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Ancient Astronomy During Vedic Era
It is with some trepidation that i start a separate thread for this. The reason is that i wish to educate myself as to the extent of ancient Astronomy in the Indian subcontinent. It appears that the Indian astronomers of yore were skilled in calculating the positions of the planets and in predicting eclipses. How accurate were their predictions and calculations. what system did they use ? did they borrow from the Greeks (or vice versa) or were the Indian developments relatively autochthonous. We will try to compile a list of the texts that treat this subject and decipher what they have to say

First some links






For last two years I did lot of reading and tried to understand logic behind Vedic astrology and how it was used.

Sage Parasara father of Ved Vyasa authored Brihat Parasara Hora Shastra which is Vedic Astrology encyclopedia is written in the form of dialogues.

In ancient India astrology was very advance. Understanding of seven planets was very advance and correct to this date. In Vedic astrology retrograde planets and its roles are very well defined. Which tells they have complete knowledge of planets movement? Dasa system is based on Sun and Moon. Importance of Moon movement, tells complete knowledge of eclipse. It gives importance of Waning and Waxing moon. Importance of strength and degree from Sun and earth is very well documented.
Complex calculation of Dig Bala, Sad bala, aspects on other planets, planetary intervention, Ashitakarvarga and planetary rays. These calculations require good mathematical/algebra concepts.

I came to conclusion that they have advanced knowledge of solar system, algebra and geometry. They must be recording planetary movement for years to come to these concepts. I still don’t think that they have received some divine lecture and wrote everything in one shot.

During my visit to Greenwich planetarium, UK, it was written on one of display, there is a dispute between Arabs and Indians regarding who invented Zero, Greeks and Indian regarding planetary movement.
ideally we may want to keep this thread solely for Astronomy during the vedic era and not later day Hindu astronomy- this can go on in the Indian science thread to avoid two threads with overlapping content.

One R^igvedic mantra that provides an apparent allusion to a northern latitude is this one:

amI ya R^ikSA nihitAsa uccA naktaM dadR^ishre kuha cid diveyuH |
adabdhAni varuNasya vratAni vicAkashac candramA naktameti ||

"this great Bear set high above": amI ya R^ikSA nihitAsa uccA

more later
When the realization that Hindu astronomy was accurate dawned on the Western world during the 18th and 19th centuries, there was an immediate knee jerk reaction to trash it. see the passage below , extracted from an online book by Koenraad Elst. If the Ancient Hindu astronomy were to be accepted as authentic, then the entire Biblical account would have to be consigned to the dustbin, or so the argument went. Western scientists often have an agenda as this demonstrates. If a thesis opposes their viewpoint, then the thesis must be discarded, even if acceptance of their prior belief (e.g. the earth was created in one day or 10 days circa 4000 BCE) led to absurd conclusions. Such a behavioral trait is obviously not encouraged in the sanatana dharma. Of the six pramanas , instruments of gaining knowledge, perception(pratyaksham) and inference(anumaanam) come first. When combined with the 3 fold technique of Sravanam, mananam, Nididhyasanam , we have a powerful means of acquiring knowledge whether it is objective knowledge or subjective knowledge.

But we digress, the effort to denigrate and ridicule everything that had a Hindu nexus, was begun in right earnest. After all if a people were invaded (and lost) so many times in history they could not possibly have anything worthwhile to offer in the way of science. This is pretty much the argument advanced today by many in the west in many a context. But the wheel of reason turns ever so inexorably , even if it turns a mite slowly for our taste and surely the day will come when India and Indians will become synonymous with the higher pursuits of the human spirit.

2. Astronomical data and the Aryan question


2.2.1. Astronomical tables

<span style='font-size:14pt;line-height:100%'>One of the earliest estimates of the date of the Vedas was at once among the most scientific. In 1790, the Scottish mathematician John Playfair demonstrated that the starting-date of the astronomical observations recorded in the tables still in use among Hindu astrologers (of which three copies had reached Europe between 1687 and 1787) had to be 4300 BC.3 His proposal was dismissed as absurd by some, but it was not refuted by any scientist. </span>

Playfair’s judicious use of astronomy was countered by John Bentley with a Scriptural argument which we now must consider invalid. In 1825, Bentley objected: “<span style='font-size:14pt;line-height:100%'>By his [= Playfair’s] attempt to uphold the antiquity of Hindu books against absolute facts, he thereby supports all those horrid abuses and impositions found in them, under the pretended sanction of antiquity. Nay, his aim goes still deeper, for by the same means he endeavours to overturn the Mosaic account, and sap the very foundation of our religion: for if we are to believe in the antiquity of Hindu books, as he would wish us, then the Mosaic account is all a fable, or a fiction.”</span>4

Bentley did not object to astronomy per se, in so far as it could be helpful in showing up the falsehood of Brahminical scriptures. However, it did precisely the reverse. Falsehood in this context could have meant that the Brahmins falsely claimed high antiquity for their texts by presenting as ancient astronomical observations recorded in Scripture what were in fact back-calculations from a much later age. But Playfair showed that this was impossible.

<span style='font-size:14pt;line-height:100%'>
Back-calculation of planetary positions is a highly complex affair requiring knowledge of a number of physical laws, universal constants and actual measurements of densities, diameters and distances. Though Brahminical astronomy was remarkably sophisticated for its time, it could only back-calculate planetary position of the presumed Vedic age with an inaccuracy margin of at least several degrees of arc. With our modern knowledge, it is easy to determine what the actual positions were, and what the results of back-calculations with the Brahminical formulae would have been, e.g</span>.:

“Aldebaran was therefore 40’ before the point of the vernal equinox, according to the Indian astronomy, in the year 3102 before Christ. (…) [Modern astronomy] gives the longitude of that star 13’ from the vernal equinox, at the time of the Calyougham, agreeing, within 53’, with the determination of the Indian astronomy. This agreement is the more remarkable, that the Brahmins, by their own rules for computing the motion of the fixed stars, could not have assigned this place to Aldebaran for the beginning of Calyougham, had they calculated it from a modern observation. For as they make the motion of the fixed stars too great by more than 3” annually, if they had calculated backward from 1491, they would have placed the fixed stars less advanced by 40 or 50, at their ancient epoch, than they have actually done.”5

(<i>ed.note: there is a point to be made here. If the Brahmanas of yore were so sophisticated as to be able to back calculate planetary positions over several thusand years, surely they muxt have been sophisticated enough to observe the planetary positions and we are paying them a huge compliment when we acknowledge that they had such abilities </i>)

So, it turns out that the data given by the Brahmins corresponded not with the results deduced from their formulae, but with the actual positions, and this, according to Playfair, for nine different astronomical parameters. This is a bit much to explain away as coincidence or sheer luck.


3Playfair’s argumentation, “Remarks on the astronomy of the Brahmins”, Edinburg 1790, is reproduced in Dharampal: Indian Science and Technology in the Eighteenth Century, Academy of Gandhian Studies, Hyderabad 1983 (Impex India, Delhi 1971), p.69-124.

4John Bentley: Hindu Astronomy, republished by Shri Publ., Delhi 1990, p.xxvii; also discussed by Richard L. Thompson: “World Views: Vedic vs. Western”, The India Times, 31-3-1993. On p.111, we find that Bentley has "proven" that Krishna was born on 7 August in AD 600 (the most conservative estimate elsewhere is the 9th century BC), and on p.158ff., that Varaha Mihira (AD 510-587) was a contemporary of the Moghul emperor Akbar (r.1556-1605).

5J. Playfair in Dharampal: Indian Science and Technology, p.87.

6Quoted in S. Sathe: In Search for the Year of the Bharata War, Navabharati, Hyderabad 1982, p.32.

7N.S. Rajaram: The Politics of History, p.47.

8J. Playfair in Dharampal: Indian Science and Technology, p-118.

9J. Playfair in Dharampal: Indian Science and Technology, p.88-89.

10R.L. Thompson: Vedic Cosmography and Astronomy, Bhaktivedanta Book Trust, Los Angeles 1989, p. 19-24. Unfortunately, he gives no examples of the early use of Kali-Yuga, contenting himself with references to Indian publications offering such examples, unlikely to convince Western scholars, viz. S.D. Kulkarni: Adi Sankara, Bombay 1987, and G.C. Agrawala: Age of Bharata War, Motilal Banarsidass, Delhi 1979. Kulkarni’s book (p.281ff) offers Kali-Yuga dates such as 509 BC, but from marginal Sanskrit sources which most Western scholars would consider unreliable.

11On that day, Hindu astrologers gathered for prayer-sessions on hilltops to avert the impending catastrophe; they were moderately successful.
For those interested in a detailed discourse of the astronomical allusions that help dating I am in the process of preparing such a resource.

It is still the begining but several import allusions with accompanying star maps have already been put in. See the following file:
Astronomical references in the vedic texts

Note that these span a rather large time range an the text and actual mantra containing them are also indicated in the file.

Please access it and tell me if you can read the sanskrit fonts
<b>B. G. Sidharth - The Celestial Key to the Vedas: Discovering the Origins of the World's Oldest Civilization</b>
Good source.

Great work! I also had been thinking of doing something like this for a long while! A Dover Publications book titled "Star Names" has most Indian nakshatras and coordinates listed. Although it lists greek and arabic names most profusely. Do you know of any other reference which has an exhaustive listing of Indian asterisms, stars, constellations, nakshatras etc with their coordinates?

I can read the Sanskrit fonts fine. In the first one the word "mR^igashIrSha" is missing the "repha". The spellings that I have seen for this nakshatra are "mR^iga-shirA" or "mR^iga-shIrSha" and the corresponding name of the month is "mArga-shIrSha". I have not yet come across a "mR^iga-shIrShA" spelling, but doesn't really make any difference.

Also noticed that you chose to break-up the sandhis in the sanskrit text. Any particular reason for that?

This may not be directly relevant to the thread, but I think the Nakshatra Suktam is a beautiful Vedic poem, which paints a vivid picture of the constellations adorning the night sky. It occurs in the Taittiriya Brahamana and the various devas are inter-woven with the nakshatras. I wonder if anything useful can be gleaned from it. Maybe some of the more knowledgeable members of this forum could attempt a translation...

Here are the various nakshatras mentioned in the suktam:

No. Name Presiding deity
1 krittikA agni
2 rohiNI prajApati
3 mRgazIrSa soma
4 ArdrA rudra
5 punarvasU aditi
6 tiSya bRhaspati
7 AzreSA sarpa
8 maghA pitR
9 phalgunI aryamA
10 phalgunI bhaga
11 hasta savitA
12 citrA indra
13 svAtI vAyu
14 vizAkhe indrAgni
15 anUrAdhA mitra
16 rohiNI indra
17 vicRtau pitR
18 ASADhA ApaH
19 ASADhA vizvedeva
20 zroNA viSNu
21 zraviSThA vasu
22 zatabhiSaj indra
23 proSThapada ajaekapAt
24 proSThapada ahirbudhniya
25 revatI pUSA
26 asvayujau asvins
27 apabharaNI yama
AK thanks for the correction, will be incorporated in a future edition with more examples. As for mR^igashIrSha- yes this is the most common and probably the right spelling. I just picked that spelling from Tilak's book. But in say the TB nakShatra sUktaM it is mR^igashIrSha with a not A- will change it to that.

shridatta, as for the taittirIya brAhmaNa nakShatra sUktaM there are some differences of the deities and constellation names from your list, actually your list seems to be from the taittirIya saMhitA:

citrA indra
should be :chitrA tvaShTar: tvaShTA nakShatraM abhyeti chitrAM .
rohiNI indra
jyeShTha indra :indro jyeShThAmanu nakShtraMeti .

vicRtau pitR
mUlA nirR^iti

zatabhiSaj indra
shatabhiShak varuNa

it also include abhijit: tanno nakShatraM abhijidvijitya ...
Here is a neat little essay on Tithi, Nakshatra and raashi

Tithi, Nakshatra, Raashi …
M. R. Dwarakanath

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->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.

<span style='font-size:14pt;line-height:100%'>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). </span>
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.<!--QuoteEnd--><!--QuoteEEnd-->

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) ;

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->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)

For Beginners in Jyotish-1
More from Koenraad Elst's book on AIT. Both the Zodiac or Raashi(Solar) and the nakshatra (Lunar)system appear to have originated in India (and not in Babylon or in China)

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->2. Astronomical data and the Aryan question


Apart from the hard evidence, there are a few elements in Hindu astronomical tradition which would not count as evidence all by themselves, but which may gain a new significance when studied in the company of the more solid elements already considered.  We will mention four of them: the Saptarshi cycle, the Vedic description of a particular eclipse, cosmic number games in Vedic texts and ritual, and the surprising presence of the Zodiac.

2.4.1. The Saptarshi cycle

A lesser-known Hindu system of time-reckoning is the Saptarshi cycle of 3600 years (possibly based on the 60-year cycle, see ch. 2.4.5. below).  At any rate, by the Christian age we find writers who take this concept of a 3600-year cycle literally, and it is hard to either prove or refute that this may have been a much older tradition.

The medieval Kashmiri historian Kalhana claimed that the previous cycle had started in 3076 BC, and the present one in AD 525.  J.E. Mitchiner has suggested that the beginning of the Saptarshi reckoning was one more cycle earlier, in 6676 BC: “We may conclude that the older and original version of the Era of the Seven Rsis commenced with the Seven Rsis in Krttika in 6676 BC, used a total of 28 Naksatras, and placed the start of the Kali Yuga in 3102 BC. This version was in use in northern India from at least the 4th century BC, as witnessed by the statements of Greek and Roman writers; it was also the version used by Vrddha Garga, at around the start of the Christian era.”22 This would roughly coincide with the start of the Puranic dynastic list reported by Greco-Roman authors as starting in 6776 BC.

Indeed, the Puranic king-list as known to Greek visitors of Chandragupta’s court in the 4th century BC or to later Greco-Roman India-watchers, started in 6776 BC.  Pliny wrote that the Indians date their first king, “Liber Pater” (Roman equivalent of Dionysus), to “6,451 years and 3 months” before Alexander the Great (d. 323 BC), while Arrian puts “Dionysus” as head of the dynastic list at 6,042 + 300 + 120 = 6,462 years before Sandrokottos (Chandragupta), to whom a Greek embassy was sent in 314 BC.23 Both indications add up to a date, give or take a year, of 6776 BC.  This would, according to the implicit chronology of Puranic tradition, be the time of Manu’s enthronement, Manu being the Aryan patriarch who established his kingdom in North India after having survived the Flood.  One of Manu’s heirs was Ila, ancestress of Yayati, whose five sons became the patriarchs of the “five peoples” who form the ethnic horizon of the Vedas, one of them being Puru; in Puru’s tribe, then, one Bharata started the Bharata clan to which most of the Vedic seers belonged.

It so happens that in the 7th millennium BC, the oceans were still in the process of recovering the ground they lost during the ice Age, when the sea level was for thousands of years nearly a hundred metres below the present level.  The importance of the Glaciation, which peaked ca. 16,000 years ago, in the reconstruction of Eurasian migration histories can hardly be overestimated.  The Channel between Britain and France, with sea bottom at ca. 40 metres, was a walkway until it was inundated again in ca. 6500 BC, when the sea was already more than halfway back to its normal (or at least its present) level.  This means that for centuries before and for some more centuries after that time, the sea level was progressively rising.  Since large populations had settled in the coastal areas vacated by the receding sea at the beginning of the Ice Age, the progressive melting of the ice-caps led to the progressive flooding of ever higher-situated population centres, for several millennia until perhaps 5,000 BC.

One can imagine what would happen if today the sea level would rise a mere 10 metres: densely populated countries like the Netherlands and Bangladesh would get largely submerged, along with major cities like New York and Mumbai, and at least a quarter of the world population would have to move.  But that was, for several millennia, the human condition: one after another, low-lying villages had to be abandoned to the rising sea.  It must have seemed like a law of nature to them that the sea was forever rising, forcing men to seek higher habitats.  And this process was probably continuous only when looked at from a distance, the reality being more like periods of stable sea levels followed by sudden jumps, catastrophes when considered on the scale of a human lifetime.  Most probably, that is the origin of the Flood story.24 The Puranas describe Manu as the leader of mankind after the Flood, and if we apply a realistic average length to the rulerships of the kings mentioned in the Puranic dynastic lists, Manu may have lived in the 7th millennium BC, the time of the rising waters, warranting the suspicion that the Flood story is related to historical events at the end of the ice Age.

The myth of Atlantis and other submerged continents probably has a similar origin.  The Tamils have a tradition of a submerged land to India’s south, of which the Maledives and Sri Lanka are remaining hilltops: KumArIkhaNDam or, in the parlance of the Madras-based Theosophical Society, Lemuria. The city in which their poets’ academy or Sangam (recorded in the early Christian era, but claimed to be ten thousand years old) was established, was said to have been moved thrice because of the rising waters.  Though it is hard to see how poets working at the turn of the Christian era could have a memory of events five millennia older, one cannot dismiss as pure fable a story which tallies neatly with the known geological facts of the rising sea level at the end of the Ice Age.

And if such memory was possible, the existence of a system of time-reckoning going back that far is not impossible either.  But we must admit that for the time being, this is merely “not impossible”.  However, even if we let the Saptarshi cycle start only in 3076 BC, unrelated to Manu and the Flood, this is still hard to reconcile with the theory of an Aryan invasion in the 2nd millennium BC.

2.4.2. A remarkable eclipse

For another chronological marker, Rg-Veda 5:40:5-9 describes a solar eclipse.  From the description, one can deduce a number of conditions determining the times at which it could have taken place: it was at that site a central, non-total eclipse, which took place in the afternoon on the Kurukshetra meridian, on a given day after the summer solstice, at least in the reading of P.C. Sengupta.  Only one date satisfies all conditions, which he calculated as 26 July 3928 BC.25 We have to add, however, that this calculation stands or falls with the accuracy of the unusual translation of the word brahma as “solstice”.  This reading is supported by later scriptural references to the same event, Shankhayana Aranyaka 1:2,18 and Jaiminiya Brahmana 2:404-410.  N.S. Rajaram has identified an even more explicit use of brahma in the sense of “solstice”: in Rg-Veda 10:85:35, where brahma is associated with the division of the solar cycle in two halves.26

Moreover, the astronomical interpretation (e.g. by B.G. Tilak) of Rg-Veda 10:61:5-8, where brahma is the equinox and the fruit of the union between a divine father and daughter, i.e. the two adjoining constellations MRgashira/Orion and Rohini/Aldebaran, if not more abstractly the intersection of two related celestial circles, may be cited in support: equinox is not the same as solstice, but it is at least one of the cardinal directions, a purely astronomical rather than a religious concept; the common meaning of brahma would then be “cardinal direction”.  The division of the ecliptic in 4 parts of 900 by the solstice axis and the equinox axis is already obliquely referred to in RV 1:155:6, so the concept of “cardinal direction” was certainly understood.  Still, this construction remains sufficiently strange to be a reasonable ground for skepticism.  On the other hand, it is up to the skeptics to come up with a convincing alternative translation which fits the context.

2.4.3. Cosmic data in Vedic ritual

A different type of astronomical evidence, not to fix a precise date but to give an idea of the scientific spirit of the Vedic Aryans, is the interpretation of numerical facts about the Vedas as implicit references to astronomical data.  If this seems far-fetched, it should be borne in mind that ancient mythology and religion were primarily concerned with the visible heaven-dwellers, i.e. the heavenly bodies.  Many myths are nothing but anthropomorphic narrations of celestial phenomena such as eclipses, solstices and equinoxes, the angular relations between the orbiting planets (e.g. the regular overtaking of the planets by the fast-moving moon, therefore imagined by the Greeks as a huntress, Artemis), the analogy between the twelve-month solar cycle and the twelve-year Jupiter cycle, and even the precession.27

Apart from this figurative representation, there is also a numerical representation of astronomical data in ancient traditions.  Thus the Bible, written by a satellite culture of the astronomically astute Babylonians, used the device of enciphering astronomical data in all kinds of contingent numerical aspects of the narrative, e.g. the ages of the antediluvian patriarchs in Genesis turn out to be equal to the sums of the planets’ synodic cycles (period from one conjunction with the sun till the next): Lamech dies at age 777 = 399 (number of days in Jupiter’s synodic cycle) + 378 (Saturn’s); Mahalalel at 895 = 116 + 779 (Mercury:  Mars); Yared at 962 = 584 + 378 (Venus + Saturn).  Similarly, the symbolism of 12 and 13, referring to the lunar months in a year, is omnipresent in the Bible: 12 sons of Jacob plus 1 daughter; 12 tribes of Israel with a territory plus the 1 priestly tribe of Levi; 12 regular apostles of Jesus plus the one substitute for the traitor Judas, Matthias; the “thirteen-petalled rose” as Talmudic symbol of the Torah.

In the past decades, scientists and orthodox religionists have often made fun of attempts to connect religion with science, as in Frithjof Capra’s Tao of Physics and numerous other books.  Yet, in ancient religious texts we already see this attempt of religious thinkers to keep up with the latest in science, as outlined above for astronomy.  In his Gospel, John takes the trouble of counting the fish caught by the apostle-fishermen in their nets: 153.  Number theory was fairly advanced among the Pythagoreans, and some of its remarkable findings were well-known among the educated in the Hellenistic world.  They were aware of the unique property of 153: it is equal to the sum of the third powers of its own constituent figures: 1 + 125 + 27.  Somehow, John assumed that the religious depth of his text would gain from including some allusions to mathematics.  In ancient Pagan civilizations, this fusion of religion and proto-science was the done thing; it was usually the priests who used their leisure to develop scientific knowledge, for they were not troubled by the conflict between faith and religion which would characterize the Christian and Islamic Middle Ages.

<span style='font-size:14pt;line-height:100%'>So in the Vedas as well, we find astronomical data enciphered in all kinds of ways.  Thus, the Hindus’ most sacred number 108 is, with an inaccuracy of only 1%, the distance earth-sun expressed in solar diameters (i.e. the radius of the earth’s orbit divided by the sun’s diameter), as well as the distance earth-moon expressed in lunar diameters.  Subhash Kak has checked if such numerical combinations as just cited from Genesis also appear in the Vedas.28 They do, though they are often quite complicated and only obvious to someone well-versed in the idiosyncrasies of the multiple Vedic calendar systems.  An easy example is: the number of hymns in books 1, 2, 3 and 4 of the Rg-Veda adds up to 354, the number of days in the Lunar year consisting of 12 moon cycles.  Similarly, the total number of hymns in books 4, 5, 6 and 7 is 324, the number of days in the so-called Nakshatra year, being the duration of the sun’s stay in 24 of the 27 lunar mansions. Coincidence? </span>

According to Kak: “By adding the hymn counts of the ten books of the Rig-Veda in different combinations, we obtain numbers that are factors of the sidereal periods and the five synodic periods (…) The probability of this happening is about one in a million.  Hence whoever arranged the Rig-Veda encoded into it not only obvious numbers like the lunar year but also hidden numbers of great astronomical significance.”29

This choice of numbers in a cosmically meaningful way is also present in the construction of the Vedic altar, such as the numbers of bricks in each layer being equal to the number of days in given planetary cycles.30 It involves fairly complicated arithmetic, and shows the kind of concern which the Vedic seers had for the harmony between their own religious practices and the astronomical cycles.  That mentality led logically to painstakingly accurate observations and calculations, and thereby supports the suspicion of reliability of the internal Vedic astro-chronology.

2.4.4. The Zodiac

To conclude this brief acquaintance with Vedic astronomy, we want to draw attention to the possible presence in the Rg-Veda of a momentous cultural artifact, the origin of which is usually situated in Babylonia in about 600 BC: the twelve-sign Zodiac.  In RV 1:164:11, the sun wheel in heaven is said to have 12 spokes, and to be subdivided into 360 pairs of “sons”: the days (consisting of day and night), rounded off to an arithmetically manageable number, also the basis of the “Babylonian” division of the circle in 3600.  The division in 12 already suggests the Zodiac, and we also find, in the footsteps of N.R. Waradpande, that a number of the Zodiacal constellations/rAshis (classically conceived as combinations of 2 or 3 successive Lunar mansions or nakshatras of 13020’ each) are mentioned: SiMha/Leo (5:83:3 and 9:89:3), KanyA/Virgo (6:49:7), Mithunal/Gemini (3:39.3), and VRshabha/Taurus (6:47:5 and 8:93:1).31

<span style='font-size:14pt;line-height:100%'>Here again, the precession has located them where we would expect them in about 4000 BC.  The VRshabha rAshi is said to have stabilised the heavens with a mighty prop, apparently a reference to the Taurus equinox in the 4th millennium BC; the same verse links the Taurus month with its opposite, Shukra/JyeshTha (coinciding with Scorpio, which contained the autumnal equinox), confirming it least that VRshabha, “bull”, is used here in an astronomical-calendrical sense.  That the seasons are linked with the constellation which is “heliacally rising” (i.e. rising just before dawn) is perhaps indicated by RV 8:93:1: “Surya, thou mountest up to meet the vRshabha”, the sun rises as if to meet the constellation which is just above the horizon. </span>
We are aware that, like the Chinese, the Hindus link the season to the lunar constellation/nakshatra in opposition, i.e. the one which rises at sunset and may contain the full moon.  This approach, if applied to modem astrology, would mean that those who think they are Taurus (sun in Taurus) would become its opposite, Scorpio (sun opposite Scorpio, full moon in Scorpio).  By contrast, the Babylonians linked the seasons to the solar constellation/rAshi in heliacal rising.  If that method were used in modem astrology, those who consider themselves Taurus (sun in Taurus) would find themselves to be Aries (last constellation to rise before the sun-in-Taurus rises).32 However, Waradpande’s discovery seems to imply that the Hindus too used the constellation (at least the rAshi, not the nakshatra) in heliacal rising, like the Babylonians did.

If in Rg-Vedic astronomy the twelve constellations are not linked to the time of the year when they are heliacally rising, but to the time when they are “inhabited” by the sun (as is the practice in modem Hindu astrology), then the whole story would move up at least a thousand and possibly two thousand years, putting the Rg-Veda in about 2000 BC.  This is because the sun is in mid-Taurus a month before Taurus’s heliacal rising, or about 30 of the cycle, a distance covered by the precession of the equinox in about two thousand years.  But it is unlikely that they considered the constellation containing the sun rather than the constellation heliacally rising, as astronomy was based on actual observation more than on calculation, and consequently required that the constellation be visible.33 The constellation temporarily inhabited by the sun is invisible, and that is why the ancients made do with the constellation rising before the one in which the sun is located (heliacal rising), or the one rising when the sun sets, in practice the one inhabited by the full moon (opposition).

The difference between the sun, which obscures the constellation it inhabits, and the moon, which is seen against the background of the constellation it inhabits, explains why a moon-based system uses moon-in-constellation or, via full-moon-in-constellation, sun-in-opposition (the full moon being by definition opposite to the sun); while a sun-based system had to make do with a derivative relation between sun and constellation, typically the constellation’s heliacal rising.  The implication is that India originally had both systems: a Lunar 27-part Zodiac (nakshatras) using the opposition, exactly like in China (and its derived system of 12 months, based on combinations of 2 or 3 nakshatras and still in use); and a Solar 12-part Zodiac (rAshis) using the heliacal rising, exactly like in Babylonia.

The Mithuna rAshi/Gemini is said to destroy darkness and to be basis (budhna) of heat (tapes) (RV 3:39:3).  During Gemini’s heliacal rising in 4000 BC, the sun was in Cancer, then coinciding with our month of May, in northern India the first month of summer (May-June), a season of drought and extreme heat.  During Leo’s heliacal rising, around summer solstice in 4000 BC, the rainy season began.  Therefore, verse 5:83:3 says: “Like the charioteer driving the horse by the whip, he releases the messengers of shower.  From afar the roars of the siMha declare that the rain-god is making the sky showering.” It could not be clearer.

Leo is followed by Virgo, indicating the second half of the rainy season, when the water level in the rivers rises dramatically: in verse 6:49:7, she is called “the purifier KanyA with ChitrA as her life”, and equated with the river Saraswati, the “waterstream-full”.  At this point I must disagree with Waradpande, who takes Saraswati, “waterstream-full,” in its literal meaning, when obviously it is used as the name of the Vedic river.  But at least the reference - the reference to ChitrA, the asterism Spica, the most conspicuous part of the constellation Virgo, dispels any lingering doubt that in this context, KanyA/Virgo does indeed mean the sixth constellation of the Zodiac.

If this is correct, it means that the Zodiac is as old as the oldest Veda, and that the Zodiac itself helps to date the Vedas to the age when Leo and Virgo were connected with the rainy season.  Even if we consider sun-in-Virgo rather than Virgo’s heliacal rising, this would still indicate the centuries around 2000 BC, well before the 1500 BC taught in our universities as the earliest possible date of the Rg-Veda.  Either way, it also upsets the current assumption that the Zodiac was invented in Babylon in the last millennium BC.

2.4.5. India as the metropolis

<span style='font-size:14pt;line-height:100%'>Off-hand, while trying to give a solid astronomical basis to Vedic chronology, we discover a case of cultural transmission in which India is no longer a rather late receiver but, on the contrary, the extremely ancient source. Indeed, both the solar and the lunar Zodiac may well originate in India.  If the Rg-Veda does refer to a 12-part Zodiac, it precedes the Babylonian Zodiac by centuries even in the lowest AIT-based chronology for the Vedas.  As for China: in his famous Science and Civilization in China, Joseph Needham notes, again by using the precession as a time marker, that the Chinese 27-part Zodiac dates back to the 24th century BC.34 He recognizes a common origin with the Hindu nakshatra Zodiac, and then surmises that the Hindus had it from China, on the assumption that the Vedic references to the nakshatras are from 1500 BC at the earliest.  But that assumption, a by-product of the AIT, is seriously undermined by all the data we have been considering here. </span>

Another indication for Indian influence on Chinese astronomy is the 60-year century, known in Vedic literature (the Brhaspati cycle) and still commonly used in the Chinese calendar.  The 6th-century astronomer Aryabhatta reports that he was 23 when the 60th cycle ended, implying that the system was set rolling in 3102 BC.  In China, the system was adopted a few centuries later: according to Chinese tradition, it started with the enthronement of the legendary Yellow Emperor in 2697 BC.

A stellar myth which was apparently transmitted from India to China is the notion that after death, the souls go to the Scorpio-Sagittarius region of the sky (specifically Phi Sagitarii), where the autumnal equinox was located in the 4th millennium BC.  There, they were to be judged by Yama or a similar god of the dead.

The influence of Indian astronomy on both China and Babylonia confirms the Vedic-Harappan civilization’s status as the world metropolis in the 4th-3rd millennium BC.  In the official cults in imperial China and in Babylon, stellar science, stellar symbolism and stellar worship were central.  But the same central place had already been accorded to astronomy in the Vedas, as we have seen here (if only fragmentarily, for numerous Vedic motifs not discussed here are also related to astronomy, e.g. the twelve Adityas or divine children of the sun, Prajapati as personification of the year cycle, etc.); and also in the culture and religion of the Indus-Saraswati civilization, as Asko Parpola and others have shown.35

Remark that Parpola often tries to make sense of Harappan data by referring to Vedic data, on the AIT-based assumption that the Aryan invaders integrated Harappan astronomy and religion.36 This is again a case of multiplying entities without necessity: instead of saying that there are two cultures which happen to share some astro-religious lore, we might assume that these two cultures are one, until proof of the contrary.  Parpola’s arguments for a Harappan origin of Vedic and Hindu cultural items, e.g. of astronomy-based nomenclature (names like KRttikA, “of the Pleiades”), are just as much arguments for an identity of Vedic and Harappan.37 The point to remember is that even Parpola, often cited as an argument of authority by Indian defenders of the AIT, fully acknowledges the continuity between Vedic and Harappan culture.  The common emphasis on astronomy in both Vedic and Harappan sources is certainly an indication of their close kinship if not their identity.


22J.E. Mitchiner: Traditions of the Seven Rishis, Motilal B Delhi 1982, p. 163.  I thank Prof. Subhash Kak for this reference.

23Pliny:Naturalis Historia 6:59; Arrian: Indica 9:9. I thank Dr. Herman Seldeslachts for checking these references.

24The worst case was probably the Black Sea, which was a lake during the Ice Age, until some time in the 7th millennium BC.  When rising waters in the Mediterranean inundated the dry Bosporus straits and plunged into the Black Sea, the latter rose dramatically, forcing coast-dwellers to flee as much as a mile a day for months on end.  Many of them didn’t survive, and entire states (or whatever political units were in existence) were drowned.  The fact that the Biblical Flood story has Noah land on Mount Ararat, not far from the Black Sea, may be due (apart from the presence of a boat-like rock formation there) to the memory of the Black Sea flood drama.  In most parts of the world, the flooding of coastal villages must have been more gradual.

25P.C. Sengupta: “The solar eclipse in the Rgveda and the Date of Atri”, Journal of the Royal Asiatic Society of Bengal Letters, 1941/7, p.92-113, also included in his Ancient Indian Chronology, Calcutta 1947; discussed in K.V. Sarma: “A Solar Eclipse Recorded in the Rgveda”, in Haribhai Pandya et al., eds.: Issues in Vedic Astronomy and Astrology, Motilal Banarsidass.  Delhi 1992, p.217-224.

26N.S. Rajaram (with D. Frawley): Vedic ‘Aryans’ and the Origins of Civilization, WH Press, Québec 1995, p.106.

27This position is argued powerfully in the classic study by Giorgio de Santillana & Hertha von Dechend: Hamlet’s Mill, David R. Godine, Boston 1992 (1969); in Norman Davidson: Astronomy and the Imagination, Routledge & Kegan, London 1986 (1985); and in Thomas D. Worthen: The Myth of Replacement. Stars, Gods and Order in the Universe, University of Arizona Press, Tucson 1991.

28S. Kak: Astronomical Code of the Rig-Veda, Ch.5-6.

29Georg Feuerstein, Subhash Kak and David Frawley: In Search of the Cradle of Civilization, Quest Books, Wheaton IL 1995, p. 208.

30Kak: Astronomical Code, Ch.4.

31Argued in N.R. Waradpande: New Light on the Date of the Rgveda, Sanskrit Bhasha Pracharini Sabha, Nagpur 1994, p.13-24.

32This remains true whether one uses the Tropical (abstract, solstice/ equinox-based) or the Sidereal (visible, constellation-based) Zodiac, a question which is not really relevant here.  The Vedic Zodiac was sidereal, more based on observation than on calculation; the tropical Zodiac apparently dates from the time when sidereal and tropical signs coincided (around the turn of the Christian era), i.e. when the constellation of Aries filled the 300 sector following the spring equinox in the sun-earth cycle, a tropical sector known since then as Aries regardless of the position of the constellation Aries.

33Other possible Vedic indications that the seers used the concept of heliacal rising, are the descriptions of the last stars fading before the almost-rising sun: RV 1:50:2, and metaphorically RV 7:36:1, 7:81:2, 9:69:4.

34Joseph Needham: Science and Civilization in China, part 1, ch-20: “Astronomy”, p.253-254.

In order to read these articles one needs a basic knowledge of Astronomy. here is an online course on Astronomy. I would like to draw your attention in particular to chapter 7 (Timekeeping and the celestial sphere) where most of the terminology (ecliptic, sidereal day , tropical year ) is explained and there are some good graphics to boot. Of course the author of these lectures does not give any credit to Vedic astronomy,probably because of his ignorance of the matter. No matter, we can rectify the same as the Indians become more and more familiar with tis historic legacy.


Some Definitions to get started

(ēklĬp´tĬk, Ĭ-) , the great circle on the celestial sphere that lies in the plane of the earth's orbit (called the plane of the ecliptic). Because of the earth's yearly revolution around the sun, the sun appears to move in an annual journey through the heavens with the ecliptic as its path. The ecliptic is the principal axis in the ecliptic coordinate system . The two points at which the ecliptic crosses the celestial equator are the equinoxes . The obliquity of the ecliptic is the inclination of the plane of the ecliptic to the plane of the celestial equator, an angle of about 23 1/2 °. The constellations through which the ecliptic passes are the constellations of the zodiac .


(ē´kwĬnŏks) , either of two points on the celestial sphere where the ecliptic and the celestial equator intersect. The vernal equinox, also known as “the first point of Aries,” is the point at which the sun appears to cross the celestial equator from south to north. This occurs about Mar. 21, marking the beginning of spring in the Northern Hemisphere. At the autumnal equinox, about Sept. 23, the sun again appears to cross the celestial equator, this time from north to south; this marks the beginning of autumn in the Northern Hemisphere. On the date of either equinox, night and day are of equal length (12 hr each) in all parts of the world; the word equinox is often used to refer to either of these dates. The equinoxes are not fixed points on the celestial sphere but move westward along the ecliptic, passing through all the constellations of the zodiac in 26,000 years. This motion is called the precession of the equinoxes . The vernal equinox is a reference point in the equatorial coordinate system .

equatorial coordinate system

the most commonly used astronomical coordinate system for indicating the positions of stars or other celestial objects on the celestial sphere . The celestial sphere is an imaginary sphere with the observer at its center. It represents the entire sky; all celestial objects other than the earth are imagined as being located on its inside surface. If the earth's axis is extended, the points where it intersects the celestial sphere are called the celestial poles; the north celestial pole is directly above the earth's North Pole, and the south celestial pole directly above the earth's South Pole. The great circle on the celestial sphere halfway between the celestial poles is called the celestial equator; it can be thought of as the earth's equator projected onto the celestial sphere. It divides the celestial sphere into the northern and southern skies. An important reference point on the celestial equator is the vernal equinox , the point at which the sun crosses the celestial equator in March. To designate the position of a star, the astronomer considers an imaginary great circle passing through the celestial poles and through the star in question. This is the star's hour circle , analogous to a meridian of longitude on earth. The astronomer then measures the angle between the vernal equinox and the point where the hour circle intersects the celestial equator. This angle is called the star's right ascension and is measured in hours, minutes, and seconds rather than in the more familiar degrees, minutes, and seconds. (There are 360 degrees or 24 hours in a full circle.) The right ascension is always measured eastward from the vernal equinox. Next the observer measures along the star's hour circle the angle between the celestial equator and the position of the star. This angle is called the declination of the star and is measured in degrees, minutes, and seconds north or south of the celestial equator, analogous to latitude on the earth. Right ascension and declination together determine the location of a star on the celestial sphere. The right ascensions and declinations of many stars are listed in various reference tables published for astronomers and navigators. Because a star's position may change slightly (see proper motion and precession of the equinoxes ), such tables must be revised at regular intervals. By definition, the vernal equinox is located at right ascension 0 h and declination 0°.

Another useful reference point is the sigma point, the point where the observer's celestial meridian intersects the celestial equator. The right ascension of the sigma point is equal to the observer's local sidereal time . The angular distance from the sigma point to a star's hour circle is called its hour angle ; it is equal to the star's right ascension minus the local sidereal time. Because the vernal equinox is not always visible in the night sky (especially in the spring), whereas the sigma point is always visible, the hour angle is used in actually locating a body in the sky.
The precession of the equinox, where the position of the equinox falls short by 50.3 seconds each calendar year(and makes a complete cycle in 25,791 years was kown to the Ancient Vedics long before the greek Hipparchus observes it in the 2nd century BC. Of course we have to wait until we get to Copernicus before anybody had a clue as to what was going on.

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->2.3. THE PRECESSION OF THE EQUINOX

2.3.1. The slowest hand on the clock

<span style='font-size:14pt;line-height:100%'>The truly strong evidence for a high chronology of the Vedas is the Vedic information about the position of the equinox.  The phenomenon of the “precession of the equinoxes” takes the ecliptical constellations (also known as the sidereal Zodiac, i.e. those constellations through which the sun passes)12 slowly past the vernal equinox point, i.e. the intersection of ecliptic and equator, rising due East on the horizon.  The whole tour is made in about 25,791 years, the longest cycle manageable for naked-eye observers.  If data about the precession are properly recorded, they provide the best and often the only clue to an absolute chronology for ancient events. </span>

<span style='font-size:14pt;line-height:100%'>If we can read the Vedic and post-Vedic indications properly, they mention constellations on the equinox points which were there from 4,000 BC for the Rg-Veda (Orion, as already pointed out by B.G. Tilak)13 through around 3100 BC for the Atharva-Veda and the core Mahabharata (Aldebaran) down to 2,300 BC for the Sutras and the Shatapatha Brahmana (Pleiades).14 </span>

Other references to the constellational position of the solstices or of solar and lunar positions at the beginning of the monsoon confirm this chronology.  Thus, the Kaushitaki Brahmana puts the winter solstice at the new moon of the sidereal month of Magha (i.e. the Mahashivaratri festival), which now falls 70 days later: this points to a date in the first half of the 3rd millennium BC.  The same processional movement of the twelve months of the Hindu calendar (which are tied to the constellations) vis-a-vis the meterological seasons, is what allowed Hermann Jacobi to fix the date of the Rg-Veda to the 5th-4th millennium BC.15 Indeed, the regular references to the full moon’s position in a constellation at the time of the beginning of the monsoon, which nearly coincides with the summer solstice, provide a secure and unambiguous chronology through the millennial Vedic literature.

<span style='font-size:14pt;line-height:100%'>It is not only the Vedic age which is moved a number of centuries deeper into the past, when comparing the astronomical indications with the conventional chronology.  Even the Gupta age (and implicitly the earlier ages of the Buddha, the Mauryas etc.) could be affected.  Indeed, the famous playwright and poet Kalidasa, supposed to have worked at the Gupta court in about 400 AD, wrote that the monsoon rains started at the start of the sidereal month of Ashadha; this timing of the monsoon was accurate in the last centuries BC.16 This implicit astronomy-based chronology of Kalidasa, about 5 centuries higher than the conventional one, tallies well with the traditional “high” chronology of the Buddha, whom Chinese Buddhist tradition dates to ca. 1100 BC, and the implicit Puranic chronology even to ca. 1700 BC.17 </span>

2.3.2. Some difficulties

These indications about the processional phases may be unreliable insofar as their exact meaning is not unambiguous.  To say that a constellation “never swerves from the East” (as is said of the Pleiades in the Shatapatha Brahmana 2:1:2:3) seems to mean that it contains the spring equinox, implying that it is on the equator, which intersects the horizon due East.  But this might seem insufficiently explicit for the modem reader who is used to a precise and separate technical terminology for such matters.  But then, the modem reader will have to accept that technical terminology in Vedic days mostly consisted in fixed metaphorical uses of common terms.  This is not all that primitive, for the same thing will be found when the etymology of modern technical terms is analyzed, e.g. a telescope is a Greek “far-seer”, oxygen is “acid-producer”, a cylinder is a “roller”.  The only difference is that we can use the vocabulary of foreign classical languages to borrow from, while Sanskrit was its own classical reservoir of specialized terminology.

Another factor of uncertainty is that the equinox moves very slowly (10 in nearly 71 years), so that any inexactness in the Vedic indications and any ambiguity in the constellations’ boundaries makes a difference of centuries.  This occasional inexactness might possibly be enough to neutralize the above shift in Kalidasa’s date - but not to account for a shift of millennia (each millennium corresponding to about 14 degrees of arc) needed to move the Vedic age from the pre-Harappan to the post-Harappan period, from 4000 BC as calculated by the astronomers to 1200 BC as surmised by Friedrich Max Müller.

<span style='font-size:14pt;line-height:100%'>On the other hand, it is encouraging to note that the astronomical evidence is entirely free of contradictions.  There would be a real problem if the astronomical indications had put the Upanishads earlier than the Rg-Veda, or Kalidasa earlier than the Brahmanas, but that is not the case: the astronomical evidence is consistent. </span> Inconsistency would prove the predictable objection of AIT defenders that these astronomical references are but poetical tabulation without any scientific contents.  However, the facts are just the opposite.  To the extent that there are astronomical indications in the Vedas, these form a consistent set of data detailing an absolute chronology for Vedic literature in full agreement with the known relative chronology of the different texts of this literature.  This way, they completely contradict the hypothesis that the Vedas were composed after an invasion in about 1500 BC.  Not one of the dozens of astronomical data in Vedic literature confirms the AIT chronology.

2.3.3. Regulus at summer solstice

In the Shulba Sutra appended to Baudhayana’s Shrauta Sutra, mathematical instructions are given for the construction of Vedic altars.  <span style='font-size:14pt;line-height:100%'>One of its remarkable contributions is the theorem usually ascribed to Pythagoras, first for the special case of a square (the form in which it was discovered), then for the general case of the rectangle: “The diagonal of the rectangle produces the combined surface which the length and the breadth produce separately.” This and other instances of advanced mathematics presented by Baudhayana have been shown by the American mathematician A. Seidenberg to be the origin of similar mathematical techniques and ‘discoveries’ in Greece and Babylonia, some of which have been securely dated to 1700 BC. So, 1700 BC was a terminus post quem for Baudhayana’s mathematics, which would reasonably be dated to the later part of the Harappan period which ended in ca. 1900 BC. </span>

However, Seidenberg was told by the indologists that these Sutras, or any Vedic text for that matter, were definitely written later than 1700 BC.  But mathematical data cannot be manipulated just like that, and Seidenberg remained convinced of his case: “Whatever the difficulty there may be [concerning chronology], it is small in comparison with the difficulty of deriving the Vedic ritual application of the theorem from Babylonia. (The reverse derivation is easy)… the application involves geometric algebra, and there is no evidence of geometric algebra from Babylonia.  And the geometry of Babylonia is already secondary whereas in India it is primary.”18 To satisfy the indologists, he said that the Shulba Sutra had conserved an older tradition, and that it is from this one that the Babylonians had learned their mathematics: “Hence we do not hesitate to place the Vedic (…) rituals, or more exactly, rituals exactly like them, far back of 1700 BC. (…) elements of geometry found in Egypt and Babylonia stem from a ritual system of the kind described in the Sulvasutras.”19

This is then one of those “entities multiplied beyond necessity”: a ritual, annex altar, annex mathematical theory, which is exactly like the Vedic ritual, annex altar, annex mathematical theory, only it is not the Vedic ritual but a thousand or so years older.  Let us simplify matters and assume that it was Baudhayana himself who devised his mathematical theories “far back of 1700 BC”.  Is there a way to find independent confirmation of this suspicion?  Yes, there is: the precession of the equinoxes.

In their Vedic Index of Names and Subjects, A.A. MacDonell and A.B. Keith cite the opinion of several philologists about a reference to a solstice in Magha in the Baudhayana Shrauta Sutra (as well as in the Kaushitaki Brahmana 19:3), to which the Shulba Sutra is an appendix.  Magha is the asterism around the star Regulus, but the name is used for an entire month (names of months are typically the name of the most prominent one of the two or three asterisms/nakshatras which make up that one-twelfth of the ecliptic), spatially equivalent to a zone of about 300 around that star, so any deduction here must take a fair degree of imprecision into account.  The 18th- and 19th-century philologists cited disagree about whether a Magha solstice was in 1181 BC or in 1391 BC.  The authors themselves consider it “only fair to allow a thousand years for possible errors”, and settle for a date between 800 BC and 600 BC, “quite in harmony with the probable date of the Brahmana literature”.20

However, it is very easy to calculate that Regulus, currently at almost exactly 600 from the solstitial axis, was on that axis about 60 x 71 years ago, i.e. in the 23rd century BC, Though we must indeed allow for an inexactitude of up to 150, equivalent to about 1100 years, the Magha solstice described is much more likely to have been in 2200 BC than in 1100 BC, and Keith and MacDonell’s 600 BC is quite beyond the pale.  It may have taken place even before the 23rd century BC: maybe only the asterism around Regulus had reached the solstitial axis but not yet the star itself.  Most likely, then, this reference to a Magha solstice confirms that the Bra and Sutra literature including the Baudhayana Shrauta Sutra (annex Shulba) dates to the late 3rd millennium BC, at the height of the Harappan civilization.  In that case, Seidenberg’s reconstruction of the development and transmission of mathematical knowledge and the astronomical references in the literature confirm each other in placing Baudhayana’s (post-Vedic!) work in the later part of the Harappan period.

2.3.4. One Veda can hide another

At this point, the only defence for the AIT can consist in a wholesale rejection of the astronomical evidence.  This can be done in a crude way, e.g. by simply ignoring the astronomical evidence, as is done in most explicitations of the AIT.  A slightly subtler approach is to explain it away, as is done by Romila Thapar, who affirms her belief in “the generally accepted chronology that the Rig-Vedic hymns were composed over a period extending from about 1500 to 1000 BC”.  When “references to what have been interpreted as configurations of stars have been used to suggest dates of about 4000 BC for these hymns”, she raises the objection that “planetary positions could have been observed in earlier times and such observations been handed down as part of an oral tradition”, so that they “do not constitute proof of the chronology of the Vedic hymns”.21

This would imply that accurate astronomical data were indeed made from the 5th millennium onwards, and that they were preserved for more than two thousand years, an unparalleled feat in oral traditions.  If such a feat is not an indication of literacy and of written records, at the least it supposes a mnemotechnical device capable of preserving information orally, and the one that was available then was verse.  So, some poems with the memory-aiding devices of verse, rhythm and tone must have been composed when the information was available first-hand, i.e. close to the time of the actual observation, and those hymns would of course be the Vedic hymns themselves.  Otherwise, one has to postulate that the Vedic hymns were composed by borrowing the contents of an earlier tradition of verse, composed at the time when the equinox was observed to be in Orion.

In other words, the Rg-Veda contains literal (though unacknowledged) quotations from another hymns collection composed 2,500 years earlier.  This is as good as asserting that Shakespeare’s works were not written by Shakespeare, but by someone else whose name was also Shakespeare. However, the point to remember is that even Romila Thapar does not deny that somebody’s actual observation of these celestial phenomena was the source of their description in the Vedas.

It is not good enough for those who don’t like this evidence, to object that they are not convinced by these astronomical indications of high antiquity, on the plea that their meaning might be somewhat unclear to us. it is clear enough and undeniable that the Vedic seers took care to mention certain astronomical positions and phenomena.  A convincing refutation would therefore require an alternative but consistent (philogically as well as astronomically sound) interpretation of the existing astronomical indications which brings Vedic literature down to a much later age.  But so far, such a reading of those text passages doesn’t seem to exist.  In no case is there astronomical information which puts the Vedas at as late a date as “generally accepted” by Prof. Thapar and others.


12The sidereal Zodiac, used in astrology by most Hindu and some Western astrologers, consists of the actually visible constellations on the ecliptic.  It is contrasted with the tropical Zodiac, an abstract division of the ecliptic in twelve equal sectors of which the first one starts by definition at the equinox axis.  This tropical Zodiac, used by most Western and some Hindu astrologers, is unrelated to the background of constellations (it could be constructed even if the universe consisted only of the sun and the earth); but it does not figure anywhere in the present discussion.  As far as we know, the process of abstraction from visible constellations to geometrical sectors took place only in the Hellenistic period, ca. 100 BC, and was unknown to the Vedic seers, though they did know the solstice axis and equinox axis.

13We are aware that the equinox axis never points exactly towards the constellation Orion, which lies south of the ecliptic; but it is understand a that the relatively starless area between the constellations of Gemini and Taurus was named after the conspicuous constellation Orion which lies nearby on the same longitude.

14Remark that the second half of the 3rd millennium BC, the high tide of the Harappan cities, is also identified by K.D. Sethna (KarpAsa in Prehistoric India: a Chronological and Cultural Clue, Impex India, Delhi 1981) as the period of the Sutras, the Vedas being assigned to the pre-Harappan period, all on the basis of the evidence of material culture (with special focus on cotton/karpAsa) as attested in the literary and archaeological records. According to Asko Parpola, Indus~Saraswati seal 430 (reasonably datable to the 24th century BC) depicting the Seven Sisters seems to refer to the observation of the Pleiades.

15Hermann G. Jacobi: “On the Date of the Rgveda” (1894), reproduced in K.C. Verma et al., eds.: Rtambhara Studies in Indology, Society for Indic Studies, Ghaziabad 1986, p-91-99.

16“We can, therefore, say that about 2000 years have elapsed since the period of Kalidasa”, according to P.V. Holay: “Vedic astronomy, its origin and evolution”, in Haribhai Pandit et at.: Issues in Vedic Astronomy and Astrology, Rashtriya Veda Vidya Pratishthan & Motilal Banarsidass, Delhi, P.109.

17The argument for a higher chronology (by about 6 centuries) for the Guptas as well as for the Buddha has been elaborated by K.D. Sethna in Ancient India in New Light, Aditya Prakashan, Delhi 1989.  The established chronology starts from the uncertain assumption that the Sandrokottos/ Chandragupta whom Megasthenes met was the Maurya rather than the Gupta king of that name.  This hypothetical synchronism is known as the “sheet-anchor of Indian chronology”. In August 1995, a gathering of 43 historians and archaeologists from South-Indian universities (at the initiative of Prof. K.M. Rao, Dr. N. Mahalingam and Dr. S.D. Kulkarni) passed a resolution fixing “the date of the Bharata war at 3139-38 BC” and declaring this date “to be the true sheet anchor of Indian chronology”.

18A. Seidenberg: “The ritual origin of geometry”, Archive for History of Exact Sciences, 1962, p. 488-527, specifically p-515, quoted by N.S. Rajaram and D. Frawley: Vedic Aryans’ and the Origins of Civilization, WH Press, Québec 1995, p-85.

19A. Seidenberg: “The ritual origin of geometry”, Archive for History of Exact Scieces, 1962, p.515, quoted by N.S. Rajaram and D. Frawley: Vedic ‘Aryans’ and the Origins of Civilization, p.85.

20A.A. MacDonell & A.B. Keith: Vedic Index of Names and Subjects, vol. 1 (1912, reprint by Motilal Banarsidass, Delhi 1982), p.423-424, entry Nakshatra.

21Romila Thapar: “The Perennial Aryans”, Seminar, December 1992. <!--QuoteEnd--><!--QuoteEEnd-->
By now we must have discerned that there are differences between the Western and vedic astrological systems. This paper summarizes these differences. Note that the Indian system is similar to the Ptolemaic system. The Arab/Persian astronomers were familiar with Hindisa and the Surya Siddhanta

Western Astrology and Vedic Astrology the difference:

Page Title: sayana and nirayana Western Astrology and and Vedic Astrology the difference

Related Links : |Services |Free Reading |The Difference Between Sun Sign in Western Astrology and the Lagna or the Birth Sign in Hindu Vedic Astrology

There are many ways to say sensible and interesting things about another person using numerology, tarot, palmistry, Western astrology and of course Vedic astrology. It's obvious how various methods give us different information because they regard subjects from different angles. So it is with Vedic astrology. (1. View the Resources or 2. Get your FREE Vedic Astrology Reading)

Although it is very tempting to compare your Indian horoscope with your Western horoscope and perhaps even to try to see which one of the two compares the best, this is exactly what you should NOT do. Here you have two different methods that may work well side by side however each must be interpreted and approached in different manners.

That is the joy of the two systems of astrology. Just like Western Medicine and Aurvedic (Herbal) Medicine, two different systems of treatments for the same sickness or symptoms. The Hindu system of astrology (Visit the Home Page) uses the concept of fixed Zodiac. The western system uses the concept of moveable Zodiac.

The "ayanamsa" is the distance or the difference at present moment of time between the fixed and movable Zodiac. The Hindu system of astrology is known as Nirayana System because:

<span style='font-size:14pt;line-height:100%'>The earth revolves around the Sun once in 365 days 5 hours 48 minutes and 46 seconds. Considered from the earth, the Sun appears to complete one round of the ecliptic during this period. This is called a tropical year .In the span of a tropical year, the earth regains its original angular position with the Sun. It is also called the year of seasons since on this Earth-Sun cycle depends the occurrence, and timing, of seasons. If we consider the revolution of the Sun around the earth from one vernal equinox (around 21st March, when the day and night all over the globe are equal) to the next vernal equinox, it takes one tropical year to do so.</span>

<span style='color:purple'>However, if at the end of a tropical year from one vernal equinox to the next, we consider the position of the earth with reference to a fixed star of the zodiac (The Ayanamsha is based on the position of the constant star Spica), the earth appears to lie some 50.26 seconds of celestial longitude to the west of its original position. In order for the earth to attain the same position with respect to a fixed star after one revolution, it takes a time span of 365 days 6 hours 9 minutes and some 9.5 seconds. This duration of time is called a sidereal year .The sidereal year is just over 20 minutes longer than the tropical year; this time difference is equivalent to 50.26 seconds of celestial longitude.</span>

Each year, the Vernal equinox will fall short by 50.26 seconds along the zodiac reckoned along the fixed stars. This continuous receding of the Vernal equinox along the zodiac is called as the precession of equinoxes

<span style='font-size:14pt;line-height:100%'>This in other words, means that the plane of the equator intersects the plane of the ecliptic at a constantly shifting point. This point, the first point of Aries or the vernal equinox, goes on receding westward at a rate of approximately 50.26 seconds of arc each year. This is called the precession of the equinoxes. The result of this precession is a slow increase in the right ascensions of almost all fixed stars in the zodiac. This precession takes some 25,800 (or approximately 26,000) years to complete one circle. As will be seen, an appreciation of this precession is of paramount importance in the understanding of the basic concepts of Vedic astrology</span>
(The sayana and the niryana system)

It has been seen that because of the precession of equinoxes at a rate of 50.26 seconds per year, the distance between the Vernal equinox (the 1st point of the movable zodiac) and the 1st point of Mesha (Aries) on the fixed zodiac has been progressively increasing. This distance at any given epoch is called as the Ayanamsha .The ayanamsha thus indicates the difference between the fixed zodiac and the movable zodiac. The system that considers the fixed zodiac is called the Niryana (without ayana!) system, while the one that considers the movable zodiac is called the Sayana (with ayana!) system. The Niryana values of planetary longitudes can be obtained by subtracting the ayanamsha for a given time from the Sayana longitudes.

The Niryana and the Sayana zodiacs coincided in the year 285 AD when the ayanamsha was zero. At the rate of precession of equinoxes stated above, the ayanamsha on the 1st of January, 1995 is 23°47'26". The equinoctial precession completes one round in aproximately 26,000 years, as mentioned earlier, so that the fixed and movable zodiacs coincide regularly after this time span. The ayanamsha reckoned on the basis of considering the year 285 AD as the year when the Sayana and the Niryana zodiacs coincided.

The Sidereal and Tropical Zodiac

The Ayanamsha is based on the position of the constant star Spica. Intermediary data can be calculated by interpolation. Some Western computer programmes offer the possibility to make a calculation based on the sidereal zodiac. However, sometimes the ayamamsha for the sidereal zodiac used in such programs is slightly different than the Lahiri Ayanamsha. So, it is valuable to calculate the planetary positions by hand.

Table 1:

1 January 1920 22°45´
1 January 1930 22°53´
1 January 1940 23°01´
1 January 1950 23°10´
1 January 1960 23°18´
1 January 1970 23°26´
1 January 1980 23°35´
1 January 1990 23°43´
1 January 2000 23°51´

How do you start? First you take the positions from the Western horoscope and deduct the relevant Ayanamsha. For example: a person born in 1950 has the Sun on 25° Pisces. The Ayanamsha for 1950 is 23°10´. Deduct this from the position of the Sun: 25° - 23°10´ = 1°50´. Therefore, the Sun in the Vedic horoscope will be on 1°50´ Pisces.

Now let us make it a little bit more difficult. Another person born in 1950 has the Sun on 15° Pisces in the Western horoscope. The Ayanamsha for 1950 is 23°10´. Deduct this from the position of the Sun (23°10´ - 15° = 8°10´ then 30° - 8°10´ = 21°50´). The Sun is now 21°50´ Aquarius. Continue calculating in this manner with the remaining planets and the ascendant.


Now you are in for some surprises! It appears that someone, who thought their Sun sign was Pisces, now appears to have an Aquarian Sun! This can be a real shock. What is important is the complete image that has appeared. Most probably in the new horoscope the Piscean-energy will be visible in another manner (for example, perhaps the Moon will now appear in Pisces, or the ascendant will move to Pisces in the Vedic horoscope)
In addition, you must remember that you are naturally accustomed to Western Sun sign and Western horoscope, so the Eastern one will initially feel strange. Learning to be flexible and open to different approaches, which may give different results, is difficult at first. The secret is to open your mind to the possibilities within a new method

For more information you can visit the following web page http://www.yournetastrologer.com/basic/b01.htm

<img src='http://jyotisha.00it.com/Hintr1.jpg' border='0' alt='user posted image' />

Here is another link to the Astronomy of Ayabhatta

<img src='http://csep10.phys.utk.edu/astr161/lect/time/celestialtime.gif' border='0' alt='user posted image' />
Locating stars and constellations on the celestial sphere is facilitated by a star map. The following map is an example of a star map of the northern hemisphere sky for a winter evening (click on the map for a larger version with labeling for the constellations).


<img src='http://csep10.phys.utk.edu/astr161/lect/time/starmap-small.gif' border='0' alt='user posted image' />

Star map for winter evening in the Northern hemisphere

This star map was produced by the Star Maps on demand service of Mount Wilson Observatory. Another source of star maps is the Starry Night program for Windows and Macintosh computers. Here is an online map that shows the position on the celestial sphere of the Sun, Moon, and planets for arbitrary time, date, latitude, and longitude of the observer. (The map is a circle, which you should imagine holding over your head with directions properly aligned to simulate the celestial sphere.)

To use star maps effectively, you need to know your latitude and longitude on the surface of the Earth, and the offset of your timezone from the Greenwich meridian. Here is a link to the Census Gazeteer, which will return latitude & longitude of locations in U.S. specified by either name or zip code (and also links to online U.S. maps). Likewise, here is a link to information about timekeeping and timezones.

Thanks for some good posts.

There are several Astronomy software packages available that would plot the star-charts for you. Nicer ones also include solar, lunar, planetary and eclipse calculations. Following links are useful for this purpose:


Compilation of links:

It is interesting that Vedic astronomy is based on the sidereal zodiac . It is my inference that the sidereal year is a period based on an inertial frame of reference. An inertial frame of reference for those not well versed in mechanics is a coordinate system that is either at rest or in uniform rectilinear motion, IOW a frameof reference where there are no inertial forces. The immediate consequence of such a restriction is that this excludes a coordinate system based on the Sun since the Sun is itself a body in orbital motion.. The following is an explanation for the genesis of the general principle known as Mach's principle. Mach's principle in effect defines an inertial frame of reference as an intuitive definition for a concept that has been around since Isaac Newton.

This is all very welll but why did the ancients in india insist on using a sidereal zodiac, unlike the later practice of their western counterparts. Could it be that the vedics were quite familiar with the notion of an inertial frame of reference, long before the likes of Galileo, Newton and Copernicus , and by inference knew the fundamental principles of mechanics ? Indeed, an intriguing thought, but not very far fetched given their facility with celestial geometry..

The following is not a very clear explanation but it serves the purpose (and saves me the bother of writing a better explanation)

Mach’s Principle
Newton’s laws are said to only hold in inertial reference frames. What then are inertial reference frames? These are normally defined as frames in which Newton’s laws, such as F = ma, are valid, which is circular reasoning. You can say these are reference frames in which there are no inertial forces, such as linear acceleration, the centrifugal force, or the Coriolis effect. Now, you can modify Newton’s laws so they also work in non-inertial reference frames by including terms that correspond to so-called fictitious forces. Linear acceleration is described by mg, so F = ma is modified to F = ma + mg. More complicated terms can be added that correspond to the centrifugal force and the Coriolis effect. Now, the equations can then deal with these effects, but the terms are just added in an ad hoc way, and it doesn’t address the underlying question as to what actually causes these effects. You could say that according to Newton’s first law, bodies at rest tend to stay at rest, and bodies in motion tend to stay in motion. If you are in a car which suddenly accelerates, your body wants to maintain its pervious motion, which was the slower velocity, and so you feel yourself pinned against the seat. If the car suddenly turns a sharp corner, your body wants to maintain its previous motion, which was a straight line, and so you feel yourself thrown to one side of the car. You’re prevented from going straight by the fact you are inside the car. If you tie a rock to a string, and spin it around, it’s prevented from going straight by the string, and so it goes in a circle. The Moon is prevented from going straight by the gravitational pull of the Earth, and so it goes in a circle, meaning orbit the Earth.

Things prefer to go straight, and if they are prevented from going straight, they try to go as straight as possible, meaning travel in a big circle with gradual curvature rather than a small circle with tight curvature. So often things spinning quickly flatten out if they can. The primordial Solar System and spiral galaxies formed into pancake shapes, and the Earth is slightly flatter at the poles, and bulges at the equator. Newton conducted an experiment where he took a bucket of water, and tied one end of the rope to the handle, and the other end to the ceiling. He rotated the bucket as many times as he could, twisting up the rope, and then released it, so it was spinning on its own. He observed that the water was higher at the edge than in the middle. It’s as if the water was trying to get as far as it could from the axis of rotation, so it wouldn’t have to turn as tight a circle. This “trying to get as far as you can from the axis of rotation” is called the centrifugal force.

Now, when you say “objects at rest tend to stay at rest” or “objects in motion tend to stay in motion”, the question that arises is “with respect to what?” At rest with respect to what? In motion with respect to what? Newton himself thought the answer was space itself. He thought that space itself formed a frame of reference. He advocated that there existed some sort of universal frame of reference. Einstein showed that there is no preferred reference frame, and that all things are relative, as it were. Even before Einstein, many people were uncomfortable with the idea that empty space itself could serve as a frame of reference. You can’t exactly hammer a nail into empty space and measure from that.

An alternative has been suggested by various people throughout history, including Galileo and Newton. It was that distant matter could serve as a frame of reference. In 1863, Ernest Mach (1836 – 1916) published “Die Machanik” in which he formalized this argument. Einstein was greatly influenced by it, and in 1918, he named it “Mach’s Principle”. This was one of the primary sources of inspiration for Einstein’s theory of General Relativity, although you could say his theory advanced beyond it. Scholars still debate whether Einstein’s theory is truly Machian at a fundamental level. Brans-Dicke Cosmology, where G is replaced by varying scalar field, is an attempt to make general relativity more Machian.

Before Einstein, various people such as Galieo commented on the similarity between inertial forces and gravity. Einstein took this a step further and said that they are in fact the same thing. In Einstein’s thought experiments with the elevator, they are indistinguishable. If you were in an elevator that is in free fall, it’s the same as if you were in an elevator in deep space. You wouldn’t be able to tell the difference. If you were in an elevator that is sitting still on the surface of the Earth, it would be the same as if you were in an elevator on a rocket accelerating at a rate of 1 g. You wouldn’t be able to tell the difference. Therefore, acceleration and gravitation are equivalent. Actually, in the free fall case, there is a slight difference. If you were in an elevator in free fall, and you suspended two apples next to each other in the middle of the air, they would slowly get closer together, since their paths, both towards the center of the Earth, converge. These are called tidal effects. However, this small effect would not be observable locally. Ignoring that, the cases are the same. This is called the Weak Equivalence Principle. It states that the effects of inertial fields are the same as gravitational fields, and the absence of inertial fields is the same as the absence of gravitational fields.

The Strong Equivalence Principle takes it a step further, and says that not just the effects of gravity and inertia are the same, but that all laws of physics are the same regardless of whether you are in a gravitational field or a non-inertial reference frame. You can discover how all laws of physics behave in a gravitational field by postulating that their laws in a freely falling inertial frame are identical to the laws in Special Relativity, meaning when there are no gravitational fields.

Now, if gravity and inertia are the same thing, you could say that gravity is really inertia. Even if it looks like you’re going straight, if you are traveling through a gravitational field, that means you’re traveling through curved spacetime, which means you’re not really traveling straight, and thus you feel inertial effects, which we call gravity. Another way to describe it is to turn it around, and say that inertia is really gravity. You feel the gravitational attraction of not just nearby matter, like the Earth, but all the matter in the Universe. The Universe is homogeneous and isotropic, which means there is pretty much the same amount of matter in all directions. Thus the gravitational attraction from all of this matter usually cancels out, and you feel no net gravitational attraction. However, if you are in a non-inertial reference frame, then that is no longer true. You feel a net residual gravitational attraction from the rest of the matter in the Universe, which you call inertial effects.

If you are in a car that suddenly accelerates, you feel the effect of being pinned to your seat, or if it turns a sharp corner you feel yourself thrown to one side. In both cases, you feel the effect of acceleration which is a change in the velocity vector. In the first case, it’s changing it’s magnitude. In the second case, it’s changing it’s direction. In what reference frame are you accelerating? You’re motionless with respect to the inside of the car. You could say you’re accelerating with respect to the road beneath the car. However, you would feel the same effect if you were in a spaceship far from any planet. So what reference frame would you choose? The only logical one is the reference frame of the center of mass of all the matter in the observable Universe. Since the vast majority of the matter in the observable Universe is in distant galaxies, you are essentially accelerating with respect to distant galaxies. Now to then say that the effect you feel is literally the gravitational attraction of distant galaxies is more problematic. However, the mere fact that this is the reference frame to use when discussing this subject can’t really be disputed. What other reference frame would you use? With Newton’s bucket experiment, the entire bucket was rotating, so the water was motionless with respect to the sides of the bucket. I didn’t write this for the purpose of advocating Mach’s Principle. It’s just the idea has been tossed around since Galileo, and no one has come up with a better explanation for inertial effects. We still can’t explain it completely. Most people don’t even attempt to explain it. They just add the extra terms to Newton’s equations to allow for non-inertial frames, and don’t give it any more thought.

Mach’s Principle remains controversial, although no one suggests an alternative. They just don’t like the idea that every day you personally feel the effects of distant galaxies. There are also a lot of ridiculous misconceptions and misinterpretations surrounding it. Some people who say they are against it, are really against some of the absurd versions of it. For instance, some people think Mach’s Principle says that matter interacts instantly with distant galaxies. Of course, that would have been the 19th Century view, such as may have been held by Ernest Mach, but Einstein proved that nothing can go faster than light, so of course that wouldn’t be the modern view. For instance, in the 19th Century, they thought electromagnetic interaction took place instantly due to an electric or magnetic field. Two electrons would instantly feel each other’s presence due to an electric field. Today, we would say the two electrons exchange a virtual photon which causes their interaction. In the 19th Century, they may have thought matter interacted instantly with distant galaxies. Today, we would say that the distant galaxies emitted virtual gravitons that traveled through space for billions of years before being absorbed by the water in Newton’s bucket experiment, or your body when you’re sitting in the car. The reaction of your body to acceleration is due to the interaction between your body and virtual gravitons that were originally admitted billions of years ago by long dead stars in distant galaxies.

Another misinterpretation of Mach’s Principle is that some people think that the property of mass itself is somehow created by interaction with other matter. They think distant galaxies somehow give mass to your body, and if it wasn’t for distant galaxies, you’d be massless like a photon. This is ridiculous. Mach’s Principle doesn’t say anything like that. If you imagine a universe containing only one object, that object would have zero inertia, not because it has no mass, but because there is no other matter in the Universe to gravitationally attract it. According the particle physics, mass is an intrinsic property of massive particles. Particles do not acquire mass as a result of interacting with other matter.

On the Internet, on a sci-physics newsgroup, I once read an absurd statement that said, “If matter gets mass from Higgs particles, then where does that leave Mach’s Principle?” The person who wrote this was profoundly ignorant. First of all, Higgs particles do not give mass to other particles. The interaction between the fermion terms and the Higgs terms in the Lagrangian allow for the existence of fermion masses. This is a good thing because the Standard Model Lagrangian without the Higgs mechanism predicts that fermions are massless. However, it is ridiculous to say that Higgs particles give mass to other particles. Second of all, Mach’s Principle has nothing to do with giving mass to anything. According to particle physics, mass is an intrinsic property of some particles, and they don’t get it from anywhere else. The person who wrote that had no clue what either the Higgs mechanism or Mach’s Principle are, and their statement was utterly ridiculous at several levels simultaneously.
Nice to see you participating in this thread Ashok. Feel free to express your own views on vedic astronomy.
Here is a sample from Richard Thomson's vedic cosmography

Vedic Cosmography and Astronomy
by Richard L. Thompson
Sample Chapter

Vedic Physics--The Nature of Space, Time, and Matter
Extending Our Physical World-View
The Position of Krishna
Mystic Siddhis
The Activities of Demigods, Yogis, and Rishis

Vedic Physics--The Nature of Space, Time, and Matter
"By Him even the great sages and demigods are placed into illusion, as one is bewildered by the illusory representations of water seen in fire, or land seen on water. Only because of Him do the material universes, temporarily manifested by the three modes of nature, appear factual, although they are unreal" (SB 1.1.1).

Our ideas of the nature of space, time, and matter are essential ingredients in our understanding of the cosmos. When we look into the heavens, our direct sensory data consists of patterns of light. These patterns say nothing, in and of themselves, about the nature of the sources of this light. In order to say something about the cosmic manifestations that have produced the light, it is necessary to assume that the universe is made of some kind of "stuff", or matter, that has certain characteristics and obeys certain laws. Given such assumptions, we can then ask ourselves what arrangement of this matter, acting in accordance with the laws, would produce the observed light patterns. If we are successful in putting together a consistent explanation of the observed data based on the assumed laws and properties, then we tend to suppose that we have correctly understood the structure of the universe. In our mind's eye, our theoretical models take on an air of concrete reality, and it almost seems as though we are holding the universe in the palm of our hand.

Throughout most of modern human history, people have been limited to the surface of the earth, and they have based their ideas of the nature of matter on observations that can be performed in this limited domain, using our ordinary senses. Over the last two or three hundred years, Western scientists have used experimental observation and the analysis of experimental results to build up an extensive body of knowledge--the science of modern physics--which gives a detailed picture of the properties of matter and the laws governing its behavior. The modern Western understanding of the nature and structure of the universe as a whole is based on interpreting observed celestial phenomena within the framework of modern physics.

The thesis of this essay is that the framework of modern physics is too limited to accommodate many phenomena which occur within this universe. In particular, this framework cannot accommodate many features of the universe which are described in the Vedic literatures, and thus the Vedic accounts often seem absurd or mythological when viewed from the perspective of modern science. At the present time, certain assumptions of modern physics have been adopted by people in general as the very foundation of their world-view. These assumptions are incompatible with the underlying assumptions of the Vedic world-view, and thus they tend to block people from having free access to the Vedic literatures. In this section we will try to alleviate this difficulty by discussing the nature of the material energy, as described in the Vedic literature. Since this is a very deep and complex subject, we will be able to touch only on a few points that are relevant to the understanding of Vedic cosmology.

Extending Our Physical World-View
Before making a truly radical departure from our familiar conceptions, we begin by discussing some relatively moderate instances in which the Vedic literatures refer to phenomena and theoretical ideas which do not fit into the current framework of scientific thought. These examples illustrate two main points: (1) Although many Vedic ideas contradict current scientific thinking, they also allow for the possibility that the contradictions can be alleviated by extending the conceptual scope of modern science. (2) Many ideas relevant to our physical world-picture are alluded to only briefly in literatures such as the Srimad Bhagavatam, since these literatures were not intended to serve as textbooks of astronomy or physical science. Thus the conceptual advances needed to reconcile the Vedic worldview with modern science may be difficult to make since they require ideas that radically extend current theories, but these ideas are not explicitly spelled out in available Vedic texts.

Our first example is found in SB 3.26.34p. There we read that the ethereal element provides a substrate for the production of subtle forms by the mind, and that it is also involved in the circulation of vital air within the body. Srila Prabhupada indicates that "this verse is the potential basis of great scientific research work," and, indeed, it provides a clear idea of how the subtle mind may interact with the gross elements of the body and brain.

In the theoretical structure of modern physics, however, there is presently no place for such a conception of the mind and the ethereal element (although some physicists have begun to tentatively entertain such ideas.) As a consequence, scientists still generally adhere to the idea that it is impossible for the brain to interact with a distinct "nonphysical" mind. This in turn makes it impossible for them to give credence to many phenomena which imply the existence of such a mind, even though empirical evidence for these phenomena has existed for many years. These include the psychic phenomena studied by the parapsychologists, out of body experiences, and the spontaneous remembrance of previous incarnations by small children.

It is not our purpose here to make a case for the reality of such phenomena. Our main point is that it is very difficult for people (including scientists) to seriously contemplate particular ideas about reality unless those ideas fit neatly into a familiar and accepted conceptual system. The current theories of physics have been worked out in great technical detail, and one who lives in the conceptual universe that they provide may find that the Vedic idea of the ether seems crude and unimpressive. They may also be blocked by certain unnecessary misconceptions, such as the idea that ether must be like the "luminiferous ether" rejected by Einstein. Yet, the possibility is nonetheless there that physical theory can be extended by introducing a new conception of the ether which agrees with the Vedic conception, and is also consistent with experimental observations. And such an extended theory may provide explanations for many phenomena that are presently considered to be scientifically impossible.

Literatures such as the Srimad Bhagavatam were written for the purpose of clearly explaining certain spiritual ideas to the people in general. However, they inevitably make reference to many other ideas that were familiar to people of the ancient Vedic culture, but which may be very unfamiliar to people of modern Western background. One interesting example is the analogy given by Srila Sanatana Gosvami, in which the transformation of a lowborn man into a brahmin is compared to the transformation of bell metal into gold by an alchemical process (SB 5.24.17p).

The alchemical process itself is not described, and on the basis of modern science we might tend to regard such a transformation as impossible. Yet, the dictionary defines bell metal to be an alloy of copper and tin, and if we consult the periodic table of the elements, we find that the atomic numbers of copper and tin add together to give the atomic number of gold. This suggests that there just might be something to this example, but if so, it clearly involves an extensive body of practical and theoretical knowledge which is completely unknown to us. For Sanatana Gosvami, however, this transformation simply provided a familiar example to illustrate a point about the spiritual transformation of human beings.

The Position of Krishna
Thus far, we have discussed Vedic references to phenomena and theoretical entities which do not fit into the rigorously defined theories of modern physics, but which can be readily inserted into our ordinary picture of the world around us. In this essay, however, we will be dealing with many things that do not seem to be at all compatible with that picture. We suggest that to accommodate these things, it is necessary for us to re-examine our basic ideas concerning the nature of space.

Modern physics and astronomy began with the idea that matter is made of tiny bits of substance, each of which has a location in three-dimensional space. According to this idea, which was strongly developed by Descartes and Newton, three-dimensional space can be seen as an absolute, pre-existing container in which all material events take place. This idea is quite consistent with the picture of the world provided by our own senses, and it tends to provide an unquestioned background for all of our thinking. However, many cultures have maintained quite different ideas about the nature of space, and this is also true of the Vedic culture.

To understand the Vedic conception of space, it is necessary to consider the position of Krishna as the absolute cause of all causes. Clearly we cannot regard the transcendental form of Krishna as being composed of tiny bits of substance situated at different locations in three-dimensional space. Whether we regard the tiny bits as "spiritual" or "material", such a form is certainly limited and relative. The actual nature of Krishna's form is indicated by the following verses from the Brahma-samhita:

I worship Govinda, the primeval Lord, whose transcendental form is full of bliss, truth, substantiality and is thus full of the most dazzling splendor. Each of the limbs of that transcendental figure possesses in Himself, the full-fledged functions of all the organs, and eternally sees, maintains and manifests the infinite universes, both spiritual and mundane. [SBS 5.32].
He is an undifferentiated entity as there is no distinction between the potency and the possessor thereof. In His work of creation of millions of worlds, His potency remains inseparable. All the universes exist in Him and He is present in His fullness in every one of the atoms that are scattered throughout the universe, at one and the same time. Such is the primeval Lord whom I adore [SBS 5.35].

Here we find that the form of Krishna is made of many parts, but each part is identical to the whole. Also, all space is within the form of Krishna, but at the same time Krishna is fully present within every atom. One implication of this is that the entire universe, which is within Krishna, is fully present within every atom of the universe. Such a state of affairs cannot be visualized in three-dimensional terms, and indeed, it is not possible within three-dimensional space. It must simply be taken as an axiom describing the position of Krishna as the supreme absolute truth. Thus, the Vedic concept of space begins with a statement of Krishna's unified nature, rather than with the geometric axioms defining three-dimensional space.
Here we will introduce an idea of "higher dimensional" space which may help us understand the ideas about space which are implicit in the Vedic literature. The term "higher dimensional" is borrowed from modern mathematics, and it does not appear directly in Vedic literature. It is part of an attempt to bridge the conceptual gap between modern thinking and the Vedic world view. Naturally, since the traditional followers of Vedic culture have not been confronted with such a gap, they have not been motivated to introduce ideas to bridge it.

The most fundamental feature of the Vedic idea of space is that, according to this idea, more things can be close to one another than is possible in three-dimensional space. In the course of this chapter we will give many examples from the Vedic liturature illustrating this theme. Since the higher dimensional spaces of mathematics also allow more things to be close to one another than is possible in three-dimensional space, we have chosen the term "higher dimensional" to refer to this feature of the Vedic view of reality.

Although Krishna's situation cannot be represented three-dimensionally, we can visualize, at least in principle, how "higher dimensional" spaces of this kind can be generated, starting from Krishna's position. Krishna's situation is that He has full access to every location simultaneously. In ordinary three-dimensional space we have access, through the operation of our senses of action and perception, to locations within a limited neighborhood, and we can change that neighborhood by moving from one place to another. Thus we can see that our situation can be viewed as a restricted form of Krishna's situation. A "higher dimensional" space corresponds to a situation in which access between locations is more restricted than it is for Krishna, but less restricted than it is for beings experiencing three-dimensional space.

This concept of "higher dimensional" space is closely tied together with the idea of varying levels of sensory development in sentient beings. Access between locations depends on the operation of senses of action and senses of perception, and thus it should be possible in principle to enlarge the "space" of one's experience by increasing the scope of one's sensory powers.

These ideas about space and its relation to sense perception are implicit in the Vedic literature, and they can best be understood by giving some specific examples. The nature of Krishna's absolute position is nicely illustrated by the following story of a visit by Lord Brahma to Krishna in Dvaraka. In the story, Krishna first responds to Brahma's request to see Him by having His secretary ask, "Which Brahma wishes to see Me?" Brahma later begins his conversation with Krishna by asking why Krishna made this inquiry.

"Why did you inquire which Brahma had come see you? What is the purpose of such an inquiry? Is there any other Brahma besides me within this universe?"
Upon hearing this, Sri Krishna smiled and immediately meditated. Unlimited Brahmas arrived instantly.

These Brahmas had different numbers of heads. Some had ten heads, some twenty, some a hundred, some a thousand, some ten thousand, some a hundred thousand, some ten million and others a hundred million. No one can count the number of faces they had.

There also arrived many Lord Sivas with various heads numbering one hundred thousand and ten million. Many Indras also arrived, and they had thousands of eyes all over their bodies.

When the four-headed Brahma of this universe saw all these opulences of Krishna, he became very bewildered and considered himself a rabbit among many elephants.

All the Brahmas who came to see Krishna offered their respects at His lotus feet, and when they did this, their helmets touched His lotus feet.

No one can estimate the inconceivable potencies of Krishna. All the Brahmas who were there were resting in the one body of Krishna.

When all the helmets struck together at Krishna's lotus feet, there was a tumultuous sound. It appeared that the helmets themselves were offering prayers unto Krishna's lotus feet.

With folded hands, all the Brahmas and Sivas began to offer prayers unto Lord Krishna, saying, "O Lord, You have shown me a great favor. I have been able to see your lotus feet."

All of them then said, "It is my great fortune, Lord, that you have called me, thinking of me as your servant. Now let me know what Your order is so that I may carry it on my heads."

Lord Krishna replied, "Since I wanted to see all of you together, I have called all of you here. All of you should be happy. Is there any fear of the demons?"

They replied, "By your mercy, we are victorious everywhere. Whatever burden there was upon the earth You have taken away by descending on that planet."

This is the proof of Dvaraka's opulence: all the Brahmas thought, "Krishna is now staying in my jurisdiction."

Thus the opulence of Dvaraka was perceived by each and every one of them. Although they were all assembled together, no one could see anyone but himself.

Lord Krishna then bade farewell to all the Brahmas there, and after offering their obeisances, they all returned to their respective homes [CC ML 21.65-80].

In this story it is significant that each of the Brahma's remained within his own universe. This means that Krishna was simultaneously manifesting His Dvaraka pastimes in all of those universes. Each Brahma except ours thought that he was alone with Krishna in Dvaraka within his own universe, but by Krishna's grace our Brahma could simultaneously see all of the others. This illustrates how Krishna has access to all locations at once, and it also shows how, by Krishna's grace, different living beings can be given different degrees of spatial access, either permanently or temporarily.

Arjuna's vision of Krishna's universal form on the battlefield of Kuruksetra is another example of how Krishna can expand the sensory powers of a living being, and give him access to regions of the universe which were previously unknown to him. Before revealing this form to Arjuna, Krishna said,

O best of the Bharatas, see here the different manifestations of Adityas, Vasus, Rudras, Asvini-kumaras and all the other demigods. Behold the many wonderful things which no one has ever seen or heard of before.
O Arjuna, whatever you want to see, behold at once in this body of Mine! This universal form can show you whatever you now desire to see and whatever you may want to see in the future. Everything--moving and nonmoving--is here completely, in one place [BG 11.6-7].

Thus from one place Arjuna was able to see many different realms occupied by demigods and other kinds of living beings. To simultaneously perceive such a vast variety of scenes, Arjuna clearly had to transcend the limitations of three-dimensional space, and it is significant that Krishna made this possible through the medium of his all-pervading universal form. The story of mother Yasoda seeing the entire universe (including herself and Krishna) within Krishna's mouth is another example showing how Krishna can reveal all locations through his all-encompassing form (see KB, pp. 83-84).

It is interesting to note that the Brahmas visiting Krishna had varying numbers of heads, ranging from hundreds to hundreds of millions. It is rather difficult to understand how millions of heads could be arranged on one body in three dimensional space, and it is also difficult to see how millions of Brahmas could all be seen simultaneously within one room. We suggest that these things are made possible by the fact that the underlying "space" is not three-dimensional.

Similar observations could be made about the incident in which Banasura used 1,000 arms to simultaneously work 500 bows, and fire 2,000 arrows at a time at Krishna. In this case we are dealing with a materially embodied being living on the earth. One might wonder how 500 material arms can be mounted on one shoulder without interfering with one another. And if this is possible, how can they aim 500 bows in the same direction at once? (Do the bows pass through each other?) We suggest that stories of this kind implicitly require higher dimensional conceptions of space.

We can sum up the idea of dimensionality of space by saying that the greater is the degree of access between locations, the higher is the dimensionality of the space. Since Krishna has simultaneous access to all locations, He perceives space at the highest level of dimensionality. Different living beings will perceive space at different levels of dimensionality, and thus they will have access to different sets of locations (or lokas.)

It is interesting to note that the idea of higher dimensional access between locations is a key feature of quantum mechanics. The quantum mechanical atom cannot be represented in three-dimensional space. In fact, to represent something as commonplace as an atom of carbon, quantum mechanics makes use of a kind of infinite-dimensional space called Hilbert space. The three-dimensional bonding of carbon and other atoms is made possible by the higher dimensional interactions within the atoms. Thus, although the idea of higher dimensional realms may seem to be an extreme departure from accepted scientific thinking, it is possible to interpret modern physics as laying the groundwork for such an idea.

Mystic Siddhis
The eight mystic siddhis provide a direct illustration of how sentient beings can operate at different levels of sensory power by being endowed to varying degrees with Krishna's primordial potencies. Srila Prabhupada gives the following description of some of the mystic siddhis:

...a mystic yogi can enter into the sun planet simply by using the rays of the sunshine. This perfection is called laghima. Similarly, a yogi can touch the moon with his finger. Though the modern astronauts go to the moon with the help of spaceships, they undergo many difficulties, whereas a person with mystic perfection can extend his hand and touch the moon with his finger. This siddhi is called prapti, or acquisition. With this prapti siddhi, the perfect mystic yogi can not only touch the moon planet, but he can extend his hand anywhere and take whatever he likes. He may be sitting thousands of miles away from a certain place, and if he likes he can take fruit from a garden there (NOD, pp. 11-12).
The prapti siddhi provides a perfect example of what we mean by the extension of access between locations. Consider the yogi on the earth who reaches out his hand to touch the moon. Does the yogi experience that his hand moves up through the atmosphere and crosses over thousands of miles of outer space, followed by a greatly elongated arm? This hardly seems plausible. We suggest that this siddhi actually allows the yogi to directly reach any desired location, and thus it requires higher dimensional connections between remotely separated regions. The idea here is that Krishna always has direct access to all locations, and by His grace this power of direct access can be conferred to varying degrees on various living beings.
The following verses in the Eleventh Canto of Srimad Bhagavatam show that the eight siddhis are indeed obtained by partial realization of Krishna's inherent potencies:

1. anima -- becoming smaller than the smallest. "One who worships Me [Krishna] in My atomic form pervading all subtle elements [bhuta-suksma and tan-matram], fixing his mind on that alone, obtains the mystic perfection called anima" (SB 11.15.10).

2. mahima -- becoming greater than the greatest. "One who absorbs his mind in the particular form of the mahat-tattva and thus meditates upon Me as the Supreme Soul of the total material existence achieves the mystic perfection called mahima" (SB 11.15.11).

3. laghima -- becoming lighter than the lightest. "I exist within everything, and I am therefore the essence of the atomic constituents of material elements. By attaching his mind to Me in this form, the yogi may achieve the perfection called laghima, by which he realizes the subtle atomic substance of time" (SB 11.15.12).

4. prapti -- acquisition. "Fixing his mind completely in Me within the element of false ego generated from the mode of goodness, the yogi obtains the power of mystic acquisition, by which he becomes the proprietor of the senses of all living entities. He obtains such perfection because his mind is absorbed in Me" (SB 11.15.13).

Similar statements are made about the other siddhis. According to the purport to SB 11.15.13, "Srila Bhaktisiddhanta Sarasvati Thakura states that those who pursue such perfections without fixing the mind on the Supreme Lord acquire a gross and inferior reflection of each mystic potency."

The Activities of Demigods, Yogis, and Rishis
In the Srimad Bhagavatam there are many references to the mystic powers of demigods, yogis, and rishis. These living beings are clearly endowed with more highly developed sensory powers than ordinary human beings such as ourselves, and they also are able to operate within a more extensive realm of activity than the space-time continuum of our ordinary experience. (Note that in accordance with Vedic usage, we are using the term "sensory" to refer to both senses of perception and senses of action.)

A typical inhabitant of the higher planets has a life-span of 10,000 celestial years, measured in days and nights of six months (SB 4.9.63p). However, many demigods live for a much longer period. Thus demigods such as Indra hold official positions in the universal administration for the span of one manvantara, or 71x12,000 celestial years, and their total life span is much longer.

The demigods have the power to assume any desired form (SB 8.15.32p), and to appear and disappear at will before ordinary human beings. Thus SB 9.21.15 says that demigods such as Lord Brahma and Lord Siva appeared in human form before Maharaja Rantideva, and SB 1.12.20p says that Indra and Agni appeared before Maharaja Sibi in the form of an eagle and a pigeon. There are also many instances in the Bhagavatam indicating that demigods on higher levels of karmic merit can appear and disappear at will before lesser demigods. For example, Indra's guru, Brhaspati, made himself inaccessible to Indra after Indra offended him (SB 6.7.16).

Our thesis is that this ability to appear and disappear is not "just" a matter of mystical power. Rather, it demonstrates an important feature of the physical world in which we live. This world contains many manifestations which are not accessible to our ordinary senses, but which are accessible to more highly developed beings, such as the demigods. There is a hierarchy of "dimensional" levels within the universe, and beings on one particular level can operate within a larger continuum than beings on lower levels. The spiritual realm of Vaikuntha and Goloka Vrndavana is on a still higher level. Thus Brahma, the topmost demigod within the material universe, became completely bewildered when Krishna revealed the spiritual world to him.

In SB 1.16.3 it is said that during Maharaja Pariksit's horse sacrifices, even a common man could see demigods. It appears that in Vedic times demigods often visited the earth and engaged in various dealings with human beings. However, only qualified persons were generally able to see them. Even recently, after the advent of Lord Caitanya, demigods used to invisibly visit the home of Jagannatha Misra to glorify the Lord (CC AL 14.172-174).

The Bhagavatam often alludes to the idea that by acquiring higher spiritual qualifications, one's sensory powers will be enhanced, and one will automatically be able to experience phenomena within a broader realm of existence. (It is also emphasized, of course, that such automatic developments should not be exploited for sense gratification, since this would divert one from the actual goal of spiritual life.) One example of this is given by the instruction of Narada Muni to Dhruva Maharaja that by chanting the mantra, "om namo bhagavate vasudevaya," he would soon be able to see "the perfect human beings (khe-caran) flying in the sky" (SB 4.8.53).

One method that was sometimes used to travel from the higher planets to the earth is mentioned in (SB 3.8.5p), where we read that great sages can travel from Satyaloka to the earth via the Ganges river, which flows all over the universe. Srila Prabhupada points out that this form of travel is possible in any river by mystic power. It hardly seems plausible that this method of travel involves swimming up or down stream over vast distances, and, of course, the connection between the earthly Ganges and its celestial counterpart is not visible to us. We suggest that this process of travel involves higher dimensional connections between locations, and that the river serves as a kind of guiding beacon to direct such higher dimensional transport. In the case of the Ganges, the course of the river from higher planets down to the earth must also be higher dimensional.

In KB p. 534 there is a description of how Citralekha, a mystic yogini, traveled in outer space from Sonitapura to Dvaraka and transferred Aniruddha back to Sonitapura in a sleeping condition. This is another example of a form of travel that seems to require higher dimensional connections for its operation.

The Vedic sastras mention many remarkable events which are said to have taken place on the earth in the remote past. Many of these events involve phenomena that we do not experience today, and one might ask why this should be so, if these events actually did occur at one time. One reason for this given in the Bhagavatam is that prior to the beginning of Kali-yuga, natural processes on the earth operated in a different mode than they do today (see SB 1.4.17p). The sensory powers of all living beings were on a higher average level than they are at present, and advanced beings such as demigods and great sages regularly visited the earth. Thus the earthly realm of ordinary human life was more intimately linked up with higher realms of material and spiritual reality than it has been since the start of the Kali-yuga.

This idea leads naturally to the following tentative scenario for the history of the last few thousand years: Once the Kali-yuga began, demigods and higher beings greatly curtailed communications with people on the earth, and the general sensory level of human beings also declined. For some time, people continued to believe in stories about the earlier state of affairs on the earth due to the authority of tradition. However, due to the lack of feedback from higher sources and the natural cheating propensity of human beings, the traditions in various parts of the world gradually became more and more garbled, and people began to lose faith in them. Finally the present stage of civilization was reached, in which old traditions are widely viewed as useless mythology, and people seek knowledge entirely through the use of their current, limited senses.

Regions on this Earth Not Visible to Our Senses
We have been developing the idea that the three-dimensional continuum of our experience does not constitute the totality of spiritual or material reality. One feature of this idea is that there exist worlds, or realms of experience, which are located here on the earth, but which cannot be perceived or visited by human beings possessing ordinary sensory powers. Of course, the most striking example of this is Krishna's transcendental dhama of Vrndavana. In CC AL 5.18p it is stated that Krishna's abode is unlimited and all-pervading, and yet it is identical to the Vrndavana of this earth. This implies that within the tract of land called Vrndavana in India there exists a completely real realm of spiritual existence which is not accessible to the senses of ordinary conditioned beings. This is another example of higher dimensional connections, and it implies that two (or more) worlds of experience can co-exist in parallel, in the same location.

The holy dhama of Navadvipa is another example of this (and, of course, Navadvipa dhama is also identical to Vrndavana.) Srila Bhaktivinod Thakur states in the Navadvipa Mahatmya that, "The dhama of Navadvipa, within Gaura Mandala, and served by the Ganga, is situated in eternal splendor. . . . The form of Gaura Mandala, eternally transcendental to the material world, is like the sun. The materialist's eye is covered by the cloud of illusion, and because of this he sees only the secondary transformations of that spiritual energy, the dull, inert material world" (NM, p. 4).

The transcendental realms of Navadvipa and Vrndavana are purely spiritual, but there are also material examples illustrating the idea of parallel worlds co-existing in one place. For example, the Bhagavatam states that Maru and Devapi, two ancient royal princes belonging to the Surya and Soma dynasties, are still living in the Himalayas in a place called Kalipa-grama. By the power of mystic yoga they will prolong their lives until the beginning of the next Satya-yuga and then revive the lost Surya and Soma dynasties by begetting children (SB 9.12.6, 9.22.17-18).

If we go to the Himalayas we will certainly not be able to perceive Maru and Devapi using our ordinary senses, even though they are human beings possessing gross material bodies. It can also be argued that we will not be able to perceive the surroundings in which they live. A human being cannot live without interacting with his material surroundings. Even a yogi who is simply living on air requires an undisturbed sitting place. Could it be that the material accoutrements and sitting places of these two persons are directly visible and accessible to us, even though they themselves are invisible? We suggest that they are actually living in a setting which is entirely inaccessible to our senses, but which can be seen and entered by a person, such as an advanced yogi, whose senses can operate on an appropriate level.

Here the objection may be raised that a co-existing invisible world cannot be on the same level of reality as our world because it must be "subtle", transparent, or ghostlike in nature, whereas our own world is opaque and substantial. Our reply is that such a co-existing world is not invisible to us because it is made of transparent substance distributed within our own three-dimensional continuum. Rather, it is invisible because it lies in a higher dimension, and is entirely outside of our continuum. It can be in the "same place" as we are by virtue of higher dimensional interconnection. A person with higher sensory powers is able to perceive this world not because he can discern some nearly transparent substance lying within his own three-dimensional space, but because his senses are not restricted to three-dimensions, and have access to broader realms of material or spiritual reality.

We should note that the basic elements of earth, water, air, fire, and ether are present in some form on all levels of reality, both spiritual and mundane. In SB 11.21.5 it is stated that these five elements constitute the bodies of all conditioned souls, from Lord Brahma down to the nonmoving creatures. Also CC AL 5.53 states that, "the earth, water, fire, air and ether of Vaikuntha are all spiritual. Material elements are not found there."

The five material elements (pancha bhuta) are described in the Bhagavad-gita as separated energies of Krishna. Their counterparts in Vaikuntha are evidently similar enough to them to warrant being called by the same names. However, the spiritual elements must belong to Krishna's internal potency. It would therefore seem that the spiritual world and the material world are similar in the sense that both contain variegated forms containing solid, liquid and gaseous constituents. At the same time, they have distinct qualitative features, of which one of the most notable is the presence of the modes of passion and ignorance in the material world, and their absence in the spiritual world. Material realms on various dimensional levels will also possess similar variegated forms, but the higher realms will be characterized by greater predominance of the mode of goodness over the modes of passion and ignorance.

As a final point, we note that the history of the Madhva-Gaudiya sampradaya sheds some light on the higher dimensional nature of reality. In SB 1.4.15p Srila Prabhupada points out that Vyasadeva is residing in Samyaprasa in Badarikasrama. Many people in India make a pilgrimage to Badarikasrama every year, but it is not possible for an ordinary person to meet Vyasadeva. However, it is said that Madhvacarya met Vyasadeva there and took initiation from him. It was through this higher dimensional link that the Madhva-Gaudiya sampradaya was passed down from Srila Vyasadeva to the recent line of acaryas.

I. Works by His Divine Grace A.C. Bhaktivedanta Swami Prabhupada. These works are all published by the Bhaktivedanta Book Trust in Los Angeles, California.

Bhagavad-gita As It Is (1983)

Sri Caitanya-caritamrita (1974)

Krishna, the Supreme Personality of Godhead (1-vol. edition, 1986)

Nectar of Devotion (1985)

Srimad Bhagavatam (1987)
II. Other works.

Bhaktivinod Thakur, Navadwip Mahatmya, trans. Banu das, ms.

Bhaktisiddhanta Saraswati Goswami Thakura, Sri Brahma-samhita (Los Angeles: Bhaktivedanta Book Trust, 1985).
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Last updated on February 7, 1996.
Astronomical Applications of Vedic Mathematics.
Kenneth Williams
2000 139p. Contents: Introduction to Vedic Mathematics. Prediction of Eclipses: Prediction of the Times Of Contact of the Moon’s Penumbral and Umbral Shadows With the Earth. Partial Phase. Total Phase. Approximate Position of the Eclipse Path. Time of Total Eclipse For an Observer on Earth. Bessel’s Method, Early Eclipse Prediction, Solution of Eclipse Equation. Kepler’s Equation: A Transcendental Equation, Solution of Kepler’s Equation. Introduction to Triples: Notation & Combination, Triple Addition, Quadrant Triples, Rotations, Subtraction, Half-Angle Triple. Triple Code Numbers, Angles in Perfect Triples. Prediction of Planetary Positions: Heliocentric Position, Mean Anomaly, Geocentric Position, Geocentric Longitude, Geocentric Correction, Planet Finder. Spherical Triangles Using Triples: Triple Notation & Formulae for Spherical Trigonometry, Cosine Rule to Find an Angle, Sine Rule to Find Angle, Cotangent Rule to Find Angle, Polar Cosine Rule. Right Angled Spherical Triangles. Spherical Triangles Using Code Numbers. Determinants. Quadruples. Addition of Perpendicular Triples, Rotation About A Coordinate Axis. Quadruples & Orbits, Inclination of Orbit, Angle Between Two Directions. Inclination of Planetary Orbits. Calculation of Radius Vector.

Applications of Vedic mathematics


K. R. Williams; Rs. 125.


A. P. Nicholas, K. P. Williams, J. Pickles; Rs. 225.

ASTRONOMICAL APPLICATIONS OF VEDIC MATHEMATICS: Kenneth Williams; Rs. 195. All the three books have been published by Motilal Banarsidass Publishers Private Limited, 41, U.A. Bungalow Road, Jawahar Nahar, Delhi-110007.

THE PATH-BREAKING book Vedic Mathematics written by Bharati Krishna Tirthaji, a former Sankaracharya of Puri, was published posthumously by the Hindu Vishwavidyalaya of Varanasi in 1965, at the instance of Manjula Devi, to whom the manuscript was entrusted by Tirthaji. Soon the book was published by M.B. publishers and it was in hibernation till it caught the attention of the British savants who have hailed the contribution of Tirthaji by discovering newer facets. The outcome is the availability of a dynamic and vibrant choice of approach in applying Vedic mathematics effectively in various branches of mathematics. What continues to be in vogue can be seen to be static and sleepy through routine methods of handling problems. Books published abroad in U.K. for British institutions using Vedic Mathematics have now been brought out by the renowned publishers of Indology books as Indian editions.

Steering clear of the controversy which is yet to be settled, the mathematical content of the books under review opens vistas missed by our curricular experts and textbooks writers, teachers and paper setters. To clinch the issue, how many are even today, familiar with negative digits in numerals and interpretation of identities in mental calculation?

It is rare to find religious heads evincing interest in mathematics, leave alone expounding with passion the unconventional strategies that empower one to put aside paper and pencil and get at the answers to problems of calculation mentally. Unlike abacus-dependent calculation skills, they turn out to be promotive of self-esteem and self-confidence in the practitioner. As varying treatments are evoked, it is not akin to robot like behaviour.

Tirthaji enumerates Sutras or Aphorisms, 16 in number and 13 Upasutras or corollaries and succeeds in showing how they go beyond the capabilities of calculator devices, the use of which has a debilitating effect on the learners and users. Their role in effecting a tie-up of mathematical processes in the entire gamut of mathematics carries with it a novelty that is not known to majority of mathematics educators. British scholars show that they lend themselves to extensions not conceived by the propounder himself. According to Tirthaji, "Vedic mathematics" that he has chosen for the title of his book is Vedic-inspired. It will help to assess his stand if one could refer to the book Mathematics As Known To The Vedic Samhita by M.D. Pandit published in 1993 by Sri Satguru Publications.

Narinder Puri of Roorkee University brought out Indian editions of Vedic Mathematics and related literature by non-Indian authors in the 1990's and popularised the contributions in India and abroad, organising conferences involving the authors and conducting courses.

In the book, The Natural Calculator, the author shows how natural processes of the mind are associated with mental calculation. Since multiplication operation reveals remarkably the properties of number, the book deals mainly with it. Prodigies are recognised by their ability to give instantly products of large numbers. The book is so written that it can be gone through, in any desired sequence. Algebraic proofs justifying the approaches are given at the end of the book. Problem-solving skills get a boost. The objective is to show how reliance on the calculator is harmful, as it deprives the mind from exercising its capabilities which get frozen through repetitive endeavour. Major part of mathematics education can be directed to give one-line response to basic operations, singly or combined.

The experience is exhilarating and delightful, once one gets settled in the Vedic way. Availability of choice and the judgement that it entails provides one with expertise to shun routineness, the bane of curricular learning today. As Tirthaji affirms, there is flexibility, innovativeness and creativity in mathematical computation and this brings mathematics to life. The criteria for looking upon an activity as natural are spelled out by advent of increasing speed and accuracy. To put it in other words, calculation requiring pencil and paper is objective and external, whereas when resorted to mentally is subjective and internal and as vouchsafed by transcendental meditation is deeper. Instructional standards today centre round general methods but Vedic mathematics emphasises that every problem is unique with its own singularly arrived at solution. To ignore this tantamounts to underestimating children's capabilities to hold and remember.

There are nine chapters, each of which is flagged with a bordered version of the experiences in brief of child prodigies who during the last four centuries exhibited extraordinary powers of mental calculation and baffled the audiences. Some of them blossomed into professors of mathematics like Aitken. The book is presented in prescribable format with models and exercises for practice with answers given at the end. It closes with general exercises with hints for two sections. A list of references is also provided.

In the second book the authors deal exclusively with the versatility of the single sutra "Vertically and crosswise" (urdhwa thryagbhyam). They point out that while the applications of this sutra are extraordinarily diverse and wide-ranging, they cannot claim that they have exhausted its applicability. The methods get started in a big way in chapter I with coverage gathering momentum in the subsequent chapters. Applications embrace basic calculations, logarithms, exponents, trigonometric functions and solutions of simultaneous, transcendental polynomial and differential equations. The link between arithmetic and algebra is revealed through treatment of polynomial on the analogy of place value notation.

In Astronomical Applications of Vedic Mathematics the author affirms that his is a personal contribution to new application of Vedic mathematics. He professes no thorough or complete treatment of the topics taken up, admitting that the ideas given can lend themselves to further development and continuance of application to other areas of astronomy. To make the material intelligible to as wide a readership as possible, rigour is curtailed. Besides chapters on prediction of eclipses and planetary positions, the book carries illustrations, four appendices and planet finder circles, three in number. Answers and exercises of chapter V on spherical triangles are provided at the end. Books of reference are mentioned, followed by glossary and Vedic sutras with English rendering.

The printing and get-up are excellent. Proof-reading has been done well . The books will be a weighty addition to mathematics education section of school and college libraries, if not included already. One looks forward to further improved editions of these books in the near future.


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