Discovery of the Original Boundaries of Nakshatras

Zero Points of Vedic Astronomy

Part 2 of 8 - A Tale of two Yogatārās

“If you change the way you look at things, the things you look at change.” — Wayne Dyer

It was the winter break of 2017, shortly after winter solstice. I was looking at the coordinates of yogatārās given in Sūrya Siddhānta 8.1–9. Sūrya-Siddhānta has been a very influential astronomical text for a long time in India and even abroad. Before British had invaded India, Sūrya-Siddhānta was being used in England in 1428 CE [1]. I wanted to confirm whether the coordinates given in Sūrya-Siddhānta are polar coordinates or sidereal ecliptic coordinates. I have explained what these coordinates mean in the first part of this series of articles [2]. Polar coordinates change with time as they depend on the position of celestial poles which change their positions due to the phenomenon of precession. Sidereal ecliptic coordinates do not change with time significantly as they depend on the position of ecliptic poles, which do not change their positions significantly. There could be minor changes due to the proper motion of stars or change of ecliptic plane itself, but these changes are small enough to be neglected over the known period of human history. Now if the coordinates given in Sūrya-Siddhānta were sidereal ecliptic coordinates, it would have been obvious to researchers with knowledge of astronomy. As discussed in my previous article [2], modern astronomers use tropical ecliptic coordinates, while Indian astronomers used sidereal ecliptic coordinates. The ecliptic longitudes in these two systems differ by a constant value due to two different points on the ecliptic being used for zero longitude. This is similar to current longitudes of places with Greenwich being on prime meridian compared to the longitudes of places in ancient world with Ujjain being on prime meridian. The difference is a constant equal to the difference in longitudes of Ujjain and Greenwich. It was obvious that longitudes given in Sūrya-Siddhānta do not differ by a constant value from the current ecliptic longitudes. However, there was something very odd about the longitudes of two yogatārās, those of Aśvinī and Revatī. Aśvinī is the first in the list and Revatī the last, see Table 1. To understand what was odd, we need to understand the peculiarities of Indian nakṣatra system.

  1. The Concept of nakṣatras

Vedic people had been carefully observing the sky since the dawn of civilization. It takes the moon ~27.32 days to return to the same position among the stars. Based on this measurement, the path of moon in the background of the stars was divided in 27 or 28 divisions, each division being called a nakṣatra or lunar mansion. Figure 1 illustrates the principle of the division of celestial sphere in nakṣatra zones. K and K′ represent north ecliptic pole and south ecliptic pole respectively. A, B, C, and D are the boundaries of nakṣatras on the ecliptic. In a 27 nakṣatra system, there will be 27 such points on the ecliptic through which the boundaries of nakṣatras will pass. As the nakṣatras have equal span in the 27 nakṣatra system according to Sūrya Siddhānta 2.64, each nakṣatra has a span of 13° 20′ on the ecliptic.

Each nakṣatra zone comprises of the area bound by two great semi-circles passing through K and K′ and through its boundaries on the ecliptic such as KAK′BK, KBK′CK, KCK′DK, and so on. It should be noted that in the ancient Indian system it was not necessary for the yogatārā and stars belonging to a nakṣatra to fall within the zodiac, which is a region spanning 8° on each side of the ecliptic. Figure 2 shows the order of nakṣatras in a cyclic manner. Each nakṣatra was recognized by a group of stars and out of these stars, one star was designated a conjunction star (yogatārā) in Hindu astronomy. If a nakṣatra has only one star in its group, then that star is the yogatārā of that nakṣatra by default. Astronomical text Sūrya Siddhānta gives the coordinates of each yogatārā as shown in Table 1.

2. The Coordinates of yogatārās

The list of nakṣatras in Sūrya Siddhānta 8.1–9 begins with Aśvinī and ends with Revatī. Since Sūrya Siddhānta follows the system of 27 equal divisions of the ecliptic, each nakṣatra has a span of 13° 20′. Longitude of the yogatārā is called dhruvaka in Sūrya Siddhānta and latitude is called Vikṣepa. Dhruvaka and vikṣepa are universally translated as polar longitude and polar latitude respectively.

Based on his assumption that coordinates given in Sūrya Siddhānta are polar longitudes and latitudes, Burgess [3] identified the yogatārās as shown in Table 2, Column 3. These identifications are currently accepted by most scholars. I have added the Ecliptic coordinates (J2000.0) of these yogatārās in columns 4 and 5. The data for ecliptic coordinates (J2000.0) were obtained using Stellarium software by setting the date to January 1, 2000 at 12:00 noon and noting the ecliptic longitudes and latitudes by selecting the specific stars. If we compare Table 1, column 4 and Table 2, Column 3, we find that the longitudes do not differ by a constant value, which would be the case if the longitudes given in Sūrya Siddhānta were ecliptic longitudes.

* As identified by Burgess [3]

** J2000.0 ecliptic coordinates based on Stellarium software.

*** For Uttara-bhādrapadā, longitude matches γ Pegasi, while latitude matches a Andromeda.

However, it did not deter me from continuing my investigation. I have no faith in colonial era scholarship. I do not accept anything written by colonial era scholars unless I can corroborate it myself. The question is how do I know that the yogatārās identified by Burgess [3] are the same yogatārās our ancestors had given coordinates of? Burgess has identified the yogatārās based on his assumption of these coordinates being polar coordinates. What if that is not true? How can I be sure that the very first yogatārā in the list, the yogatārā of Aśvinī is β Ari and not some other star? How can I be sure that the very last yogatārā in the list, the yogatārā of Revatī is ζ Psc and not some other star? How can I be sure of anything at all? I asked these questions as I looked at the longitudes of the yogatārās of Aśvinī and Revatī given in Sūrya Siddhānta because something was very strange and nobody has even noticed it.

3. A tale of two yogatārās

Indian astronomical texts give the coordinates of yogatārās of different nakṣatras and the number of prominent stars in these nakṣatras. Colonial era scholars have identified these stars, but how can we be sure that these identifications are correct? For this, we need to have at least one identification that we can be 100% sure about and then we can go around the ecliptic examining successive identifications. In my research, I found that identification to be that of the yogatārā of Rohiṇī. Figure 3 shows sky map of relevant nakṣatras under discussion. According to astronomical texts, the number of stars is 5 in Rohiṇī nakṣatra [4]. Astronomical texts, e.g. Bṛhat Saṃhitā 47.14, also talk about Rohiṇī-Śakaṭa-Bheda which means the penetration of the cart of Rohiṇī. Looking at Figure 3, you can see that the five stars identified as belonging to Rohiṇī nakṣatra roughly form the shape of an oxen-driven cart used in India. Aldebaran (α Tau) is the brightest among these stars and should be the yogatārā of Rohiṇī. Burgess has identified Aldebaran (α Tau) as the yogatārā of Rohiṇī, see Table 2. From this we can conclude that other yogatārās, if different from currently accepted identifications, are also in the same vicinity as currently accepted ones.

Figure 3 also shows the accepted yogatārā of Revatī, ζ Psc A, and the accepted yogatārā of Aśvinī, β Ari. There is something strange about the yogatārā of Revatī, ζ Psc A. It is very dim star with apparent magnitude of 5.20. Its longitude given in Sūrya Siddhānta 8.1–9 is 359° 50′. It is so close to origin (360° or 0°) that it is considered to be at the origin. Why would such a star be chosen at the origin? Pingree and Morrissey write [4]:

It is disturbing that ζ Piscium is so dim, and that its alpha is 0;7h or nearly 2° too high on the assumption that the original list was drawn up in A.D. 425, though the situation, of course, improves as one increases that date. But there are no other visible stars in the neighbourhood.

There is something strange about the accepted yogatārā of Aśvinī, β Ari, as well. Sūrya Siddhānta 8.16 says that there are two stars in Aśvinī nakṣatra and the yogatārā of Aśvinī is the northern of the two. Burgess has selected β Ari and γ Ari as belonging to Aśvinī nakṣatra and chosen β Ari as the yogatārā of Aśvinī, which is the northern of the two [5]. However, if you choose α Ari and β Ari as belonging to Aśvinī nakṣatra, then α Ari becomes the yogatārā of Aśvinī, as α Ari is north of β Ari. The star α Ari is brighter than β Ari as shown in Figure 3 and more deserving of being the yogatārā of Aśvinī. Burgess has justified his selection of β Ari over α Ari based on their longitudes as follows [5]:

The Sūrya Siddhānta designates the northern member of the group as its junction star: that this is the star β Arietis (magn. 3.2), and not a Arietis (magn. 2), as assumed by Colebrooke, is shown by the following comparison of positions:

Colebrooke was misled in this instance by adopting, for the number of stars in the asterism, three, as stated by the later authorities, and then applying to the group as thus composed the designation given by our text of the relative position of the junction-star as the northern, and he accordingly overlooked the very serious error in the determination of the longitude thence resulting.

In the first row above, Burgess has given the ecliptic longitude of the yogatārā of Aśvinī as 11° 59′ and ecliptic longitude as 9° 11′. The longitude of the yogatārā of Aśvinī is given as 8° in Sūrya Siddhānta 8.2 and the latitude is given as 10° in Sūrya Siddhānta 8.6, see Table 1. Assuming these to be polar coordinates, Burgess has calculated the ecliptic coordinates. Then further assuming the data to be from 560 CE, Burgess has given the ecliptic coordinates of β Ari in row 2 and α Ari in row 3. Burgess has then chosen β Ari over α Ari as the longitude of β Ari is closer to the longitude of the yogatārā of Revatī . However, there is a major problem with the ecliptic longitudes of both α Ari and β Ari, which no one has pointed out so far in my knowledge. If we take the origin at the yogatārā of Revatī, ζ Psc A, then both α Ari at 17° 37′ and β Ari at 13° 56′ are outside the boundaries of Aśvinī nakṣatra as the span of each nakṣatra is only 13° 20′. Can you imagine that the very first yogatārā in the list given in Sūrya Siddhānta is outside its boundary? However, the yogatārā is well within the boundary if you accept that the longitude given as 8° in Sūrya Siddhānta 8.2 is ecliptic longitude. The coordinates of the yogatārā of Aśvinī are given as 8° longitude and 10° latitude in Sūrya Siddhānta, Paitāmaha Siddhānta, Mahābhāskarīya and Laghubhāskarīya, and by Brahmagupta, Vateśvara, Lalla, and Gaṇeśa [4]. It was never changed as would be expected in a sidereal ecliptic coordinate system.

Hamal (α Ari), which is the brightest star of the Aries constellation, has apparent magnitude of 2.00 and J2000.0 ecliptic longitude and latitude of 37° 40′ and 9° 58′ respectively. The ecliptic latitude of 9° 58′ of Hamal matches closely with the latitude of 10° given in Sūrya Siddhānta. This raises the possibility that the yogatārā of Aśvinī is Hamal (α Ari) instead of Sheratan (β Ari). The confirmation comes from Jain astronomy texts, which contain amazing amount of information that has not been properly studied yet. According to Jambudwīpa Prajñapti 7.191, the number of stars in Aśvinī nakṣatra is three. If you look at Figure 3, it is obvious that these three stars are α Ari, β Ari, and γ Ari. It becomes obvious then that α Ari is the yogatārā of Aśvinī among them as it is the brightest, the most northern and has the best match with latitude. If this is so, then the beginning of Aśvinī nakṣatra is 8° to the right of α Ari denoted by point A in Figure 4. Point R in Figure 4 represents the currently accepted beginning of Aśvinī nakṣatra, which coincides with the currently accepted yogatārā of Revatī being at the end of Revatī or beginning of Aśvinī. The difference in longitude of these two points is 10°. This is what I noticed while looking at the longitudes of the yogatārās of Aśvinī and Revatī. While the text says they are 8° apart, they are actually 18° apart. I would not have noticed it if I had accepted the coordinates as polar coordinates and the yogatārā of Aśvinī as β Ari. This difference of 10° is of monumental significance in dating the ancient Indian texts as each degree represents 72 years and a difference of 10° means that many ancient Indian texts are seven centuries older than their accepted dates. This also has massive implications for history of science, especially astronomy. Further corroboration for the beginning of Aśvinī nakṣatra being 8° away from α Ari comes from European astronomy.

In a paper published in 1904 on the passage of the vernal equinox from Taurus into Aries, it is stated that the longitude of α Ari for 1900 CE was 36° 15′ and the longitude of first point of Aries was 28° 22′ [6]. It is obvious that the longitude of first point of Aries here refers to the original boundary of Aries as in the tropical ecliptic coordinate system this point is at the origin having zero longitude. Figure 4 shows the sky configuration in 1900 CE, which confirms that the longitude of α Ari for 1900 CE was indeed 36° 15′, see the ecliptic longitude on date in the figure. This means that α Ari was 7° 53′ or approximately 8° from the boundary of Aries. The Indian equivalent of Aries is Meṣa rāśi. This means that α Ari was at 8° from the boundary of Meṣa rāśi. Varāhamihira has stated in Bṛhat Jātaka 1.4 that the beginnings of Meṣa rāśi and Aśvinī nakṣatra coincide. This then means that α Ari was at 8° from the boundary of Aśvinī nakṣatra denoted by Point A in Figure 4. So why was the boundary of Aśvinī nakṣatra shifted from Point A to Point R? There was a very strong reason for it, which relates to precession of equinoxes and peculiarities of Indian calendar system. I will explain this in much greater detail in one of my future articles. For now I will provide further evidence that the original yogatārā of Revatī was not ζ Psc A but some other star. A figurative description of the change of the yogatārā of Revatī is given in Chapter 72 of Mārkaṇḍeya Puarāṇa. In this story Revatī was dropped from the firmament and later reinstated. The conclusive proof comes from Jain astronomy texts. Jambudwīpa Prajñapti 7.189 gives the positions of nakṣatras relative to moon’s path. For Revatī nakṣatra, it is stated that the position is always north of moon’s path. Moon goes roughly 5° north to 5° south of ecliptic. The currently accepted yogatārā of Revatī, ζ Psc A, is right on the ecliptic, see Figure 3. So it was clearly not the yogatārā of Revatī nakṣatra according to Jain astronomy as the original yogatārā of Revatī nakṣatra had latitude greater than 5°. As Jambudwīpa Prajñapti is dated to 4th or 3rd century BCE [7], till that time the boundary of Aśvinī nakṣatra was at a point on ecliptic 8° from Hamal (α Ari). There is more to this point (Point A in Figure 4) than meets the eye. I will show in the next article that this point is intimately connected to the original zero point of Indian astronomy.

References:

1. Neugebauer, O. (1952). “Hindu astronomy at Newminster in 1428”. Annals of Science, 8:3, 221–228.

2. https://medium.com/@rajarammohanroy/zero-points-of-vedic-astronomy-f4f8febb0b05

3. Burgess, E. (1860). Translation of the Surya-Siddhanta: A Text-Book of Hindu astronomy, with notes, and an appendix. Journal of the American Oriental Society, 6: 141–498 (information on page 355).

4. Pingree, D. and Morrissey, P. (1989). On the identification of the “Yogatārās” of the Indian Nakṣatras, Journal for the History of Astronomy, 20 (2): 99–119.

5. Burgess, Translation of the Surya-Siddhanta, page 327.

6. Maunder, E.W. and Maunder, A.S.D. (1904). Note on the date of the passage of the vernal equinox from Taurus into Aries. Monthly Notices of the Royal Astronomical Society, 64 (5): 488–506.

7. Sridharan, R. (2005). Mathematics in Ancient and Medieval India, in Contributions to the History of Indian Mathematics, edited by G. G. Emch, R. Sridharan and M. D. Srinivas, Gurugram, India: Hindustan Book Agency, page 7.

More about the author

I am a seeker in search of the true history and heritage of India. I have strong scientific background (B.Tech. in Metallurgical Engineering from Indian Institute of Technology, Kanpur and Ph.D. in Materials Science and Engineering from The Ohio State University, USA) and a deep interest in ancient Indian texts. My work on Indology spans three different fields: cosmology, astronomy, and history.

Email: rajarammohanroy108@gmail.com

Next: Zero Points of Vedic Astronomy: Part 3 of 8 — The Clock in the Sky

Vedic Scholar, Materials Scientist, Author of books on Vedic Astronomy, Jain Astronomy, and Ancient Indian History