Astronomy Seminar 1
At first glance, the cosmology described in the Bhagavata Purana may appear to be a mythical narration. Thompson helps demystify the account while simultaneously examining complementary treatises such as the Surya-siddhanta, which offer complex details of empirically verifiable astronomical data from a geocentric perspective. He illustrates how the accounts offered in both the Surya-siddhanta and Srimad-Bhagavatam mirror one another, albeit using different frames of reference.
TRANSCRIPT: Astronomy Seminar 1. VIHE Seminar: Gita Nagari - 1990 / (205)
I’m going to speak initially about the material in the first chapter. Basically there are two principal subdivisions of Vedic astronomy and cosmology that are important. One is called Jyotiṣa Śāstra and the other is what we call Purāṇic cosmology. So the Fifth Canto of the Śrīmad-Bhāgavatam is an example of Purāṇic cosmology. In other Purāṇas you find similar accounts. Basically the Bhāgavatam is giving an account of the structure of the universe and, so that’s something you’ll also see in other Purāṇas. Then there’s the Jyotiṣa Śāstra as it’s called. This is a body of literature which deals with the motion of the planets as seen by an observer on the earth. So it’s also connected with cosmology. Cosmology means your theoretical framework for understanding the universe – your idea of where things are and how they’re situated. So the Jyotiṣa Śāstra has a cosmology, but primarily it’s a system of mathematical calculations used to determine where the planets are located in the sky at any given time. With these calculations you can also determine when eclipses of the sun and moon will occur. You can determine when a planet will be in conjunction, that is when they come to the same location in the sky, and so on.
So all these different calculations can be performed. So in order to understand the Fifth Canto, the proposal that I am making in this book is that you also have to understand the Jyotiṣa Śāstra, because Jyotiṣa Śāstra and the Fifth Canto fit together as part of one unified tradition. So one has to understand everything together. So the first point that I want to do then is cover, basically, some of the material in this first chapter.
The first chapter gives an introduction to the Sūrya-siddhānta and the Jyotiṣa Śāstra in general. There are different categories of writings in this area of Jyotiṣa Śāstra. One main category is called the Siddhāntas. Siddhāntas are basically textbooks of mathematical astronomy. They’re written in Sanskrit. So I have here the Sūrya-siddhānta – just an example of the kind of thing you can get in the library. This particular volume is the Sūrya-siddhānta with a commentary by an astronomer, an Indian astronomer with the name Parameśvara, and his commentary was written, they think, about in the early 1400’s. So there are different manuscripts of different ages going back to about 1100 as far as they can trace them. But the work itself is quite an ancient work. So the first question in considering the Sūrya-siddhānta and other similar works has to do with the question of their authenticity as far as our paramparā system is concerned. So I started this chapter with some information in that regard, and I’ll briefly cover that. The main point to make there is that Śrīla Bhaktisiddānta Sarasvatī, when he was a young man, was very much involved in Vedic astronomy. I list here a series of works that he produced in that area. He actually published two magazines in Bengali and in those magazines, I guess in serial form, he published quite a number of different works. So we have here “Bengali translation and explanation of Bhāskarācārya Siddhānta-śiromaṇi Goladhyaya with Basanabhasya.” Well Bhāskarācārya is a famous Indian astronomer who lived around 1100 AD, or that period. And the Siddhānta-śiromaṇi is one of the main Jyotiṣa Śāstras.
One point about these literatures is that many of them are written by historical astronomers in fairly recent times, for example this Bhāskarācārya, who lived in the 1100’s. Another example would be Āryabhaṭa; he’s a very famous Indian astronomer. He lived in the 6th century AD. Most of those for whom we have dates at all are within the medieval period – that is after the time of Christ. So another example, there’s a whole series: Bengali translation of Ravichandrasayanapashta, Laghujataj, with annotation of Bhaṭṭopala. So there’s a whole series of works. Actually Śrīla Bhaktisiddānta Sarasvatī was extremely prolific in translating and commenting on these various astronomical works, and he was considered to be a very great expert in astronomy at that time. Of course he was a very young man at that time. I think he was hardly 20 years old. An indication of what he was trying to accomplish is given in a brief summary of his writings. Let’s see, where is that, oh yeah, it says here,
In 1897 he opened a ”Tol” [it’s kind of school], named Saraswata Chatuspati in Manicktola Street for teaching Hindu Astronomy nicely calculated independently of Greek and other European astronomical findings and calculations.
So that gives an idea of what he was trying to accomplish with this because there was a tendency to try to introduce the European scientific system of astronomy. In fact, many Indians, even Vaiṣṇavas, were proposing that should be done because European astronomy was better – it was more scientific. So evidently Bhaktisiddānta Sarasvatī was stressing the value of the traditional astronomical system. So another interesting point is that the title "Bhaktisiddānta Sarasvatī" is based on the Sūrya-siddhānta. Śrīla Prabhupāda states this in a purport in the Caitanya-caritāmṛta. So I’ll briefly read this as it introduces the Sūrya-siddhānta:
These calculations are given in the authentic astronomy book known as the Sūrya-siddhānta. This book was compiled by the great professor of astronomy and mathematics Bimal Prasād Datta, later known as Bhaktisiddhānta Sarasvatī Gosvāmī, who was our merciful spiritual master. He was honored with the title Siddhānta Sarasvatī for writing Sūrya-siddhānta, and the title Gosvāmī Mahārāja was added when he accepted sannyāsa, the renounced order of life.
So that’s in the purport to Ādi-līlā 1.3.8.
So of course the point has been made that Bhaktisiddānta Sarasvatī did not continue to publish works on astronomy after he began his preaching mission, which became the Gaudiya Math. However, he did refer to these works in his different writings, and in fact I checked into this. Bhaktisiddhānta Sarasvatī wrote a commentary on the Caitanya-caritāmṛta. So the different references that Śrīla Prabhupāda gives to the Sūrya-siddhānta and the Siddhānta-śiromaṇi, at least as far as I am aware, are all on the Caitanya-caritāmṛta. And I checked, in each case where Śrīla Prabhupāda gives such a reference, Bhaktisiddānta Sarasvatī made some reference to the Sūrya-siddhānta or the Siddhānta-śiromaṇi in his commentary. And in fact he cited these works just as he would cite anything else, just as authorities. So that is, gives an idea to the status of these particular works, the Sūrya-siddhānta and the Siddhānta-śiromaṇi.
So at the same time, it should be stressed that these works do not have the same status, as for example, the Śrīmad-Bhāgavatam. Of course the Śrīmad-Bhāgavatam is known as Amala Purāṇa; it’s said to be the spotless Purāṇa. That implies that even some other Purāṇas have spots. In fact, we know that there are Purāṇas in the modes of goodness, passion, and ignorance. So that means that there is Puranic literature that is under the modes of material nature, whereas the Śrīmad-Bhāgavatam is not. As for the Jyotiṣa Śāstra, one cannot say that the Jyotiṣa Śāstra is perfect. In fact the Jyotiṣa Śāstra is subject to change with time. In the very introduction of the Sūrya-siddhānta that is openly stated. It is stated there that if the description of astronomy given here differs from what was described in the earlier works, it is due to the changes wrought by the passage of time. So that is actually stated in the text and, in fact, Bhaktisiddānta Sarasvatī himself was involved in changing the Sūrya-siddhānta. He was, in his Bengali translation... I should point out by the way, in the section that I just quoted, Śrīla Prabhupāda said that he wrote the Sūrya-siddhānta. I should clarify that – he translated it into Bengali with some commentary. The Sūrya-siddhānta is a very old Sanskrit work. So included in his translation there was a set of bija corrections. Now I’ll explain what those are. The word the word bija of course means seeds. So these astronomical systems in the Jyotiṣa Śāstra...
Answer: Yeah if someone could help them... [some commotion] These bija corrections are small quantities which are inserted into the calculations in order to make them more accurate, in agreement with observations. So I don’t know how Śrīla Bhaktisiddānta Sarasvatī arrived at a particular bija correction that he listed in his translation, but it’s clear that this was a standard practice. In other words, these astronomical systems are not meant to be perfect. In fact, the general understanding of the universe in the Vedic literature is that as a whole the universe is beyond human comprehension. In the very beginning of the Fifth Canto of the Bhāgavatam, Śukadeva Gosvāmī states that in very clear terms. And actually I have his statement in about three different places in this book. But he says that, you see Mahārāja Parīkṣit asked him to describe the universe – of course as it relates with the pastimes of Kṛṣṇa – and Śukadeva Gosvāmī says that “even if I could spend an entire lifetime describing the mysteries of the universe still you would not fully understand it, so I’ll just give you a very brief description.” So the basic idea in the Vedic literature is that the universe is difficult to fully describe. In fact, it's not possible to do that.
So therefore in these Vedic astronomical calculations a practical approach is taken. These are definitely approximate calculations. However, they’re designed so that you can perform these calculations by hand. This is an important point when we consider any comparison of Vedic astronomy with modern astronomy because someone will make the mistake of, “Well, modern astronomy is much more accurate than Vedic astronomy; therefore it’s vastly superior, more scientific.” However this criticism misses the real point of the Vedic astronomy. Vedic astronomy is a practical system so that any person can sit down and do all the calculations himself, without need of computers or anything like that. Actually in preparing this book, I acquired some experience with the complexities of modern astronomical calculations. We acquired some computer programs for modern astronomy because we did a comparative study of Vedic astronomy, modern astronomy, and also Greek astronomy, which is another whole subject which we’ll be talking about. So to describe the motion of a planet such as Mars, let’s say, with modern astronomy you have to type in about three solid pages of numbers. If you can imagine 3 pages with nothing but solid numbers, you know, many numbers, each of which will have about 15 decimal places or so. In fact, it’s rather difficult to type them all into the computer and get them right. That alone was quite a task. And then the calculations performed with these numbers are rather complicated – there are all kinds of sines and cosines and so forth. And you really need a computer to do these calculations. I’d hate to think of trying to do them by hand.
But the calculations in the Sūrya-siddhānta are much simpler. Nonetheless they’re fairly complicated. The Sūrya-siddhānta calculations also involve 15 digit numbers and you have to multiply and divide them and so forth. But it’s actually something that you can handle by hand. It’s interesting that when some of the first European astronomers went to India, this happened in the early 1700’s, there was one European astronomer who went to South India to observe an eclipse of the sun which was due to occur there. So he noted that there were people there who could calculate in advance that that eclipse of the sun was going to occur, simply by sitting down on the ground and manipulating little shells. They didn’t even have anything written on paper. So, actually you know the word calculate, calculus originally means stone. And calculation originally meant moving stones around. The stones represented numbers. So in this case these people were using shells. So they would just sit and maneuver the shells around and in this way do calculations. They had memorized all the different numbers that you had to know, the astronomical constants. And in this way they could calculate that an eclipse of the sun would occur on a certain date, and they had the right answer also. So it was a fairly impressive performance because however accurate Western astronomy may be, I don’t think there’s anyone who can do that with it, in other words, sit down and do that kind of calculation. So the main point then is that the calculations in the Sūrya-siddhānta are approximate and they tend to become more and more inaccurate with the passage of time. So in the course of history the procedure has been that when they become inaccurate to a certain point, then they’re corrected. So how do you correct them? Well the indication is that this is done using observation.
A: Yes, how do you correct them?
So the cover of this book has an observatory. This particular observatory was in Benares. I don’t know if it still exists. This drawing was made by some early British adventurers about 200 years ago. So these, apparently there have been quite a number of observatories in recent years of this basic type in India. There’s one in Jaipur I believe and there’s also one in New Delhi which I’ve actually seen, although I didn’t get to go in. But you can see it from the roadside. These observatories consist of very large structures like this thing on the cover, I believe – I don’t know because there’s no text to describe it – but it’s a device for measuring the position of the sun. On this slanted staircase they would arrange a bar of some kind that would cast a shadow on this curved arrangement, and then they would measure accurately where the shadow fell. And in this way they would be measuring the position of the sun. And then on the back, this circular thing, well there are various instruments here, no description exactly what they all do, but they are for measuring the position of the sun, the moon, and all the different planets. So periodically the Vedic astronomy was updated. So that’s a basic description.
Now the next point that I’d like to discuss is: How does the Vedic astronomy view the universe? What is the basic picture that it has? Well, the first point is that the Sūrya-siddhānta and these other astronomical works are geocentric as opposed to heliocentric. So the heliocentric system is the modern system for the sun, moon, and planets. The basic idea is that the sun is fixed in one place and the different planets including the earth orbit around the sun, with the exception of the moons, which orbit around their respective planets. And of course the earth has one moon. So that’s the heliocentric system. Now the geocentric system maintains that the earth is in the center and the sun and different planets and the moon orbit around the earth. So the Sūrya-siddhānta is geocentric. And in fact, Vedic cosmology in general is geocentric. So I want to say a little bit about heliocentric and geocentric systems because that’s of course a very important issue.
Q: Is that a concept that is established because that’s the way it is? Or as a method or system for calculation?
A: Well it’s interesting – there’s a historical controversy behind that. You can look at it both ways. You can say: Well, it’s a practical system of calculation on the one hand. In fact, I understand that the US Navy still uses a geocentric system of astronomy, because if your interest is in moving ships around then you’re concerned with how things are moving with respect to the earth, which you view as fixed. Because then you can use the positions of planets and the sun and the moon and so forth for navigation. If you know where they are with respect to the earth and you see where they are from your ship, then you know where your ship is. So they are using that as a system of calculation.
When the heliocentric theory was first introduced in Europe by Copernicus and so forth, there was controversy as to whether this is just a system of calculation or whether this describes reality. So Galileo claimed: Well, this describes reality. But then there were people in the Church who didn’t like that because they were dedicated to the Ptolemaic system. Ptolemy was a Greek astronomer, in fact, practically the Greek astronomer that is really known historically, and he also had a geocentric system of astronomy which was used in Europe up to the time of Galileo and so forth. So the Catholic Church had adopted that system. And so when Galileo began presenting the heliocentric system it was going against Church authority. So there was that famous trial in which they put him under arrest and so forth, and they were arguing that: Well, it’s alright to have a heliocentric system as long as you say that that’s just a system of calculation, but you’re not trying to say that it represents reality. So one point that I’m going to discuss a bit further today is that you can view the question of heliocentric versus geocentric from the point of view of relativity. That is that you can say these are 2 different relative ways of looking at the same thing. Now modern scientists will say that the solar system is definitely really heliocentric, not geocentric, and the Vedic system is essentially geocentric. So there is a difference there and there’ll be a lot to say about that, and that’s the basic situation.
Q: Why did it become a religious issue, when it’s not really described in the Bible?
A: Well it’s not described in the Bible. It became a religious issue because the Church had placed its authority behind that system and the Church was regarded as infallible. So if they put their authority behind a faulty system that meant they really weren’t infallible, so that was a very serious issue. That’s the whole issue of science versus religion. Traditionally in the middle ages the idea was that the Church is infallible, but then the scientists came along and kept showing again and again that there were doctrines supported by Church authority that turned out to be wrong; and so gradually they eroded people’s confidence in the church. So that’s the basic crisis in religion versus science in the modern world. Now we’re concerned with the same issue ourselves. In our case, right in the scriptures that we follow, primarily the Śrīmad-Bhāgavatam, there’re all kinds of descriptions of the universe – they’re right there. So if they are wrong then what becomes of Kṛṣṇa consciousness? It loses its authority. If the Bhāgavatam is wrong about the tangible physical features of the universe that at least potentially are within reach of our senses, then why should we think that it’s right about transcendental topics that are beyond the realm of our senses? This is the thinking
A: Yeah, why did they get into it in the first place?
Well, of course, they got into it as a matter of gradual development of historical tradition. It must be said though that the Bible gives a geocentric picture of the universe. I once read a book by a Christian on the subject. I was looking into the whole issue of geocentric versus heliocentric, and it’s interesting that there are a couple of Christians even today who are writing books defending the geocentric system. And so they gave arguments from the Bible as to why you should do that, and made a pretty good case as far as I could see. And they had all kinds of quotes. They made a number of interesting points; for example, one thing I never realized was that the Michelson-Morley experiment indicated that the universe must be geocentric. I never had any idea that that was so, but this fellow explained it. Maybe I can discuss that later on. But in any case the history of it is that the, well I’ll go into details later, I better continue with the present topic. Yes, so this whole issue of heliocentric versus geocentric is going to be essential in all these different considerations. So to go further, what I wanted to do was begin discussing some of the specific details of the Sūrya-siddhānta. And to do that I have to introduce some elementary concepts concerning astronomy. So I asked for this globe to be provided – here it is – this is the demonstration for today. So here we have a globe.
One point to make is that the Sūrya-siddhānta presents the earth as a globe. That’s important; it’s definitely a globe. And the Sūrya-siddhānta gives the diameter of the earth. The diameter is given as 1600 yojanas. Now this unit of measure, the yojana, is interesting. It’s somewhat variable in length and there are various definitions of it. Basically there are two categories of definitions. One is that there is sort of simple practical definitions. For example, there is a unit called the hasta – that’s a cubit from what I understand – goes from your elbow to the tip of your fingers. So a certain number of hastas is defined as one yojana. So that’s one definition. I think it was 3000 or something like that. So this of course gives you a variable measure, because whose forearm are you going to use? People have different lengths of arms.
A: Well that’s an interesting point. To be more exact, the arm of the yajña māna was used. There is actually a description of this. If a person was going to perform a sacrifice and he was financing the sacrifice – typically it would be the king – then the length of the yojana used in that sacrifice, and the length of the hasta and so forth, was of his arm. After all, he was the one financing the sacrifice. So this was the method. There are other definitions. Another definition is that a yojana is four crosa and a crosa – that’s a shout – a crosa is defined as the distance that a person with good hearing can hear the shout of a person with good lung power, barring wind and other things that might . . .
Right, a crosa is two miles and that gives you a yojana of about 8 miles. But again that’s somewhat variable. Now the astronomers are not satisfied with something like that. They need something more precise. So there are, as far as I’m aware, two standards for the length of the yojana in the different Jyotiṣa Śāstras, and this is mentioned by the one commentator named Parameśvara. Actually he’s the same commentator who wrote the commentary on the Sūrya-siddhānta that I have here. So he points out that there are two standards and you can see that they’re followed in different texts; and to understand that, if you take a text using one standard and take the measure of something, let’s say the diameter of the earth and divide that by the diameter of the earth in the text following the other standard, you always get the same ratio whether you use the diameter of the earth or the distance to the moon or whatever. So there are two different standards and in the Sūrya-siddhānta the standard turns out to be 5 miles for the yojana. I’m going to go into actual measurements of distance later on. But this gives you a diameter for the earth which is quite accurate in modern terms. So there is a clear understanding that the earth is a globe and a clear understanding of how big it is. So if you start with the idea that the earth is a globe, an important concept in astronomy is the concept of what is called the celestial sphere.
Now here’s what the celestial sphere is. Imagine taking this globe and taking another sphere centered on the center of this globe but it has a much larger radius, many many times the radius of the globe. But imagine putting on that sphere the same lines of latitude and longitude that you have on the globe. So that sphere is called the celestial sphere. Now you can imagine if we’re standing on the earth in this enormous sphere centered on the center of the earth and extended out into space, we will see the sun, the moon, and the stars and the planets against the background of that sphere. So all of these different celestial objects will be projected against a coordinate system of latitude and longitude, because we just take the latitude and longitude on the globe and projecte it out. So in particular, there’s the celestial equator, which is just a projection of the equator of the earth, and there’s the celestial North and South Poles. Now in fact it turns out that there’s a prominent star located at the north celestial pole and that’s called the polestar. So the experience we have is that the heavens rotate once per day. That’s seen from the point of view of the earth as stationary. Of course the modern idea is that the earth is rotating and the heavens are stationary. But you can see that from a relative point of view you can say that the earth is stationary and that heavens are rotating.
In any case, the point of view in the Vedic literature is that the heavens are rotating. So the rotation, the daily rotation of the heavens, is called the kāla-cakra, it’s called the wheel of time. So what you can imagine then is that this celestial sphere is rotating. So the grid of latitude and longitude lines projected out into space is fixed relative to the stars. That’s the way the celestial sphere is set up. So that means that it’s not fixed relative to the planets and the sun and the moon. They move against the background of the fixed stars and thus they move against the background of this coordinate system which is projected out on the celestial sphere. So this coordinate system is the basic system for measuring the position of the planets and of the sun and the moon. Actually, in Vedic terms the sun and the moon are also called planets. By the way, in Śrīla Prabhupāda’s books generally the word loka is used, is translated as planet. However, there’s another word which applies to Venus, Mars. Jupiter and so forth, and this is graha. A graha, from what I understand, originally it means something that grabs you. That refers to astrological influence. That’s the etymology from what I can understand. They’re also called – apart from the sun and the moon – Mercury, Venus, Mars, Jupiter and Saturn are called tārā graha which means star-planets, because they look like stars to the naked eye. So in initially thinking about this idea of the celestial sphere as rotating once per day, one can look at it in terms of the idea of relative motion.
It’s a perfectly valid way of looking at it; you can say that, after all, that is what we experience. If you were to take a camera (in fact sometimes people do this) and open the shutter and have film adjusted for a long-time exposure aimed at the polestar, then you can have an exposure that would last all night let’s say. And you would see that the polestar was the fixed point of light and all the other stars formed arcs going around the polestar. So the whole sky is rotating. So this coordinate grid is a fixed reference point and that’s used in the Sūrya-siddhānta as the reference grid for measuring where the planets are located. So just as a point on the earth is measured in terms of latitude and longitude on the earth, the position of the planet is measured in terms of celestial latitude and longitude on the celestial sphere. So all the calculations in the Sūrya-siddhānta are based on this grid of celestial latitude and longitude.
Now to measure longitude on the globe, you have to have a zero point where you start; and in the modern system that is called the prime meridian and it runs through Greenwich in England. You can see it’s on the globe here – it’s marked with a heavy line. So latitude is measured, I mean longitude is measured from this, starting at zero. So on the celestial sphere there also has to be zero point for measuring longitude. And a particular star is chosen for that. This is the star that in Sanskrit is called Revatī and in Western terms is called Zeta Piscium. So that’s the particular starting point for measuring where the planets are located. And then there’s latitude, which measures how far up or down you go relative to the celestial equator.
Q: Western astronomy and the Jyotiṣa use the same star as the zero longitude?
A: No, in Western astronomy there’s a different system. Western astronomy doesn’t use a star as zero point. Instead Western astronomy uses a point called the vernal equinox. So basically to explain what that is, as you know, well to explain that properly I should first go into the next thing I was going to discuss and that is the path of the sun. Now this may seem to be a little bit like technical astronomical knowledge of questionable importance, but actually to understand the Fifth Canto it’s essential to understand how the movement of the sun is described in astronomical terms and in particular how it’s described in the Jyotiṣa Śāstras. Because if you can understand that, then it becomes easy to understand what the Fifth Canto is saying. So this is all introductory material which will lead up to the discussion of the Fifth Canto. So the sun follows a path against the background of the fixed stars. Of course the sun goes around once per day – that’s how we define days and nights, by the motion of the sun.
However, the sun does not move in the same way that the stars are moving. A given star will rise and set and then rise again in the course of 24 hours roughly, and the sun will also do that. But in the course of the day the sun moves slightly with respect to the stars. In fact, it moves by approximately 1 degree of arc against this background of the stars, and that means against this grid of latitude and longitude lines on the celestial sphere. So the sun moves on a particular path through the constellations. It goes around through the entire celestial sphere all the way around and returns to its starting point in one year. In fact, that’s the definition of a year, or solar year. So the path that the sun follows is called the ecliptic. That’s the technical term. And I’d like to say a little bit about what that path is. I think I have an illustration in the book showing how the path goes through certain constellations. I just put that in there, where is that illustration?
Q: It’s not in the book?
A: As a matter of fact, it is drawn on the globe. Well, that’s good. This globe has it. Although you may not be able to see it so well here. But here it is. It’s a path that moves along, and goes up like this, goes down; the basic point to make about it is that it’s tilted with respect to the equator. The ecliptic is what’s called the great circle, that’s another...
Comment: It's page 58.
A: Yeah, you can look on page 58 for an illustration of the celestial sphere in the book, that also shows the ecliptic. There you see the earth in the center and the large sphere around is called the celestial sphere. So you can see the equator ,which is obtained by projecting out the earth’s equator, and then you see this band here which is circular, which is called the ecliptic. So this band is tilted at 23½ degrees to the celestial equator, and the result of that is that in the course of the year the sun first moves toward the North, let’s say. Gradually it goes up towards the top of the northern part of this path. When it reaches the northernmost point, that’s what’s called the summer solstice, which occurs late in June. And that’s the time when the days are longest and the nights are shortest. And then continuing along on the same path it gradually moves towards the South. When it crosses the equator, that’s the point called the equinox. And there are two points when it crosses the equator in the spring and the fall. So when it crosses the equator the length day is equal to the length of the night. Then it continues going south until it reaches the southernmost point, which is the winter solstice, and then comes back up north again. So this is the answer to the question of how in Western astronomy the longitudes are measured. In Western astronomy the vernal equinox is taken as the zero point. Whereas in Vedic astronomy a fixed star start is taken as the zero point. That leads to a whole discussion of what’s called the precession of the equinox; that is another issue which has to be dealt with when talking about Vedic astronomy versus Western astronomy. But I won’t go into that now.
So this basic description of the celestial sphere is essentially geocentric in its orientation. That is, the whole thing is presented from the point of view of how things look from the earth, and the celestial sphere is something that’s traditional in both the West and in India. In the Sūrya-siddhānta and in many other Jyotiṣa Śāstras there are instructions for building a celestial sphere as a model. And in medieval Europe people also used to build them. This is a picture of a more modern one that has been built. Nowadays these things tend to be out of fashion because in our modern age the solar system has become sort of passé. No one cares much about it now because galaxies and quasars are supposedly the interesting things in astronomy. But so, I’ll continue in this account. But what I wanted to do was convey an idea of the content of the Sūrya-siddhānta. So the first thing I wanted to discuss is the periods of revolution of the planets. The Sūrya-siddhānta starts out by giving this information. So what you find in the Sūrya-siddhānta are very large numbers giving the number of the revolutions that a given planet will make in the course of one catur-yuga. So a catur-yuga consists of the four yugas and that lasts 4,320,000 years. So in the Jyotiṣa Śāstras generally, all different quantities describing the motion of the planets are given in terms of how much the planet moves in one yuga cycle. So you get very large numbers. So let’s see here.
I believe I have one table just to give an example. In a yuga cycle there are 57,753,336 revolutions of the moon. That’s just one example of how these numbers are presented. So from... this is in the table on page 13. So it turns out that these numbers are quite accurate. And in this Table 3 on page 13 there’s a comparison of the period of orbit of the different planets given in the Sūrya-siddhānta and in modern Western astronomy. In order to make this comparison what you want to do is to express the time it takes for the planet to go through one orbit in days, because that’s how it's expressed in modern text books. And you can do that by taking the Sūrya-siddhānta value for the number of revolutions in one yuga cycle and then you divide that into the number of days in one yuga cycle and that gives you the number of days for one orbital period. So the point is that these are quite accurate figures.
So I’d like to make one slight digression here, now turning to the Fifth Canto of the Bhāgavatam. This is discussed later in the book but I thought I’d bring it out right now. A Parivatsara is a year – it’s a very interesting thing. The Śrīmad-Bhāgavatam uses a year of 360 days. Now one might say, “Well, that’s certainly strange, because there are 365¼ days in a year. In fact you can put that out to more decimal spaces. So how is it the Bhāgavatam has a year of 360 days?” Well it turns out that the Bhāgavatam also has an understanding of the year of 365 days, but the Bhāgavatam expresses things somewhat differently. So it uses a day count for a year of 360 days and you can see that consistently throughout the Bhāgavatam. So what that means then is understanding this, and there are different names for the year: Vatsura, Parivatsura, Anuvatsura, and so on. These are different names for a year for 360 days.
Actually there is a cycle of five 360-day years that repeats itself, which is used in the Bhāgavatam. So that would mean that the number of days for Jupiter to make one orbit would be 12 x 360 – that comes out to 4320 days. Well the modern figure is 4332.587. Interesting thing there is that differs from the Bhāgavatam figure then by .29%. In other words, it’s extremely close and yet it’s expressed in the Bhāgavatam just by saying one sign per Parivatsura. So that’s kind of interesting, that they can express something that comes in 0.29% of the modern value with a simple little phase like that. But then the Bhāgavatam does it again with Saturn. It says that, let’s see, I wrote down the thing for Saturn here. Yeah, yes Saturn makes one orbit in 30 Anuvatsuras. So what that tells you is that Saturn is going to make one complete orbit in 10,800 days. Actually that number 108 comes in there. That’s off by 0.37% from the modern value.
Another one that’s interesting, I’ll just give one other and this is Mars. I thought this was pretty fascinating as an indication of the kind of knowledge that is behind some of these simple statements. The Bhāgavatam says that when Mars does not travel in a crooked way, it moves 1 sign in 3 fortnights. That is the statement that is made. Well if you work it out, 1 sign is 30 degrees and a fortnight is 15 days. So that comes out as ⅔ of a degree per day, or 0.666. So Mars, however, moves in a very complicated way – actually it’s famous for that – and it’s saying here “when it does not travel in a crooked way.” Well, I did a little computer model of the movement of Mars just to see what would happen, and on page 92 we have the results of that study. It seems that Mars sometimes reverses its motion. Of course all the major planets do that. Mars is especially prominent in that regard; it goes through what is called retrograde motion. When it moves through the sky it will move along, and then slow down, stop, go back for a while, and then go forward again, and then again slowdown, go back and go forward. So in this table I have the percentage of the time it spends moving at different rates. So below zero, that means when it’s going backwards, and then you’ll see a series of intervals in terms of degrees per day. It turns out that it spends most of the time according to this calculation, namely 23.6%, going between 0.67-0.7 degrees per day. So the Bhāgavatam is saying .666, which lands right in that interval. So what I gather from these points is that behind the apparently simple statements that you find in the Bhāgavatam there was a lot of knowledge, which I think is a worthwhile observation to make. So well, let’s see, how are we doing for time? We have half an hour. Ok that’s good. So that’s a little bit about periods.
Q: Aren’t we spending more time between 7 and 7.75?
A: Well actually you’re right about that: 26.1. But in that vicinity the curve sort of peaks up there. So ⅔ is... my basic point is that it’s giving a pretty good picture of the average motion of the planet in a simple statement which indicates that there’s a, you know, some knowledge behind the statement. That’s the basic point. So, I think if you calculate what the mean is there, you’d find it would come in that 23.6% interval. So that’s a bit about periods of motion of the planets. Now the question is: How do they move?
So here we want to discuss again this question of heliocentric versus geocentric. So basically here’s how a planet moves – I’ve used in the book Venus as an example. From the geocentric point of view, [demonstration on whiteboard] here’s the earth, here’s how the motion of Venus is described in the Sūrya-siddhānta. So they’re saying the circle (which the center is there), which is called the first cycle, and then at a point on that circle there’s another circle. Let me see...
...well anyway, which is the second cycle. The drawing in the book has it in proper proportion. This goes way too close to the earth here.
So here is now the motion of Venus, Venus will be somewhere on the second cycle. So the point is that, this point on the first cycle moves around with a certain period, and it is the center of the second cycle. And the position that Venus on the second cycle moves around that center with a certain period. And basically that’s the motion of Venus that is described in the Sūrya-siddhānta. Now there’s some more details here. This is actually an oversimplification. There’s some additional little cycles here. And this cycle actually expands and contracts as Venus goes around, so it’s somewhat elliptical; it’s not actually circular. And then the other point is that this drawing is in a plane – of course that’s easier to make drawings that way – but in fact these orbits are tilted at different angles with respect to the ecliptic.
So the plane of this first cycle is in fact the plane of the ecliptic, and the plane in which the second cycle is located is tilted at some angle; and these are just some of the details. But the basic picture is what you see here. So this describes how Venus is moving. The Sūrya-siddhānta indicates the equations that generate this, and it makes use of trigonometry. Interesting point here is that the Jyotiṣa Śāstra contains sines and cosines. They have trigonometry. Historically it’s interesting that trigonometry is in some text books said to be created by the Arabs. But if you trace the history back, the Arabs got it from India. So trigonometry is actually coming from Indians far as anyone can trace it historically. So that’s an interesting point.
So what I want to do then is compare the motions, say here, of Venus in the Sūrya-siddhānta with the motion of Venus according to the heliocentric system. So the heliocentric system, here’s the picture you have [using whiteboard]. You have the sun, and here, say, would be the earth (my circle is going to go off the edge, but anyway). So, the earth is moving in its orbit. And then you have a smaller orbit also centered on the sun, which is the orbit of Venus there. So Venus is at some point... like here; so according to this, Venus is going around the sun in its orbit, and the earth is going around in its orbit. So that’s the heliocentric picture. A better diagram is on page 13 here.
So the point to make is that from a relative point of view these two pictures are the same. And to see how they’re the same, you can just draw... there’s one key fact that has to be mentioned. It turns out that this center for the circle followed by Venus happens to be where the sun is in the Sūrya-siddhānta also. So if you compare these two figures you’ll see that this pair of lines, from earth to sun to Venus is the same as this pair of lines from earth to sun to Venus. So relatively speaking the two pictures are the same. Now they’re the same in terms of the angle which you’ll have here and in terms of the relative length of these lines. So that was the next point that I wanted to come to, namely that the Sūrya-siddhānta gives the same proportions to the solar system that you have in modern astronomy. So what do I mean by proportions?
In modern astronomy this distance from the earth to the sun is called one astronomical unit. That’s the way that they measure it. So that’s said to be about 93 million miles. So that’s one astronomical unit. So in those terms, Venus comes out to be 0.72 astronomical units. So that’s the, gives the proportions for those orbits. Well, in the Sūrya-siddhānta it comes out to be something very similar. So in Table 4 on page 14 there’s a summary of what happens if you compare these relative distances in these different orbital cycles in the Sūrya-siddhānta and modern astronomy. So if you look at Venus, for example, what you find is if you take the ratio between the size of cycle 1 and cycle 2 as indicated in the table, what you get is 0.725. And in modern terms it’s 0.72, let’s say. Of course these figures are rounded off anyway. So basically it’s saying the same thing. Now the same thing is true for all of the different planets listed in this table. Now this table leaves out the moon and the sun. In the Sūrya-siddhānta the sun is just given a single cycle – it just goes around in one cycle. And the moon also has a single cycle for orbiting the earth, although there are additional correction factors that I’m not mentioning that go into this. But that’s the basic picture. So the other 5 planets, those star planets as they’re called, have two cycles. Yeah?
Q: It’s not clear to me from that diagram, how it’s geocentric? If Venus is moving in an orbit around one point, it’s not centred on the earth, how is it geocentric?
A: Well, it's geocentric in the sense that the earth is the fixed reference point. So that’s basically what it means by geocentric.
Q: One cycle is around the earth?
A: Yeah, the first cycle’s around the earth.
Q: What does that circle indicate?
A: What does it indicate?
Q: Yeah [unclear]
A: Well, the circle can be looked at in two ways. First of all, yeah, as for how Venus moves, it will move in loops, going around like this. That’s how it will move. And, as to what the circle indicates, you see we’re accustomed to thinking in heliocentric terms. So this circle corresponds to the orbit of the earth around the sun in heliocentric terms. Or in geocentric terms what this circle really is, is the orbit of the sun around the earth. And in fact the sun is located right here. You can say in effect that the Sūrya-siddhānta it is saying that Venus is orbiting around the sun, and both Venus and the sun are orbiting around the earth. Now curiously it doesn’t come out and say that in the Sūrya-siddhānta. It just says that Venus is orbiting around the point which is moving in a cycle like this and the sun is also. That point to turns out to be the same if you look at the calculations. It doesn’t say what we’re saying, that Venus is orbiting around the sun, but in effect it is saying that. But in any case, geocentric doesn’t mean that everything moves in a circle around the earth – it means that the earth is the fixed reference point. Yeah?
Q: Do all of the star planets revolve around the same reference point, where the sun just happens to be?
A: No, two of them do, namely Venus and Mercury. Now Mars, Jupiter, and Saturn don’t. They have different reference points. Now it turns out that you can relate this to the heliocentric theory also. Basically speaking in the Sūrya-siddhānta, well it’s interesting the approach taken in the Sūrya-siddhānta to describe these things. We’re accustomed to saying there are 360° in a circle. Well, in the Sūrya-siddhānta you can have varying numbers of degrees in a circle depending on how big the circle is. They have a different idea of what a degree is. In the Sūrya-siddhānta a degree is an actual unit of distance like an inch. So if you have a circle of the right size, then there are 360° in that circle; a smaller cycle would have fewer degrees. So the Sūrya-siddhānta describes the size of these cycles in terms of numbers of degrees and that’s indicated here in Table 4. Under cycle 1 you will see if you look in that table that each cycle 1 is given as 360° but then in cycle 2 you’ll see varying values between two limits. Like for Mercury it’s 133° and 132°. As I said, those cycles expand and contract as the planet goes around; that’s an additional little feature there. So, the, that means that the cycle for Mercury is smaller than the number 1 cycle. So that directly corresponds to the idea of Mercury going in a small orbit around the sun which in turn is moving in a larger orbit around the earth.
Now for the outer planets, the second cycle is also smaller, as you can see if you look, for example, at Mars. Again cycle 1 is 360 and cycle 2 is 235 and 232. So what you have there is that for Mars the first cycle, which is the larger one in heliocentric terms, corresponds to the orbit of Mars around the sun, and the small cycle now corresponds to the orbit of the earth around the sun. So it's a slightly different way of presenting it. But that is the way Mars is treated and also Jupiter and Saturn, so that the first cycle is always the larger one and the second cycle is always the smaller one. That’s the way it’s set up. So the basic point to make then concerning the Sūrya-siddhānta is that although it has a geocentric viewpoint, and by geocentric I mean the earth is the fixed center, still the relative positions of the planets with respect to one another and with respect to the sun is the same as in modern astronomy. That is, all the ratios of lengths came out to be the same and the different angles, say earth to sun to Venus and so on, all those angles come out to be the same. Yeah?
Q: What was the reason they had for it, why would they want to show it as geocentrically instead of heliocentrically . . . [unclear]
A: Well! That would be a controversial issue. You see, what is the basis for the heliocentric theory? There’s a whole chapter, a whole discussion in the book, as to why the heliocentric is favored.
It’s very interesting to look at the history. Back in the days of Galileo it wasn’t at all clear the heliocentric was really better than the geocentric theory. Nowadays people will say, ”Well, the heliocentric theory is simpler.” But in fact it wasn’t simpler. For example, Copernicus had a more complicated, cumbersome system for describing the motions of the planets than the heliocentric model of the Ptolemaic system, which was geocentric. And in fact this was pointed out as a criticism of Copernicus. So in those days it wasn’t really clear. And it may seem surprising but it turns out that the clinching arguments used today to show that the earth is really travelling around the sun, not the other way around, involve very subtle things. I may as well mention this thing about the Michelson-Morley experiment.
For example, one basis for saying that the earth is moving around the sun is that there’s stellar parallax. What that means is this: if I’m, say, walking around in a circle then, well I’ll see that that fan keeps moving with respect to the wall in the background. So that’s called parallax, that motion. So we can see that from two different positions, a line drawn to the fan, those two lines will converge together and you can actually calculate the distance to the fan; and if you know the base line between the two points and the angles for those two lines pointing to the fan, then by trigonometry you can calculate how far away the fan is. So the two angles converge together to a point. So if the earth is orbiting about the sun and you have some star at a distance, then similarly the star should seem to move back and forth in the course of a year because in half a year, the earth goes halfway around its orbit so it’s diametrically across from its orbit with respect to where it was a half year before. So you should see the star move back and forth. It turns out that...
Q: Against what background ?
A: The other stars, more distant stars. For example, I can see the fan move back and forth with regard to the knot holes on that wall back there because it’s at a greater distance.
Q: But if you don’t know the distance to begin with how do you know which is the closer star?
A: Well, what you’d expect to find, that if stars were at various distances, and some are much further than others, and that some will move with respect to others that don’t move in relation to one another. That’s what you’d expect to see. Yeah?
A: Oh, well there are details in the discussions of orbits of planets. In the Sūrya-siddhānta they don’t always go at the same speed going around in circles. The formula indicates variable speed also. I’m simplifying some of the details. But in any case, to go back to this topic of parallax, since we’re on it, this is what you’d expect if the earth is going around the sun and there are stars out there at different distances, a lot of them very far away and some of them closer; and the closer ones seem to move back and forth with respect to the distant ones. And for many years, no one could measure such an effect – they looked with their telescopes and they just couldn’t see such an effect. This was interpreted to mean that the stars are very far away. So far... just like if I move back and forth, well even an inch, I can see some parallax with that fan there. But if I move back and forth by say a 1000th of an inch I won’t see anything. So if the stars are millions and millions and millions of times as far away as the diameter of the earth’s orbit, then you wouldn’t expect to see parallax. So the absence of star parallax is interpreted to mean that the stars are very far away, millions of times the diameter of the earth’s orbit. That’s how scientists view the matter.
But still you might ask, well, have they been able to measure parallax of some stars? And they’ll say there’s a handful of stars for which with the best telescopes they have been able to measure a very tiny amount of parallax. And the history behind this is interesting, because about a century before they did that, or two centuries or so, astronomers such as, well Flamsteed, who lived in the time of Newton for example, and Hooke, who was also an English scientist at the time of Newton, measured parallax of stars and they got values 10 or 20 times as big as those of anyone measuring today. So it’s very curious, how did that happen? Well the explanation given was that that was illusion. They were just imagining things because now we know it’s just not so. So it’s just an interesting point. There are many things like that.
There’s a fellow, an astronomer named van Maanen, who measured the rotation of galaxies. If you see pictures of galaxies they look somewhat like pin wheels, and it looks as though they must be rotating. So this fellow, with his telescope, said "Well yeah, we can see that they’re rotating,” and measured it, and published his results and so forth. Later on people decided it was totally illusion. They said that more accurate measurement showed you can’t see any rotation at all. Yet he measured it. I could go on giving you a whole bunch of stories like that. But to get back to the question of parallax, so what we argue today, are a few stars such as Alpha Centauri, which is the closest star – about 4 and a half light years away I think – for which you can measure very tiny parallax; and you need the best telescopes to do that. So, and that’s taken as demonstrating that the earth is going around the sun, but you can see that’s not an obvious point. It’s a very tiny effect which is used to derive this conclusion.
Another whole subject or topic is, well there’s the idea that just like if you’re walking in the rain with an umbrella – say the rain is coming straight down – as you walk you may get wet, because your relative motion causes, in effect, the rain to slant as it comes down, because you’re moving even though it’s coming down in a straight line. So similarly, if light is coming down from the stars and we’re moving in orbit, then light should seem to tilt in its angle just like the rain fall would be tilted. And half a year later, when we’re moving in the opposite direction, it will seem to tilt in the opposite direction. So you should be able to measure that. So people have made measurements of that, and they’ll say that, well, there’s an effect there that we can measure. But that turns out to be a somewhat complicated issue because there’s a whole discussion of about, well what happens in the light moves through, say, water? Light moves more slowly in water because it has a certain refractive index, so therefore the angle of tilt should be different. It turns out that it comes out the same. So this made people wonder: Well how do we account for that? It seems like a nice explanation. But according to this calculation, the light should be going slower; you see, if the rain is falling slower, imagine slow rain! And if you’re walking at the same speed, then the tilt of the raindrops coming down should be even greater coming under your umbrella. So if you can slow down the light, which happens when it's going through, say glass or water, then you should get a bigger effect; and this should be measurable.
So they tried it – an English astronomer named Airy tried that – and got exactly the same effect. So this was a bit of a mystery. And then finally the Michelson-Morley experiment, the subject matter there was the following thing: How does light go through outer space, which is a vacuum? Well in the 19th century the idea was there’s a medium in outer space called the ether, and light is a vibration that goes through that medium. Of course in Vedic literature we also have ether. So the idea was that, well, if light goes through ether and the earth is moving around the sun, then there’re two possibilities. One is that the ether is moving with the earth.
Now ether had to be a very rigid substance because light moves very fast, just like the speed of sound in a rigid thing, like a steel bar, is much much faster than it is in air. The idea is the more rigid the thing the faster a wave goes through it. Well light goes very fast, so ether would have to be very rigid according to the theory. Of course how can something pass through something rigid anyway? That’s a problem. But apart from that question, if the ether is stationary relative to the earth and the earth is moving around the sun, it means this huge mass of ether extending out into space is moving with the earth going around the sun. So this did not seem very plausible. So they thought: Surely the ether must be somehow stationary and the earth is moving with respect to it and going through it. Well if that’s true, then the speed of light should change in different directions at different times of the year as the earth changes direction. Because sometimes light would be going upstream against the ether and sometimes it would be going down stream. And you should be able to measure that.
So these experimenters, Michelson and Morley, devised an apparatus which would enable them to measure what they called the ether drift, in other words, the change in the speed of light caused by the fact that we’re moving through the ether at the speed of the earth’s movement in its orbit. And they found no ether drift, so that could be taken to mean that the earth is not moving with respect to the ether. So, anyway, that then led to another whole controversy. Eventually the theory of relativity came to the rescue. Einstein’s theory of relativity says that the reason the speed of light seems to be the same as you go at different speeds in the earth’s orbit is that as you move, measuring rods change length along the line of your direction of motion, and so the speed measurements come out to be the same. That in brief is the explanation given in the theory of relativity. So by giving this idea that length changes as you move, the heliocentric theory was saved. But I had never realised until reading this thing recently that that was actually the issue, or at least partly the issue, behind the theory of relativity in the Michelson-Morley experiment. So let’s see.
Are there any other questions?
Q: First you said that the stars are far enough away that you couldn’t see the parallax.
A: That’s the modern interpretation of why you don’t see it.
Q: And then they go on to measure the tilt on the earth even though they’re so far away that there should be no angle because the ratio of the distance from the atmosphere of the earth and where it’s coming from should be insignificant.
A: Well, the idea is that some stars are sort of far enough away so that it’s a very tiny parallax, but not so far away that there’s none at all. This is their viewpoint.
Q: What about the tilt when the earth moves and the light from stars is coming?
A: Well the thing about tilt that I was speaking of, well that should happen no matter how far away they are; that has nothing to do with the distance as long as you have a light source coming from outside. It’s just like the example I gave of the rain falling and the person holding the umbrella. It doesn’t matter where the rain is coming from as long as it’s just coming down. But in brief, the whole idea of this little digression was that the question of whether the earth is going around the sun or not is, empirically speaking, based on some rather subtle points. Now theoretically, the reason people really believe that the earth is going around the sun and not the other way around is Newton’s system of laws of motion and his theory of gravity. Because the idea is that the sun is a very enormous and massive object and the earth relative to the sun is like a tiny speck, practically. So according to this idea, if the sun is going around the earth it’s like this gigantic massive thing going around this tiny little speck, and that doesn’t seem to make sense. It’s like the tail wagging the dog instead of the other way around. So basically that’s what really carries conviction as to the heliocentric versus the geocentric theory. So that brings one into the whole question of gravitation. When we discuss the Fifth Canto I can give you some further insights concerning this issue of heliocentric versus geocentric. But in any case the Sūrya-siddhānta is using the geocentric scheme.
Q: What about the relative motion of the moon in that heliocentric... [unclear]
A: Well the moon is treated the same way in both heliocentric and geocentric models. The moon simply rotates around the earth
Q: But isn’t it said in Śrīmad-Bhāgavatam that the moon is at a greater distance than the sun?
A: Well we’ll be discussing that. I can say briefly, in the Sūrya-siddhānta the distance from the earth to the moon is less than the distance from the earth to the sun. So in the Śrīmad-Bhāgavatam it says the sun is higher than the moon. Now the key thing there is that different points of reference are involved.
Q: The moon is higher than the sun.
A: Did I say that in reverse? The moon is higher than the sun, yeah, in the Śrīmad-Bhāgavatam it is said that the moon is higher than the sun. There’s a different point of reference. So there’s no actual contradiction there. And I’m going to be discussing that later on – that’s one of the main topics that comes up.
A: Oh, that’s another topic! I have a discussion of that in the book here, including all kinds of things Śrīla Prabhupāda said about it. We’ll get to that a little bit later.
Q: You said cosmology means the theoretical framework of the universe?
A: The picture of what’s out there, that’s what cosmology is.
Q: Why do you use the word ‘cosmography’ in the title?
A: Well that’s a traditional word. The reason I used it is that the Fifth Canto is basically describing the universe in terms of geography. It’s describing it in geographical terms, which is an interesting approach, not exactly the modern approach. So I used this old word cosmography. It’s a word that is sometimes used. Sort of like a combination of cosmology and geography, if that makes sense.
A: Yeah, we’re talking about this one universe. So this universe – the technical term for universe is brahmāṇḍa – so brahmāṇḍa means the jurisdiction of one Brahma. So that’s what we’re basically discussing.
Q: Does the scientist have any idea of the other universes?
A: Oh, there are all kinds of speculative ideas. Yeah, scientists will talk about, you know, universes sort of bubbling up from some quantum mechanical spacetime foam. There’re all kinds of ideas.
A: Oh, the quantum mechanical many worlds theory? Yes, there’s an idea of the universe continually splitting into multiple copies of itself which then diverge from one another, and many different ideas. There’s the anthropic principle which explains how life could come about even though it seems very improbable by saying that, well, there are innumerable universes bubbling up in this foam or whatever, and the chance that life will develop in one of them is practically infinitesimal. But the ones in which life did not develop had no one there to observe them. The only ones that are observed are the ones in which life did develop. So that explains how life happens to be here – if it wasn’t, there would be no one to observe it . That’s called the anthropic principle. Books have been written about that.
Q: How do the modern astronomers calculate the distances of the stars and how do those compare to the Vedas?
A: Well basically in modern astronomy the distances to the stars are calculated by what they call the ‘cosmic distance ladder’ and it’s a matter of going up rung by rung using difference methods. So what they’ll do is with just a small handful of nearby stars, they measure the distance based on parallax, as I was describing. Then to get a bit further they use something called statistical parallax based on groups of stars. Just briefly to give you an idea on how that works: Suppose you have a bunch of stars, a lot of them, and they are going in all directions almost equally. So what you do is you measure how they are moving laterally, perpendicular to your line of sight, and then you use what is called the Doppler effect, the redshift, to measure how they are moving along your line of sight. Then you say: The motion laterally and the motion along the line of sight statistically must be about the same. Should never doubt about that. And we can actually measure the angular motion perpendicular to line of sight and the absolute velocity along the line of sight. Those two being equal, that tells us what distance corresponds to a given angular change; that in turns tells us how far away the cluster of stars is. So they use that for some cluster of stars. Now you might notice there are a few variables in there and assumptions which can get you into trouble. Beyond that they go step by step through a whole series of different schemes for measuring distance. If I get to it there’s a chapter in this book, which is Chapter 7, which I don’t know if I’ll cover this or not because there are other more important things. But this talks about the use of redshift for measuring distance of galaxies and so forth. And it reveals there’s a whole controversy in astronomy. I think we’re supposed to quit at this point because it’s time for arati.
[Lecture ends 1:27:40]