), corresponding to the year circa 2350 BC. (The numbering of the hymns demonstrates use of the decimal system).

Yajur Veda and Atharva Veda reveal a definite calendrical awareness - many sacrifices, including the Gavam Ayana, are of different lengths of time based on the daily cycle of the Sun. For reasons of ritual, the day was divided into 3,4,5 or 15 equal divisions, each with a different name. Apart from naming twenty seven stars beginning with Krttika, these Vedas mention five planets and name two of them - Juipter (Brihaspati) and Venus (Vena).

The Taittriya Brahmana speaks highly of nakshatravidya (nakshatra= stars, vidya= knowledge) and states clearly the existence of scholars of this science.


The Ardha-Magadhi Prakrit texts are composed of the fragments and oral traditions of the original Jain texts known as Punva. This recasting was the effort of the Svetambara sect, and this body of work consists of forty five or fifty books. The basic texts are:
a) Angas: these concern rituals, legends, and doctrines. Of the twelve Angas, two - Sthananga and Bhagavatisutra - relate to astronomy and mathematics. The others are - Acaranga, Sutrakrtanga, Samavayanga, Jnatrdharmakatha, Upasakadasa, Antakrtadasa, Anuttera-aupapa-tikadasa, Prasna-Vyakarana, Vipakasutra and Drstivada.

b) Upangas - these too are twelve in number, of which Suryaprajnapati, Candraprajnapati and the Seventh Section of Jambudvipaprajnapati concern themselves with astronomy. The second section of Jambudvipaprajnapati discusses Time, the concept ranging from asankhyata ('inscrutable infinitesimal Time') to sirsaprahelika i.e. millions of years.

c) Prakirnakas - these are miscellaneous texts, ten in number.

d) Chedasutras - these nine books state the rules that govern monastic life, including jurisprudence.

e) Mulasutras - of the four Mulasutras - Uttaradhyayana, Avasyaka, Dasavaikalika and Pinda-inryukti - the first contains some facts on astronomy and mathematics.

The Culikasutra of two parts - Nandisutra and Anuyogadvarasutra- is a treatise on astronomy and mathematics.

Jain post-canonical literature is represented by work such as Tattvarthadhigama Sutra by Umasvati (AD 185-219) on astronomy and cosmology; the 7000-verse Trilokaprajnapati by Yati Vrsabha (AD 473-609) of which chapter 27 is on astronomy; Jyotisakarandaka by Padaliptacharya (based on the Suryaprajnapati) that contains the total of Jain views and observations on astronomy; Karananuyoga or Ganitanuyoga of the Digambara sect, a comprehensive text on Jain astronomy.

The Centre of the Universe

Mount Meru was regarded as the central axis of the Earth, the latter seen as a motionless planet. These two, along with the constellations, planets, continents, rivers, seas and mountains constitute Jambudvipa (literally, 'rose-apple land'). Certainly, this had a metaphysical aspect as well- Mount Meru is the subtle inner essence that generates everything (or Reality). Awareness of the subjective reality of all creation (that everything is connected) is sometimes expressed through the diagram of the Jambuvriksha, i.e. the world tree. The cosmic diagrams of Jain literature depict Mount Meru at the centre, and the outermost limit illustrates the twelve months, the planetary cycles and the movements of the Sun the Moon. The Polar Star is depicted as being directly above Mount Meru.

In addition to these works, there were the books on astronomical yantras (devices). Mahendra Suri's (AD 1348) Yantraraja was followed by the Ustaralayayantra by Meghalaya (circa AD 1500) which discusses the use and construction of the astrolabe (an instrument to determine the altitude of planets and stars). These two are the major works in this field.

Of the eighteen early siddhantas written by Pitamaha, Surya, Vyasa, Atri, Vasistha, Kasyapa, Parasara, Narada, Garga, Manu, Marici, Lomasa (Romaka), Angiras, Bhrgu, Paulisa, Cyavana, Yavana, Saunaka, only five survive as extracts. Panchasiddhanta by Varahamihira (composed in AD 578) includes the siddhantas of Surya, Vasistha, Pitamaha, Paulisa and Romaka.

The later siddhantas represent a considerable advance in astronomy- they were far more precise and calculations were accurate and easier than in the past.

The Aryabhatiya (AD 499) of Aryabhata the First discussed spherical astronomy in addition to calculations for planetary positions and their mean. Solar and lunar eclipses were elaborated upon, as also the fact that the Earth's shadow was responsible for the phases of the Moon, that the Earth rotated on its axis, and the Moon revolved round the Earth.

Bhaskara the First's works- Mahabhaskariya and Laghubhaskariya- were commentaries on the Aryabhatiya. He calculated complete revolutions performed by a planet using Aryabhata's rule. Bhaskara's equation y=ax-C/b is a variation of Aryabhata's x=by+c/a. In Bhaskara's equation, a=bhajya (revolution number of planets), b=hara (divisor or civil days in a yuga), c=agra (residue of the revolution of the planets), x=gunkara (complete revolutions of a planet, i.e. ahargana) and y=phala (complete revolutions performed by a planet).


Aryabhata the First's system was followed by astronomers in Kerala (a state of southern India) who in AD 683 met in Tirunavay to launch the Parahita system of computation. This new method was an amendment of the former. The major texts were Grahacaranibandhana and Mahamarganibandhana by Haridatta. However, over the centuries it was found that observations did not correlate to the results as calculated by the Parihata system. Thus, in 1431, Parmesvara's (1360-1455) Drk system gained ascendance.

During this period, a host of other literary works on astronomy were written based on the Parihita and Drk systems. Known as Karana literature, this included:
a) Karanaratna by Devacarya. The eight chapters deal with calculations for the longitudes of the Sun, Moon, and the planets, eclipses, gnomon shadow (the shadow on a sundial cast by a stationary arm), helical visibility, planetary conjunctions and the rising of the Moon.

b) Vakyakarana (AD 1300) and Drkharana by Jyesthadeva
(AD 1500- 1610).

c) Karanasara by Sankara Variyar (AD 1500-60).

d) Karanamrta by Citrabhanu (circa 1530).

e) Sadratnamala by Sankara Varman (1800-38).

Vakyas are the mnemonics used by both systems to generate different astronomical tables. For instance, the work Candravakyas of Vararuci yields the two hundred and forty eight daily longitudes of the Moon for nine anomalistic months. Other vakyas provide, for instance, the 3031 daily lunar longitudes for 110 anomalistic months.

The Aganita-grahacara by Madhava is replete with information on the Moon, the longitudes of planets stretching over many years, and planetary motions. All of it is neatly organized into tables.

Computing the shadow of the Moon aided the calculation of time and planetary positions. Many works were composed on this topic, the major ones being: Candracchyaganita I by Paramesvara, followed by Candracchayaganita II by Nilakantha, and Candracchayaganita III and IV that remain anonymous. Other works include Chayaslaka by Acyuta Pisarati, and three anonymous texts Candracchayanayanopavah, Chayaganita (four different volumes), and Suryacchayadiganita (two different works).

There were eight important texts on astronomical rationale:

a) Lagnaprokarana by Madhava (1360 - 1440) discussing the computation of the ascendant.

b) Grahanayayadipaka by Paramesvara that dealt with the computation of eclipses.

c) Yuktibhasa by Jyesthadeva on astronomy and mathematics.

d) Rasigolasphutaniti by Acyuta Pisarati that provided calculations for measuring planetary longitudes on the ecliptic.

e) Nyayaratna by Putumana Somayaji.

f) Ganitayuktayah on astronomical theory.

g) Jyotirmimamsa by Nilakantha, composed in 1504. This work focussed on the vital role of observation in astronomy, as well as the need to correct parameters regularly on the basis of the eclipses, Sun, Moon and the planets.

h) Grahapariksakarana, also by Nilakantha, that provided details of methods of practical astronomy.



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.  1st February 2001.  <>. 

2.                  Indira Gandhi National Centre for the Arts.  Indian Cosmology, Reflections in Religion and Metaphysics.  2nd February 2001.  Indira Gandhi National Centre for the Arts.  1st February 2001.  <>. 

3.                  Muley, Gunakar.  “Aryabhata”.  Vigyan Prasar News.  August 2000.  5th February 2001.  <>. 

4.                  University of St. Andrews, Scotland.  Aryabhata, the Elder.  November 2000.  University of St. Andrews, Scotland.  28th January 2001.  <>.


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:
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

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

Lunar months - The lunar month is the time-period from completion of new-moon (conjunction of Moon with the Sun) to the next new-moon. There are two kinds of lunar months used in India, the new-moon ending and the full-moon ending. The new moon ending lunar months covers the period from one new-moon to the next. This is known as Amanta or Sukladi system. The day next to Amavasya is the fast day of the month. The full-moon ending lunar month known as Purnimanta covers the period from one full moon to the next and begins from the day after full moon. This is known as the Krishnadi system. In this two systems naming of the months in Sukla paksha are the same, but in Krishna paksa the next lunar month is denoted, e.g. Chaitra Sukla in Sukladi system is equivalent to Chaitra Sudi in Krishnadi system, but Chaitra Krishna in Sukladi system is equivalent to Vaisakha Vadi in Krishnadi system and so on.

Lunation - The month or lunation used in astronomy is the mean synodic period, which is the number of days comprised within a large number of lunations divided by the number of lunations. The present duration of lunation is 29.530589 days or 29d12h44m 2."9.


Indian Journal of History of Science, 40.1 (2005) 1-7

(Received 8 March 2004)
It is shown that the Brahmanical stories associated with Pravargya ceremony and S unahsepha legend, as well as the verses of As’vinl-s’astra corraborate our earlier conclusions about the earliest Vedic calendar. Its further development after the adoption of lunar month is briefly discussed here.
Key words: A.s’vini-s’ăstra, 5-year yuga, Gavömayanam sacrifice, Pravargya, Sunahsepha legend, Utsarjina ayanam.
In an earlier paper’ we had shown that the earliest Vedic calendar envisaged a year of 360 days consisting of 12 months of3O days each, in which 4 to 6 days were added at the end of the year to complete the ‘year of seasons’. It was later converted into a six-year yuga in which six years of 360 days were followed by an adhikamăsa of 30 days (ahorătras) by Rohita. The year was started at winter solstice heralded by the heliacal rising of As’vin1-nakatra, which was the case around 7000 BC. The twelve months had tropical names from Aruna to Sambhara and the adhikamcisa was called Mahăsvăn. The year was divided into three seasons: Agnitu, Süryartu and Candramărtu akin to caturmdsyas of the later period that are appropriate for the Indian climate. We had provided there several vedic quotations in support of these conclusions. Now, we present here evidence from the Brihmam texts of three vedas for the same.2
Gavŕmayanam, the yearlong sacrific which regulated the earliest Vedic Calendar, is described in the 12th kăncja of the Satapatha Brŕhmana3. It lasted for 361 days and divided into two semesters (satras) of 180 days each with a
* 5-76, Vivekananda Nagar, Habshiguda St. No. 8/26, Hyderabad 500007

VLuvat day in between.
It is stated that the sacrificial rituals in the second half retraced their path in the first half. Now, according to Aitareya-Brăhmcrna (18.18 and 1 8.22) the Sun reached its highest altitude on the Visuvat day, which thus, coincided with the summer solstice. This makes it clear that Gavămayanam sacrifice was started on winter solstice day. So, the first satra of 180 days which was divided into 6 months of 30 days each, covered the northward passage of the Sun (uttarăyana). Similarly, the second satra of 180 days, which was also divided into 6 months of 30 days each, covered the southward passage of the Sun (daksin&yana).Each month was further divided into 5 yac1ahas of 6 days each. As the annual sacrifice falls short of the tropical year by about 4 or 5 days, it was the practice of conducting the Pravargya and Upăsad rituals lasting for 4 or 5 days, before the beginning of the next year’s sacrifice.
The Pravargya ritual is described in the 14th kănçla of the Sat apat haBrăhmana. 3 Its contents and the story associated with it show that the yearly sacrifice was started with the heliacal rising of As’vinI-nakatra. Pravargya mainly consists of baking three earthen pots called Mahăvlra pots which were used for boiling milk to produce the hot drought of milk called Gharma. The rudiments of this ritual are stjll extant in some parts of India. Milk is boiled in an earthen pot on Makara-sańkrănti day in south India and on Rat hasaptaml day in Maharashtra. Now, Makara-sańkrănti was the day of winter solstice at the beginning of Siddhnta period. Similarly, Rathasaptami was the winter solstice day during Vedăhga-Jyotisa period and it is connected with the passing away of Bh1ma on the next day in Mahăbhdrata. So, it is clear that the Pravargya ritual was performed at winter solstice before the Gavămayanam sacrifice. The Pravargya ritual lasted for three days and it was followed by the Upäsad days of consecration (d1k. Although Upäsad days were also three in number they could be observed simultaneously with some Pravargya days so that the total number of days could be 4 or 5, as required, vide Satapatha-Brăhmana 3 .4.4. Pravargya and Upăsads represented the head and the neck of the sacrifice respectively. According to the story associated with the ritual of Pravargya, the head of the scrifice, was lost due to the breaking of Viiu’s bowstring. Sage Dadhynka, who knew how to put the head back, was threatened by Indra that he would cut off Dadhyăn ka’s head if he reveals the secret to others. So Mvinrkumaras came to help. They cut off Dadhyânka’s head and put a horse’s head in its place. When Indra cut off that head, Mvinikumăras put back Dadhyinka’s head. This ia an allegoric story telling how Mvinikumras found that winter solstice was related to As’vini-naksatra which resembles the head of a horse. In this way the Gavămayanam sacrifice could be restarted with the heliacal rising of As’vinI-nakatra.
We find further corraboration for this in the As’vinl-S!ăstra which is referred to by B.G. Tilak5 and A C Das6. It consists of the stotras to be recited before the beginning of the Gavămayanam. They are addressed to AS!vinikumăras, Uas and the Sun, in that order, which points to the heliacal rising of As’vinI-nakatra. The number of dawns on which As’vini-S!ăstra was recited is given in Taittlrlya Sal?lhită(IV 3.11)’ that contain the verses for the dawn bricks of Vedic altars. We give below the first six verses of As’vinl-S!ästra;
iyameva ydprathamăvyaucchadantarasyănz carati pravis hZz/
vadhurjagcina navagarjjănibhitraya enăm mdtimdnali sacante II
1 II
‘This, verily, is that dawned first and moved above the horizon like a new bride, followed by three great ones (Agni, Sürya, Văyu).’
chandasvastrl uasZzpepisdnci samdnaiyonimanu san caranti /
süryapatnl vicarataprajanati ketun:z kvăne ajare bhuriretasă II
2 II
‘Possessed of songs, the two Dawns, the two wives of the Sun, unwasting, rich in seed, move about displaying their banner and knowing well (their way).’
tasya panthămanutisra dgustraya adhamiso anujyotisăgul /
prajcimekd sakatyurjamekd rakati devayundm II 3 II
‘The three maidens have come along the path of 1?tu; the three fires with light have followed. One projects progeny, one the vigour and one ordinance of the pious’.
abhavadhŕ turiyŕ yajnasyapaka vayo bhavantl /
găyatriii tri ubhanijagatimanuy(ubhaii brhadarkaipyujjänŕ
savarci bharantidam /14 II

‘That which was the fourth, acting as r’Ps of the two wings of the sacrifice, has become the four-fold stoma using Gayatrl, Trstubh, Jagati, Anustubh, Brhati in the great song, which brought their light.’
pańcabhidhăncividadhăvidam yajnăsăii svasr rajanayan pańcapahca /
tăsăyu yănti prayavei a pańcancinărtipdi i rtavodhamănah II 5 II
‘The creator did it with the five; heralded five sisters with each of them, their five courses (kitavaii) assuming various forms, move in combination (prayavena).’
tn??? s’atsvasăra u.ayanti tam samănaiketu?ppratimuńcamănăIz /
rtustanvate kavayah prajănatiblzamadhye dhandasaI paniyanti
bhăsvatih II 6 II
‘The thirty sisters, bearing the same banner, move on the appointed place (ni.jkrtam). They, the wise, create the seasons. Refulgent, knowing (their way), they go by (pariyänti)amidst songs.’
We see that the first five verses refer to five dawns separately, from which we gather that during earlier times five days were added at the end of the year of 360 days. The sixth verse, however, speaks of3O dawns in groups of six that created the seasons. It thus becomes clear that during later times an intercalary month (adhikamăsa) of 30 days divided into 5 yac/ahas, was added at the end of the sixth year. B.G. Tilak5 had used this piece from AitareyaBrŕhmana to support his theory of the Arctic home of vedas that it indicated a long night of 30 normal days. But we now find a simpler interpretation appropriate for the Indian tropical latitutdes, as argued by A.C. Das.7
It has earlier been stated that according to Athanvaveda (13.3.8) Rohita created the adhikamăsa of 30 ahorătras:
ahorătraivimirta??z tnizs’adafzge trayodaiam măsam nimirtite /
The connection of Rohita with the adhikamäsa can be inferred from the story of Suna1sepha in Aitareya-Brâhmana (III). Rohita, the son of king  
Haricandra, is identified with the rising sun, particularly the rising sun of the winter solstice. Varuna, who formed the heavenly path (ecliptic) for the Sun and the Moon, had given Haricandra a boon that he would be blessed with a son on the condition that the son (Rohita) was to be sacrificed to Varun a. This means that the sacrifice was to be started with the rising sun on the winter solstice day. However Rohita ran away at the time of the sacrifice (due to the wrong length of the year). He wandered for six years after which the sacrifice was conducted with the replacement of Rohita by Sunal)sepha (adhikamäsa) at the end of the sixth year. This refers to the institution of the adhikamăa of 30 civil days at the end of six years by Rohita as referred in above quotation from the Atharvaveda. Sunal)sepha saved himself from being killed by prayers to Prajăpati (the lord of the year), Agni (sacrificial fire), Savitar (the sun), As’vins and Uyas (dawn), all pointing to the heliacal rising of As’vin1-nakatra at the start of the year with winter solstice. The six years had names: Saiivatsara, Parivatsara, Idăvatsara, Içluvatsara, Idvatsara and Vatsara.
That the legends about Mvinikumäras concerning their healing powers represented some physical phenomenon was realized by several Indologists like Bonfey.1° As the Mvinrkumras are the deities of the dawn, the heliacal rising of As’vint-nakatra was identified with the beginning of Vasanta-rtu (madhumdsa) by P. C. Sengupta.9 As the sun’s tropical longitude would be 330° the beginning of Vasanta-rtu, Sengupta derived an epoch of 3800 BC for Rgveda, which agreed with the epoch derived by B. G. Tilak in his book Orion. But we identify it with that of heliacal rising ofAIvinI-nakatra at winter solstice, because the sun gets rejuvenated at that time. Around 7000 BC, when As’vin1-nakatra had a tropical longitude of 270°, the helical rising of As’vinlnaiqatra occurred around 6th January. Then with the practice of adhikamăsa after 6 years we get the As’vinl calendar discussed by us’, which would start on 25th December on an average.

(a) Replacement of Gavămayanam by Utsarjină-ayana: The thirty-day month was suggested by the repetition of the lunar phases after about 30 days. The new moon and full moon phases were considered particularly auspicious; so special sacrifices known as Dars’a and Pńriamasa-yasti were perfonned on those days as described in the and 11th kăpcjas of Satpatha Brăhmana.3 Their observations showed that the lunar phases repeated at intervals of about 29V2 days. Hence, later, when it was decided to base the calendar on lunar months,the lunar month was also divided into 30 equal parts called tithis, which is a unique feature of the Indian calendar. The lunar month was also divided into two halves like the year. The bright half is called Sukla-paka, and the dark half is called Kyiv-paksa. The tithis are numbered Sukia-pratipada (Si) to Pauriimă (S 15) and Krna-pratipada (Ki) to Amcivasyd (K 15).
The use of lunar month required a modification of the yearlong Gavămayanam sacrifice. Taittir1ya-Saiihită(VII.5.6)7 describes this so called Utsarjinăyana sacrifice which covered 360 tithis of the 12 lunar months containing 354 days. In this sacrifice the last acfrihas of the 4th and 6t1 month during the first satra and last sac1ahas of the 7th, 9th and 11th month in the second satra were reduced by one, and there was no Visuvat day in the middle’2. As 354 days fell short of the 365 day by 11 days in the seasonal year, atirătra sacrifices were performed on ii days at the end of Utsarjinci ayanam sacrifice. In the Taittirlya San:zhită (VII.2.6.1)7 they are said to be the children of seasons in the sense that they complete the year of seasons.
(b) 5-year yuga: Further evolution of the vedic calendar is discussed by us elsewhere.’3 We give below a gist of the same. The above method of adjusting the year-length was found to be inconvenient in a calendar based on the lunar months, because the tithi of the year beginning changed from year to year (vide 1?gveda IV.33.7). Ibbus’5 introduced the pracice of formally adding 12 atircitra at the end of the year, or, cumulatively 2 additional months (60 tithis) in 5 years. In the beginning, one adhikamdsa was added at the end of the 3rd year and the second at the end of the 5th year. It was called Saiisarpa. Later it was found convenient to introduce the adhikamasa at the end of every 30 months. They were called Malimlucha when introduced in the middle of the year and Satisarpa when introduced at the end of the year. The five years were given the same names as in the 6—year yuga except the difference that Ic/uvatsara was renamed Anuvatsara and the sixth year Vatsara was dropped.
The five-yearyuga system is illustrated by several quotations from Vedic literature by R. Shamasastry’2 in Chapter II. The mathematical treatment of the  
5-year yuga calendar described in Vedaiga-JyotLya with its modifications and improvements by 30-year Dakyayan?ya sacrifice and 95-yearAgnicayana-vidhi is discussed by us in another paper.14
1. K. D. Abhyankar, ‘A search for the earlier Vedic calendar’, IJHS 28.1 (1993) 1-14.
2. K. D. Abhyankar, ‘Presiddhantic Indian astronomy — A Reappraisal, INSA Project Report (unpublished), 1998.
3. J. Eggling, ‘The Satapatha-Br&hmana, Reprinted by MLDB, New Delhi, 1994.
4. M. N. Saha and N. C. Lahiri,’Report of the Calendar Reform Committee, CSIR, New Delhi, 1958, p.266.
5. B. G.. Tikak, Arctic Home of Vedas, Tilak Press, Pune, 1925.
6. A. C. Das, Rigvedic India, Reprinted by MLDB, New Delhi, 1971.
7. A. B. Keith, Taittiriya-Sarnhită, Reprinted by MLDB, New Delhi, 1967, p.334.
8. A. B. Keith, Rgvedic Brahmanas, Reprinted by MLDB, New Delhi, 1998, pp.299-

9. B.G.. Tilak, Orion, Tilak Press, Pune, 1925.
10. R. J. H. Griffith, The Hymns of Rgveda, Reprinted by MLDB, New Delhi, 1976,
11. R. Shamasastry, Drapsa: The Vedic cycle of eclipses, Shri Panchacharya Press, Mysore, 1938, pp.38-40, Chapter II.
12. K. D. Abhyankar, ‘On pre-Siddhantic evolution of Indian calendar’, Bull. Aston. Soc. India, 26 (1998) 67-74.
13. K. D. Abhyankar,’On two important provisions in Vedäh ga-Jyotisa’, IJHS, 37.3, (2002) 213-22 1.
14. 1bhus came into prominence during the Migairsa (Orion) period of3 800 BC found by B. G. Tilak. There were three 1bhus who divided the celestial cup (ecliptic) in three different ways. The eldest 1 bhu called R bhavan divided it into two parts as before, viz. Uttardyana from Bhadrapădas to Maghă (lunar Phă1gura to Srăvana), and Daksin ayana from Phă1guia to Satabhisag (lunar Bhadrapăda to Magha). The second 1bhu named Vibhavan divided it into three parts corresponding to the three Rtus, viz. Agni R tu from Bhadrpdas to Punarvasu (lunar Phalguna to Jyestha), Suiya Rtu from Puy to Vi khă (lunar Ascha to Avin) and Candramä R tu from Anunidha to Satabhiag (lunar Kirtik to Măgha). The youngest 1bhu named Vaja divided the ecliptic into four parts on the basis of the four cardinal points, viz. Winter Solstice at Bhadrpdas (lunar Phlguna), Vernal Equinox at Mrgas’irsa (lunar Jyestha), Summer Solstice at Phălguri a (lunar Bha drapăda), and Autumnal Equinox at Mühi (lunar Mărgair a)vide rnasänam
märghas’irsoham of Bhagavatagith (referred to as best full moon (of Saradrtu) in Mgaira nakatra.





Notes and references

1. K. D. Abhyankar, ‘A search for the earlier Vedic calendar’, IJHS 28.1 (1993) 1-14.
2. K. D. Abhyankar, ‘Presiddhantic Indian astronomy — A Reappraisal, INSA Project Report (unpublished), 1998.
3. J. Eggling, ‘The Satapatha-Br&hmana, Reprinted by MLDB, New Delhi, 1994.
4. M. N. Saha and N. C. Lahiri,’Report of the Calendar Reform Committee, CSIR, New Delhi, 1958, p.266.
5. B. G.. Tikak, Arctic Home of Vedas, Tilak Press, Pune, 1925.
6. A. C. Das, Rigvedic India, Reprinted by MLDB, New Delhi, 1971.
7. A. B. Keith, Taittiriya-Sarnhită, Reprinted by MLDB, New Delhi, 1967, p.334.
8. A. B. Keith, Rgvedic Brahmanas, Reprinted by MLDB, New Delhi, 1998, pp.299-
9. B.G.. Tilak, Orion, Tilak Press, Pune, 1925.
10. R. J. H. Griffith, The Hymns of Rgveda, Reprinted by MLDB, New Delhi, 1976,
11. R. Shamasastry, Drapsa: The Vedic cycle of eclipses, Shri Panchacharya Press, Mysore, 1938, pp.38-40, Chapter II.
12. K. D. Abhyankar, ‘On pre-Siddhantic evolution of Indian calendar’, Bull. Aston. Soc. India, 26 (1998) 67-74.
13. K. D. Abhyankar,’On two important provisions in Vedäh ga-Jyotisa’, IJHS, 37.3, (2002) 213-22 1.
14. 1bhus came into prominence during the Migairsa (Orion) period of3 800 BC found by B. G. Tilak. There were three 1bhus who divided the celestial cup (ecliptic) in three different ways. The eldest 1 bhu called R bhavan divided it into two parts as before, viz. Uttardyana from Bhadrapădas to Maghă (lunar Phă1gura to Srăvana), and Daksin ayana from Phă1guia to Satabhisag (lunar Bhadrapăda to Magha). The second 1bhu named Vibhavan divided it into three parts corresponding to the three Rtus, viz. Agni R tu from Bhadrpdas to Punarvasu (lunar Phalguna to Jyestha), Suiya Rtu from Puy to Vi khă (lunar Ascha to Avin) and Candramä R tu from Anunidha to Satabhiag (lunar Kirtik to Măgha). The youngest 1bhu named Vaja divided the ecliptic into four parts on the basis of the four cardinal points, viz. Winter Solstice at Bhadrpdas (lunar Phlguna), Vernal Equinox at Mrgas’irsa (lunar Jyestha), Summer Solstice at Phălguri a (lunar Bha drapăda), and Autumnal Equinox at Mühi (lunar Mărgair a)vide rnasänam märg&s’irsoham of Bhagavatagith (referred to as best full moon (of Saradrtu) in Mgaira nakatra.


Astronomical calculations in ancient Bharatam based on scientific research: TP Verma  

There are two issues here: one is astronomical observation; the other is astronomical computation.


It is clear that Veda Vyasa was recording observed celestial events using them as his day's clock and calendar to realte events on the earth. There is little evidence of astronomical computation in the Great Epic, the Mahabharata which contains over 150 very specific astronomical observations and events such as the sequence of lunar-solar-lunar eclipses occurring within 13 tithi-s each, Bhishma waiting for the arrival of the uttarayana punyakaala to leave his mortal body, the starting and arrival nakshatra of the 42-day pariyatra by Shri Balarama along River Sarasvati and the celestial position of planets on each day of the 18-day war, apart from astronomical discussions during Krishna-Karna samvaada and the references to comets as demonstrated by Narahari Achar.


Remarkable work is ongoing to relate astronomical information contained in ancient texts of Bharatam to scientifically falsifiable geological events such as the formation of a rann, incursions of the sea or earthquakes or impacts of meteorites.


We have miles to go. The work is outside of itihaasa. It is related to time, more specifically, to kaala, mahaakaala in the bharatiya perceptions of the time as a cyclical continuum, an inexorable cosmic rhythm. These explorations will take us into realms beyond physics or astronomy into relating individual consciousness to cosmic consciousness, aatman to paramaatman.


We run into problems of semantics with critical terms such as graha. When does a graha refer to a planet and when does it refer to a comet in the ancient texts? Surely, unraveling of historical time (aha, chronology) cannot be performed by historians alone but has to be a collaboration between those who can fathom the mysteries of technical terms in the Veda and in Samskrtam, Jaina, Bauddha texts and those who can see parallels with the observations of scientists of a variety of disciplines ranging from mathematics and astronomy to atoms/strings and the big bang (or collapse, or whatever). Very ancient history has to be written by scientists and language scholars in a new collaborative enterprise which has to emerge. We have the bharata nidhi, the treasure of texts; we need the young nation to take up the challenge of reading this nidhi and conveying the contents to the present and future generations.


How do we explain the metaphor of Mahaakaala of Ujjain?






Astronomical calculations in ancient India based on scientific research


HTC, Dec. 7, 2006


"THE ASTRONOMICAL calculations made in ancient India and recorded in Puranas and other texts were not mythical but were based on scientific research which is corroborated even by the modern science", said eminent historian and epigraphist, Prof. TP Verma.

He was delivering a lecture on "The Science of Manvantara" organised by the Jnana-Pravaha, Centre For Cultural Studies and Research in Samne Ghat area here on Wednesday.

Prof. Verma, former head of the Ancient Indian History, Culture and Archaeology Department in Banaras Hindu University (BHU), said that 'manvantara' represented by an intelligent being called Manu, is an astronomical unit of time denoting one cycle of life on earth, which is equivalent to 30,84,48,000 years.

"During this period, the Sun with its planets completes one circle of our galaxy, which is termed as Parameshthi-Mandala in our ancient literature. A period of 14 such cycles of 'manvantaras' is estimated as whole life of the earth", he said, adding, "Notably, modern science believes the earth to have come into existence 4.5 billion years ago, which is endorsed by the Atharva-Veda".

"Such complicated and precise astronomical calculations also establish that script and art of writing in ancient India was in vogue long before it is now believed to have been", he said. Prof. Verma further informed that according to ancient Indian calculations, Shri Krishna was born in 3210 BC, which was the junction period of Dvapara and Kali Yugas.

Presiding over the lecture, renowned Sanskrit scholar, Prof. KD Tripathi observed, "It is the high-time when we should again revert back to our ancient tradition and try to make deeper probing of our rich and vast knowledge recorded in our literature and which has now become mysterious for us". "We are deeply impressed by the researches done in the western world and accept blindly, but we are unaware of the fact that we already possessed such knowledge, which unfortunately we lost due to our ignorance", he said.,0015002500030002.htm

Dharma protects those who protect it
Dharmo rakshati rakshitaha

S. Kalyanaraman




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