Episode 35: The Vedanga Jyotisha & Beyond

November 3, 2023

We delve into the contents of the Vedanga Jyotisha, the earliest Indian text to deal explicitly with astronomy. Then we turn to early Hindu cosmology and their explanations for various celestial phenomena, from the phases of the Moon to solar eclipses. Lastly, we briefly cover the unique cosmology of the Jains.


Good evening, and welcome to the Song of Urania, a podcast about the history of astronomy from antiquity to the present with new episodes every full moon, or thereabouts. My name is Joe Antognini.

Well last month we went through some of the early history of India, the Harappan civilization, the Aryan invasion, and the subsequent rise of Hinduism in the region. Now, as I mentioned last month, Hinduism has a large body of sacred texts, but the most important are four texts known as the Vedas. The oldest of these, the Rigveda, actually contains a number of astronomical references and is therefore our primary window into the earliest astronomy of India after the Aryan invasion.

But, of course, the Rigveda, and the other Vedas for that matter, are not the only texts to come out of early Indian civilization, even if they are among the earliest. I mentioned in the last episode that there are, in particular, a set of six texts called the Vedanga, which act as a kind of preparatory guide to the Vedas, each one teaching a different skill needed if you are to fully understand the Vedas. These six texts are collectively called the Vedanga, which literally translates to “the limbs of the Vedas.” I briefly listed the topics of the six Vedanga in the last episode, but they cover things like grammar, poetic meters, and the rubrics for performing the Vedic rituals. But for our purposes the most important of the six Vedanga is the last one, called the Jyotisha, since the topic of the Jyotisha is astronomy.

The Jyotisha is believed to have been written sometime in the middle of the first millennium BC and is attributed to an author by the name of Lagadha. But as with many of the ancient Indian texts, this is probably only when the contents were codified and formally written down. The ideas presented in the text were probably developed far earlier by many different people over the course of generations. The Jyotisha makes some comments, for instance, on the positions of the solstices with respect to the ecliptic. Because the positions of the solstices gradually change due to the precession of the equinoxes, the positions implied in the Jyotisha can be used to roughly date when the techniques were originally developed, and this points to an origin maybe around 1200 BC, plus or minus maybe a century or two. So probably these techniques were in use for more than half a millennium before they were formally written down in the Jyotisha.

One thing I should mention, too, is that when the Jyotisha was written down, it was written down in slightly different ways in different parts. There are two major recensions or versions of the text that exists and are associated with different Vedic schools. But at least in terms of the astronomical content they are fairly similar. Either way the Jyotisha forms the basis of Indian astronomy up until around the 3rd or 4th century AD, at which point a number of newer texts improve the state of the art.

Now, as I mentioned earlier, the purpose of the Vedanga was to instruct the reader in how to properly understand the Vedas and carry out the rituals they prescribe. The reason that the reader had to learn astronomy in the Jyotisha was that astronomy formed the basis for understanding and marking the calendar, and the calendar, in turn, set the times to perform various rituals throughout the year. How could you perform the right rituals on the right days if you didn’t know what day it was? And the Jyotisha is quite explicit that that is its purpose. The opening line reads:

Making obeisance with bent head to God Prajāpati, who is the supervisor of the 5-year yuga, and has day, season, half year and month as his limbs, I, being purified (śuci), shall describe systematically the correct movement of heavenly bodies, which is accepted by highest Brahmans, for the sake of the determination of the proper time of sacrifices.

And if that were not clear enough, later on the text states:

The Vedas are revealed for the purpose of performing sacrificial rites; these rites are laid down in order of time. Therefore, he who is versed in astronomy, the science of the reckoning of time, knows the sacrifices.

So, given that this is its purpose it’s perhaps no surprise that the main focus of the Jyotisha’s astronomy is on how to keep the calendar. The overall system that the Jyotisha presents is based around a five year cycle called the “yuga.” They divided this period in a number of different ways. One way was the sidereal lunar year, which had either 12 or 13 lunar months of 27 days apiece. They also tracked the synodic lunar year, which consisted of 12 synodic lunar months, or periods from full moon to full moon. This synodic lunar year was 354 days long. Since the time from full moon to full moon is fairly close to 29 and a half days, a synodic lunar year would have six months of 29 days and six months of 30 days, so that on average the synodic month was 29 and a half days long. In one 5-year yuga, there would be 3 normal years of 12 lunar months, and 2 years of 13 lunar months interspersed between the other three.

If that was not enough, there was lastly the savana, or civil year, which was similar to the year in the Egyptian calendar — it was 12 months, each of which had exactly 30 days, so it bore no relation to the position of the moon. Since this made for a year of 360 days, the calendar also requires the addition of a kind of leap year, called the pseudo-solsticial year, where every 3 years they would add 18 days to the savana year. This would bring the average length of the year to 366 days per year. Now, this is still a bit large. The year is close to 365 and a quarter days long, so the average length of the savana year was too long by 3/4 of a day. If that were all there was to it, there would be a problem, because a discrepancy of 3/4 of a day rapidly adds up. Over the course of 100 years, this would be a drift of 75 days, or about two and a half months. It seems that to address this problem there was also a system of intercalating with 21 days once every four years, which had the effect of producing an average year of 365 and a quarter days. But the main advantage of the savana year of 360 or 378 days was that on the normal cycle, one yuga consisting of five average years of 366 days was 1830 days long, and this corresponded to exactly 62 synodic lunar months and 67 sidereal lunar months. So this system was well synchronized between the lunar and solar cycles. Synchronization between the lunar and solar cycles was especially important in the Jyotisha because some of the rituals correspond to the solstices, and others correspond to the full and new moons, so the calendar had to be arranged in a way that these features would regularly line up on the calendar. Of the various kinds of years that the Jyotisha recognizes, the most important were the savana and the synodic lunar years because the schedules for most rituals were tied to your position in one of these two calendars.

Well, the year itself was divided into two halves, called “ayanas,” a bright half corresponding to the half of the year from the winter to the summer solstice when the sun is moving northward and the days are getting longer, and a dark half corresponding to the time from the summer to the winter solstice when the sun is moving southward and the days are getting shorter. Each ayana is, in turn, divided into three seasons, making six seasons in all during the year.

Like the year, the synodic month was also divided into two halves: sukla, the light half, from new moon to full moon, and krishna, the dark half, from full moon to new moon. Now, as I mentioned earlier, early Hindu astronomy kept track of several different kinds of months: the sidereal month, which is the time it takes the moon to return to the same background stars on the sky; synodic months, which is the time from full moon to full moon; and the savana month, which was a standard 30 days. But because there were sacrifices and rituals tied to full moon and new moon, the synodic month was the most important. Several days of the synodic month got their own names due to their connection to particular sacrifice. So we have “Kuhu,” which is New moon and “Raka,” which is full moon, but also “Sinivali,” which is the day before the new moon, and “Anumati,” which is the day before the full moon. One of the unique features of Indian astronomy is that there was no universal standard for what constituted the beginning of the month. There were instead two separate systems which were in use in different regions. One of these is called the “Amanta” system and begins the month at the new moon, and tended to dominate in the south. The other system is called the “Purnimanta” system and begins the new month at the full moon, and tended to dominate in the North, particularly in the Ganges river plain.

Finally, there were the days. And as with the months, the Jyotisha recognizes several different kinds of day. The most basic kind of day was the savana day, which is the period from sunrise to sunrise. Now, it seems that this was something of a later innovation. Hints from the Vedas suggest that originally the day was marked from sunset to sunset, similar to the way the Mesopotamians did it. But at least for astronomical purposes, later on the mark changed from sunset to sunrise, and even later, some astronomers also started to mark the day from midnight to midnight. Now this savana day was the one that was most commonly used, but for timekeeping purposes, astronomers also tracked two other kinds of day. One is the lunar day, or “tithi,” and consists of 1/30 of a lunation, or about 23 hours and 37 minutes. The tithi is something of a distinctive feature of the Jyotisha, but it was not much developed in later astronomical works in India, so after a few centuries it seems that it had fallen out of favor as a unit. The other was the solar day, which is exactly 1/360 of a year. This unit of time is hinted at in the Jyotisha, but doesn’t appear very explicitly, and it’s not until the early 6th century AD that it appears definitively in the Indian astronomical literature.

Finally, the day itself was divided into five parts: Udyan surya, meaning “rising sun;” Samgava, meaning “gathering of the cows;” Madhyam-din, which is mid-day; Aparahna, which is afternoon; and lastly Astam-yan, which is sunset.

In addition to the various divisions of time in the calendar, the Jyotisha also speaks of some of the properties of the solstices. The yearly cycle was taken to begin at the winter solstice, after which the Sun would move northward for six months during the first ayana of the year. Then it would turn around and start moving southward after the summer solstice. The summer solstice marked an important point in the year called the Vaishuvatiya, and was celebrated by hymns that were chanted for 21 days, 10 days before the solstice, 10 days after, and then the day of the solstice itself. These 21 days of chants surrounding the summer solstice has been interpreted as implying that the Sun was perceived to remain fixed for those 21 days around the solstice.

The texts make clear that the cause of the annual cycle we see of days getting longer leading up to the summer solstice and days getting shorter leading up to the winter solstice was well understood. Another text called the Kaushitaki Brahmana says:

The sun indeed rests on the new moon day of Magha, being about to turn towards the north. Thus they rest who are about to perform the rites of the prayaniya atiratra…. He goes for six months towards the north; they follow him with the ascending celebrations of six days each. He having gone six months towards the north stands still, being about to turn towards the south. Thus they stop, being about to perform the rites of the Vaishuvatiya day. Thus they reach him for the second time. He goes six months towards the south. They follow him with the returning celebrations of six days each. Having gone six months towards the south he stands still, being about to turn towards the north. Thus they stop, being about to perform the rites of the Mahavratiya day. … About this there is sung a sacrificial stanza: ‘Arranging the days and nights like a wise spider; six months always towards the south and six months towards the north wanders the Sun.’

The Jyotisha not only describes this general phenomenon of the days getting longer and shorter but also describes it quantitatively. According to the Jyotisha, the ratio between the length of day and night on the summer solstice is 3:2, the same ratio that the Babylonians used. Given that the Babylonians had almost certainly developed this ratio first, some scholars have wondered whether or not the appearance of this ratio in the Jyotisha was an import from Mesopotamia, but the evidence for this hypothesis is pretty minimal. It’s more likely that it was developed independently and happened to get the same ratio by coincidence. The Jyotisha goes even further and also describes the rate at which the days get longer as the solstice approaches. One line reads:

The increase of daytime and decrease of nighttime is [the time equivalent of] one prastha of water [in the clepsydra per day] during the northward course [of the sun]. They are in reverse during the southward course. [The total difference is] 6 muhūrtas during a half year.

The “prastha” referred to in this line was a unit of measurement for an amount of water coming from a clepsydra, and you may recall from the last episode that a muhurta was 1/30 of a day. Later on the Jyotisha says:

[The number of days] elapsed in the northward course or remaining in the southward course is doubled, divided by 61, and added to 12. The result is the length of daytime [in terms of muhūtras].

So the Jyotisha is part of a rather small and exclusive group of astronomical texts from the ancient world that explicitly provides a mathematical model of the length of day over the course of the year. Similar to the Babylonians they modeled it as a zig-zag function, with each day getting longer at a constant rate until the summer solstice arrives, at which point it reverses and the days get shorter at the same constant rate until the winter solstice.

Now, in reality, the change in daylight is more of a sinusoid at these latitudes, but the slope of the line that the Jyotisha mentions was probably measured around the equinoxes, since this is when the change in the amount of daylight is most noticeable. An interesting consequence of this is that from this slope we can estimate the latitude that the Jyotisha was composed at, and we find that it is consistent with being composed in northern India, which agrees with other evidence that it originated out of the western part of the Ganges river plain.

Well, the last bit of the Jyotisha that I’ll mention is the concept of the “nakshatra,” which came to be fundamental to Indian astronomy. Nakshatra literally means “guardian of the night” and was the Indian version of the zodiac. The Nakshatra were a set of 27 or 28 locations along the ecliptic that were used to mark the positions of the Sun, Moon, and planets, similar to the signs of the zodiac in Western astronomy. And like the signs of the zodiac, the nakshatra were defined in a way that was somewhat independent of their corresponding stars or asterisms, each nakshatra corresponded to a width that was exactly 1/27th of a circle, or 13 degrees and 20’. Since a sidereal month has about 27 days in it, you would see the moon move from one nakshatra to the next every day. For this reason, in English the nakshatra are often translated as “lunar mansions” since they appear to be where the Moon lives. The nakshatra differ from the signs of the zodiac in one way, though, which is that the signs of the zodiac correspond to constellations that are in fact quite close to the ecliptic. But in the case of the nakshatra, the corresponding stars or asterisms can sometimes be somewhat farther away. One of the nakshatra, for instance, is called Nishtya or Svati and corresponds to Arcturus, which is more than 30 degrees away from the ecliptic. But most of them are closer. Punarvasu, for instance, corresponds to Castor and Pollux in Gemini, Pushya corresponds to the Beehive Cluster in Cancer, Citra corresponds to Spica in Virgo, and Jyeshtha corresponds to Antares, along with two nearby stars in Scorpius. You might not be surprised to learn that the Pleiades star cluster is also a nakshatra, called Krittika, and as with every culture the world over Hindu tradition has a story to explain this asterism. The story goes like this. Once upon a time the God Prajapati fell in love with his own daughter Rohini and desired her. Lord Prajapati took the form of an antelope and chased her. Rohini, then, took the form of a deer to run away from her father. The gods became outraged at Prajapati’s actions and demanded that the god Rudra put an end to it. So Rudra took the form of a hunter and shot Prajapati with an arrow. The head of the antelope pierced by an arrow became the Pleiades. Incidentally, you may recall from episode 28 on paleolithic astronomy that most cultures around the world traditionally identify seven stars in the Pleiades with a substantial minority identifying six. India, as it happens, is a mix of both, with some traditions identifying seven stars in Krittika and others six.

Now I mentioned earlier that the nakshatra are a set of 27 or 28 locations along the ecliptic — so which is it? Well, originally there were 27 nakshatras, but later on some texts start to mention an extra 28th nakshatra called Abhijit, which consists of 3 stars in the center of Lyra. What motivated the introduction of this extra nakshatra is somewhat obscure, but because the sidereal month has 27.3 days, 27 nakshatras is somewhat too few, and the extra nakshatra may have been added to compensate, although the resulting 28 has the opposite problem of being somewhat too many.

Well, that in broad strokes is the most of the contents of the Jyotisha. The text is not incredibly long, there are only 36 verses in one recension, and 44 in the other, so it is necessarily a fairly compact text. But it was not the only text of its period to deal with astronomy, even if it was the most explicit. From some of these other texts we can glean some details about early Hindu cosmology.

The structure of the universe is divided into three regions: the lowest is “prthivi,” or the Earth; above it is “antariksha,” or the Firmament; and the uppermost region is “dyaus,” or Heaven. Each of these three regions is in turn divided into three subregions. In the Pancavimsa Brahmana we read:

Through fire, earth, and plants, thereby this world is threefold; through wind, intermediate region, and birds, thereby that world is threefold, which stands between; through sun, sky, and stars, thereby yonder world is threefold.

In this cosmology, the Sun exists in the heavens and illuminates all regions of the universe. By causing the alternation of day and night, the Sun is in a sense the creator of time itself, as well as the cause of winds and floods. One detail in the Rigveda indicates that the early Hindu astronomers understood that sunlight was composed of multiple colors and that in particular there were seven distinct colors in the Sun’s spectrum.

Now, the shape of the Earth in early Indian cosmology is somewhat ambiguous. Probably in the earliest days it was considered to be flat. The text Aitareya Brahmana states that the sun “neither sets nor rises… It only changes about and in the process makes night below and day on the other side.” There are a couple of ways that we can interpret this. Probably the original meaning was that the Earth was a flat disc, and when it was day on our side, it was night on the opposite, and when it was night on our side, it was day on the other. Other verses seem to indicate that the Earth is suspended freely in air, but of course this picture is compatible with either a flat or spherical Earth. Either way, when the astronomy of the Greeks was introduced later on, the Greek model of a spherical Earth found quick acceptance.

Indian astronomy also had a correct explanation for the Moon’s light and motion quite early on. We see in some of the early texts that the Moon does not have any light of its own and instead reflects “the brilliancy of the Sun.” One text describes it poetically as “adorned with Surya’s arrowy beam.” The Satapatha Brahmana also has a description of the Moon’s changes over the course of the month:

Now the one that burns there [the Sun] is, assuredly, no other than Indra, and that moon is no other than Vrtra. But the former is of a nature hostile to the latter, and for this reason, though this one had previously risen at a great distance from him, he now swims toward him and enters into his open mouth. Having swallowed him, he rises; and that one [the Moon] is not seen either in the east or in the west… Having sucked him empty, he throws him out; and the latter, thus sucked out, is seen in the western sky, and again increases; he again increases to serve the Sun as food.

So in this picture we see that the early Indian astronomers recognized the general west-to-east motion of the Moon over the course of the month, along with an explanation of the Moon’s phases that they are caused by the Sun.

Well, the Vedic literature also indicates that early on Indian astronomers had made note of solar eclipses. One description comes in the Pancavimsa Brahmana:

The demonic Svarbhanu struck the sun with darkness; the Gods did not discern it (the sun hidden as it was by darkness); they resorted to [the sage] Atri; Atri repelled its darkness by [his prayers]. The part of the darkness he first repelled became a black sheep, what he repelled the second time became a silvery sheep, what he repelled the third time became a reddish one, and with an arrow he set free its original appearance, that was a white sheep.

What makes this description of a solar eclipse particularly interesting is that it does not merely say that the eclipse happened as we see, for instance, in the early Greek references, but it actually correctly describes the progression of colors that the Sun is perceived to have over the course of the eclipse, from white, to red, to silver, and lastly turning black.

This description has another typical feature, which is that the sage Atri is mentioned in connection with the eclipse. This turns out to be rather common in the early descriptions of eclipses, and due to Atri’s priesthood, probably indicates that from an early time astronomy was considered to be within the purview of the Brahmanic priesthood.

Somewhat later on, we also find that Hindu astronomy develops a correct explanation for the cause of the eclipses, called “rahu and ketu.” Originally these terms, “rahu” and “ketu” had different meanings. Ketu was associated with astronomy, but simply meant some unusual transient celestial phenomenon like a comet or a meteor, and “Rahu” seems to have meant “planet,” though in other contexts it seems to have had no astronomical meaning at all. But later on, these two terms come to refer to the two nodes of the Moon’s orbit, where the orbit of the moon crosses the ecliptic on the sky. A solar or lunar eclipse can only occur if a full moon or new moon takes place as the moon is passing through one of these two nodes. The later texts make clear that the Indian astronomers understood that this was happening during an eclipse. This explanation of eclipses later traveled to China and the terms appear in the text Chiu Chih.

Well, at least in the oldest Indian astronomy, the planets play very little role. The Jyotisha does not mention them at all, although there are possibly a few oblique references to the planets in the Vedas. The 7 Adityas in the Rigveda have been interpreted to be the Sun, Moon, and five planets. Another possible reference is in Hymn 55 of Book 10 of the Rigveda. The god Indra looks around him and sees 34 lights, and this number 34 has been interpreted to mean the 27 nakshatras, the Sun, the Moon, and the five planets. But in the early literature that is about the extent of any description of the planets. And likewise, beyond the 27 or 28 nakshatras, which mostly are around the ecliptic, we don’t find any references to any other constellations in the sky.

Well, before we leave the earliest Indian astronomy behind us, I wanted to say a few words about a kind of parallel astronomy in the region, the astronomy of the Jains. Jainism is a minority religion in India whose origins are somewhat unclear, but is certainly very, very old. It may have been an early offshoot of proto-Hinduism and may have also originated in certain practices from elsewhere like Persia. But it definitely became a distinct religious tradition by around 400 BC during the late Vedic period.

Probably the most distinctive practice of Jains to outsiders is the nonviolence that adherents practice, which extends to all living things and leads to rather strict dietary practices. These dietary practices are vegetarian, though they do permit the consumption of milk as long as the cow was treated humanely. But unlike Western veganism, the prohibition on killing living things that many Jains practice extends to plants and microbes as well, so tubers and root vegetables are also not eaten since harvesting them kills the plants, as well as microorganisms in the ground. Historically, the religious practices of the Jains left them with a relatively narrow set of options for employment. Not being Hindi they obviously could not be Brahmans. They also could not be warriors due to their non-violence. And the dietary restrictions also made farming impractical. Consequently they tended to work as merchants and ended up a rather wealthy class in Indian society.

But for our purposes, the Jains had a rather distinct cosmology, which is mostly described in a text called the Suryaprajnapti, written probably around 300–200 BC. In Jainist cosmology, the Earth is eternal and was never created. One text, the Mahapurana, is quite adamant says:

Some foolish men declare that a creator made the world. The doctrine that the world was created is ill advised and should be rejected. If God created the world, where was he before the creation? If you say he was transcendent then and needed no support, where is he now? How could God have made this world without any raw material? If you say that he made this first, and then the world, you are faced with an endless regression.

The Earth was described as being a series of flat concentric rings of land, each surrounded by a concentric ring of ocean. Going from the inside out, the central circle is called Jambudvipa and has a mountain called Sadarsa Meru in the center. Jambudvipa was then surrounded by a salt ocean. Next, there is a ring of land called the Dhatuki Dvipa, which is surrounded by the black ocean Kalodadhi. Then there is another ring of land called the Pushkara Dvipa, which is finally surrounded by an impassable mountain range called Manushottara Parvata. In this geography, India itself was in the southern portion of the central circle of land.

The most unique feature of Jainist cosmology is that it holds that the celestial bodies come in pairs — that there are, in fact, two suns, two moons, and two sets of stars. The reason for this is that the Earth is divided into quarters. India, for instance, is in the southern quarter of Jambudvipa, but there is an eastern quarter, a western quarter, and a northern quarter. Above the Earth, the Sun, moon, and stars revolve in a circle parallel to the Earth about the central mountain. But there is clearly a problem here. There are four quarters to the Earth, and the Sun obviously passes through one quarter in 12 hours since the day is 12 hours long. But then how does the Sun rise 12 hours later the next morning? If the Sun set in the southern quarter, after 12 hours of night it would be just entering the northern quarter, and it would still be another 24 hours before the Sun returned to the southern quarter. So the Jains posited that there were, in fact, two Suns, 180 degrees apart from each other. That way, 12 hours after sunset, even though that Sun would now be entering the northern quarter, the other Sun on the opposite side would be entering the southern quarter and there would be a sunrise the following day right on schedule. To keep the whole sky looking the same, there was likewise a second Moon, and a second set of stars, all 180 degrees opposite their counterparts.

Well, with that we will leave early Indian astronomy behind us. But we are not done with India yet. Next month we will look at later Indian astronomy, during the Babylonian and Greek periods, and hear about some of the great Indian astronomers whose names survive to us, in particular, the great Aryabhata, one of the greatest astronomers that India produced. I hope you’ll join me then. Until the next full moon, or thereabouts, good night, and clear skies.

Additional references

  • Rao, Indian Astronomy
  • Kak, Birth and Early Development of Indian Astronomy
  • Ghosh, Descriptive Archaeoastronomy and Ancient Indian Chronology
  • Subbarayappa, A Concise History of Science in India