Discovery of the Original Boundaries of Nakshatras

Zero Points of Vedic Astronomy

Part 4 of 8 — Introducing Ashwini Paksha Ayanamsha

Currently calendar makers and astrologers use a concept called Ayanāṃśa which is the longitude difference between the zero point in ancient India and current zero point called the first point of Aries. This concept is shown in Figure 1 below. Point ♈ is the first point of Aries, from which longitude is measured in tropical ecliptic coordinate system. This point keeps changing with respect to the background stars due to precession. In ancient India, the coordinate was measured from a fixed star. This star was the star Aldebaran, the yogatārā of Rohiṇī, as discussed in my previous article [1]. As the position of vernal equinox changed in the background of stars, the first nakṣatra in the list was changed from Kṛttikā to Bharaṇī and then to Aśvinī. A Jain astronomical text Sūrya Prajñapti (10.1) gives five other systems besides the one followed by Jains, which started from Abhijit and ended at Uttarāṣāḍhā. These five systems were: 1. Kṛttikā to Bharaṇī; 2. Maghā to Āśleṣā; 3. Dhaniṣṭhā to Śravaṇa; 4. Aświnī to Revatī; and 5. Bharaṇī to Aśvinī. This shows that there were multiple conventions in place for starting the list of nakṣatras. One convention started the list from the nakṣatra on summer solstice. In this convention Maghā was first on the list. Another convention started the list from the nakṣatra on winter solstice. In this convention Dhaniṣṭhā was first on the list. This was later changed to Abhijit by Jains. Yet another convention started the list from the nakṣatra on vernal equinox. Under this convention first nakṣatra was Kṛttikā. Later it was changed to Bharaṇī, and then to Aśvinī as the position of vernal equinox changed due to precession. After that, there were no updates so the Ayanāṃśa is measured from the beginning of Aśvinī nakṣatra denoted by point O in Figure 1. The angular distance O♈ is the measure of Ayanāṃśa. The problem is that there is no agreement regarding where this point O is on the ecliptic. This has given rise to many values of ayanāṃśa [2]. There are two sets of Ayanāṃśa that are most popular, one based on the position of the yogatārā of Citrā grouped under Citrā Pakṣa Ayanāṃśa and the other based on the position of the yogatārā of Revatī grouped under Revatī Pakṣa Ayanāṃśa. Both of these values are derived from the coordinates given in Sūrya-Siddhānta.

Figure 1: Sidereal ecliptic coordinate system and the concept of Ayanamsha

1. Ayanāṃśa values

There are 3 longitude values given in Sūrya Siddhānta that are important for calculating ayanāṃśa. These values are shown in Table 1. Citrā Pakṣa Ayanāṃśa is based on assuming that the yogatārā of Citrā, Spica, was at 180° from the beginning of Aśvinī nakṣatra. I am going to call this coordinate system as Citrā system. In my previous article [1], I have shown that there were two other systems as well for the beginning of Aśvinī nakṣatra, Rohiṇī system and Kṛttikā system. In Rohiṇī system, the beginning of Aśvinī nakṣatra was at 8° west of the yogatārā of Aśvinī, Hamal. This point was 40° west of the yogatārā of Rohiṇī, Aldebaran. In Kṛttikā system, the beginning of Aśvinī nakṣatra was at 10′ east of the yogatārā of Revatī, Revati (z Psc A). This point was 40° west of the yogatārā of Kṛttikā, Alcyone. These three points are shown in Figure 2. The values of ayanāṃśa based on these three alternatives are shown in Table 2. Currently the most popular ayanāṃśa is Lahiri ayanāṃśa which is one of the Citrā Pakṣa ayanāṃśa values. Lahiri ayanāṃśa is close to 24°, while Revatī Pakṣa ayanāṃśa values are close to 20°. As the original boundary of nakṣatras was based on the Rohiṇī system, the value of ayanāṃśa based on the original system is close to 30°. I have named this Aśvinī Pakṣa ayanāṃśa as it is based on the position of the yogatārā of Aśvinī. Varāhamihira has stated in Bṛhat Jātaka 1.4 that the beginnings of Meṣa rāśi and Aśvinī nakṣatra coincide. As Meṣa rāśi is same as Aries, the beginnings of sidereal Aries and Aśvinī nakṣatra should coincide. I have shown in my earlier article [3] that the beginning of sidereal Aries is at 8° west of the Hamal and coincides with the original beginning of Aśvinī nakṣatra, as should be the case. This means that Aśvinī Pakṣa ayanāṃśa is same as the difference in longitude between sidereal Aries and tropical Aries.

Table 1: The coordinates of selected yogatārās (Sūrya Siddhānta 8.1–9)

Figure 2: Three different points denoting the beginning of Aśvinī nakshatra

Table 2: The value of Ayanamsha in different systems

I started my investigation to check whether the coordinates given in Sūrya Siddhānta are polar coordinates or sidereal ecliptic coordinates. My investigation has led to the conclusion that the coordinates given in Sūrya Siddhānta are sidereal ecliptic coordinates, but are a mix of coordinates from three different systems shown on Figure 2. Further details are given in my peer-reviewed paper and book “Zero Points of Vedic Astronomy” [4. 5]. The reason this mix up could continue is that the coordinate values of the yogatārā are only of theoretical interest. Since the coordinate values were considered to be sidereal ecliptic, they were never updated by measurement. It is important to note that the yogatārās are only useful as visual aid and the actual determination of the nakṣatras is based on the boundaries of nakṣatras. It depends on the choice of the origin as shown in Figure 2 and the rest of nakṣatras are at 13° 20′ successively. In the previous article [1], I presented my calculation of the position of sun among nakṣatras during equinoxes and solstices in Rohiṇī system and Kṛttikā system. With the introduction of Citrā system, I am including my calculations for the Citrā system.

2. The position of sun during equinoxes

Based on the boundaries of nakṣatras as illustrated in Figure 2, the dates for the position of sun among the nakṣatras during equinoxes can be calculated. These dates are shown in Figures 3 to 5 for Rohiṇī system, Citrā system, and Kṛttikā system respectively.

Figure 3: The position of sun during equinoxes in the Rohinī system

Figure 4: The position of sun during equinoxes in the Citrā system

Figure 5: The position of sun during equinoxes in the Krittikā system

3. The position of sun during solstices

Based on the boundaries of nakṣatras as illustrated in Figure 2, the dates for the position of sun among the nakṣatras during solstices can be calculated. These dates are shown in Figures 6 to 8 for Rohiṇī system, Citrā system, and Kṛttikā system respectively.

Figure 6: The position of sun during solstices in the Rohinī system

Figure 7: The position of sun during solstices in the Citrā system

Figure 8: The position of sun during solstices in the Krittikā system

These dates provide us detailed information that can be used to deconstruct the colonial narrative of our history and reconstruct the true history of India. In my next article, I will discuss the dating of the great astronomer Varāhamihira who is currently dated to sixth century but the Indian tradition places him in first century BCE.

References

1. Zero Points of Vedic Astronomy. Part 3 of 8 — The Clock in the Sky | by Dr. Raja Ram Mohan Roy | Jan, 2021 | Medium

2. Koch, D. , “Ayanamshas in Sidereal Astrology”, https://www.astro.com/astrology/in_ayanamsha_e.htm

3. Zero Points of Vedic Astronomy. Part 2 of 8 — A Tale of two Yogatārās | by Dr. Raja Ram Mohan Roy | Jan, 2021 | Medium

4. Roy, R.R.M. (2019). Sidereal Ecliptic Coordinate System of Sūrya Siddhānta, Indian Journal of History of Science, 54(3): 286–303.

5. Roy, R.R.M., 2020. Zero points of Vedic Astronomy. Mississauga, Ontario, Canada: Mount Meru Publishing.

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 5 of 8 — The Dating of Varāhamihira to 123 BCE