Discovery of the Original Boundaries of Nakshatras
Zero Points of Vedic Astronomy
Currently, the Vedāṅga Jyotiśa is dated between 1150 BCE to 1400 BCE . The Vedāṅga Jyotiśa is the first astronomical text of ancient Indian civilization and the determination of the correct date of the composition of the Vedāṅga Jyotiśa is of vital importance in discovering the correct chronological history of India.
There is a very specific observation in the Vedāṅga Jyotiśa that makes it straight forward to calculate the date of its composition. It is mentioned in the verses 6–8 of the Yajur-Vedāṅga Jyotiṣa that the winter solstice was at the beginning of the Śraviṣṭhā (Dhaniṣṭhā) nakṣatra and the summer solstice was at the midpoint of the Āśleṣā nakṣatra at the time of its composition. Figure 1 shows the position of the solstices in the background of the nakṣatras as mentioned in the Vedāṅga Jyotiṣa.
The dates for the position of sun in the background of nakṣatras were calculated in Part 3 of this series as shown in Figure 2 . From this figure, it can be seen that the date of winter solstice being at the beginning of the Śraviṣṭhā (Dhaniṣṭhā) nakṣatra was ~1832 BCE. Rohini system is used for this calculation as this was the original system. However, Kuppanna Sastry has dated the Vedāṅga Jyotiṣa to 1150 BCE to 1400 BCE using three different methods . A critical analysis of each of these methods is presented below.
1. Method 1
Kuppanna Sastry has described the first method as follows:
Verses 6, 7 and 8 of the Yajur-Vedāṅga Jyotiṣa show that at the time of Lagadha the winter solstice was at the beginning of the asterism Śraviṣṭhā (Delphini) segment and that the summer solstice was at the midpoint of the Āśleṣā segment. It can be seen that this is the same as alluded to by Varāhamihira in his Pañcasiddhāntikā and Bṛhatsaṃhitā. Since VM has stated that in his own time the summer solstice was at Punarvasu ¾, and the winter solstice at Uttarāṣāḍhā ¼, there had been a precession of 1 ¾ stellar segments, i.e. 23° 20’. From this we can compute that Lagadha’s time was 72 x 23 1/3 = 1680 years earlier than VM’s time (c. A.D. 530), i.e. c. 1150 B.C. If, instead of the segment, the group itself is meant, which is about 3° within it, Lagadha’s time would be c. 1370 B.C. 
The date of Vedāṅga Jyotiṣa in this method is calculated by the difference in the position of solstices during the time of the composition of the Vedāṅga Jyotiṣa and the time of Varāhamihira. The time difference between these observations is roughly 1,680 years. The problem with this method is that it assumes the time of Varāhamihira to be circa 530 CE. However, this dating itself is a matter of contention. As shown in my previous article , the time of Varāhamihira was ~123 BCE. If we count 1,680 years from that, we get ~1803 BCE.
2. Method 2
Kuppanna Sastry has described the second method as follows:
The date arrived at as above can be confirmed by the Sūryasiddhānta and the Siddhānta Śiromaṇi which give 290° polar longitude and 36° polar latitude to Śraviṣṭhā. From this, the actual longitude of Śraviṣṭhā got is 296° 15’. Since the siddhāntas use the fixed zodiac beginning with the vernal equinox of c. 550 A.D., and the winter solstice of this is 270°, there has been a precession of 296° 15’ — 270° = 26° 15’. Since 26 ¼ x 72 = 1890 years, the wanted time is 1890 years, before A.D. 550, i.e. c. 1340 B.C., being the same as the above, the small difference being observational. 
The date of Vedāṅga Jyotiṣa in this method is calculated by the difference in the position of the yogātarā of Śraviṣṭhā during the time of the composition of the Vedāṅga Jyotiṣa and Sūrya Siddhānta. This method uses the coordinate of the yogātarā of Śraviṣṭhā. It is similar to the third method used by Kuppanna Sastry and therefore gives similar result. The difference is that the position of the yogātarā of Śraviṣṭhā is calculated relative to the position in Sūrya Siddhānta in method 2 and relative to position in 1940 CE in method 3. Kuppanna Sastry claims that the third method is a direct method which does not depend on any other dating.
3. Method 3
Kuppanna Sastry has described the third method as follows:
We can also calculate the time directly by comparing the position of Śraviṣṭhā (β Delphini) at the time when the winter solstice was 270°, with its position in 1940 A.D. (Rt. as. 20h 36m 51s = 309° 13′, and declination 15° 42′ N). In the figure: The obliquity is about 23° 40′, γ is the vernal equinox, S is Śraviṣṭhā and R its Rt. As. position. Rγ = 360° — Rt. as. = 50° 47′. RS is the declination = 15° 42′. RS′ is the continuation of SR up to the ecliptic. Now:
(i) From the rt. angled spherical triangle RγS′, it can be calculated that RS′ = 18° 46′; S′γ = 53°13′; and angle S′ = 75° 17′.
(ii) From the rt. angled spherical triangle SS′S′′, S′S′′ = 9° 53′3′′, S′′ being the celestial longitude of S in A.D. 1940. It was at 270° at the time required. Therefore, the precession is 360° — 53° 13′ — 270° + 9° 53′ = 46° 40′. Multiplying by 72, the time is 3360 years before A.D. 1940, i.e. c. 1400 B.C. If the beginning of the segment is meant and Śraviṣṭhā is about 3° inside, it is c. 1180 B.C. Since all these is subject to small errors of observation, it would be noted that we have got from all almost the same date for VJ. 
The date of Vedāṅga Jyotiṣa in this method is calculated by the difference in the position of the yogātarā of Śraviṣṭhā during the time of the composition of the Vedāṅga Jyotiṣa and 1940 CE. There is no need to get into the details of the mathematical calculation performed by Kuppanna Sastry, as the aim was simply to estimate the date when β Delphini was at winter solstice. Nowadays the date can be accurately determined using astronomical software.
To obtain the date when β Delphini was at winter solstice using Stellarium, it is important to note that the ecliptic longitude of the winter solstice is 270° as shown in Figure 3. The date obtained by Stellarium is circa 1350 BCE as shown in Figure 4. Kuppanna Sastry estimates that β Delphini was at winter solstice circa 1400 BCE. This matches reasonably with the date obtained by Stellarium. Kuppanna Sastry next says that the currently accepted yogatara of Śraviṣṭhā, β Delphini, was 3° inside the Śraviṣṭhā nakṣatra and based on that the winter solstice was at the beginning of Śraviṣṭhā nakṣatra in circa 1180 BCE. Kuppanna Sastry then notes that all three methods yield reasonably matching dates between 1150 BCE to 1400 BCE, the difference being attributable to observational errors.
It all seems fine until it is realized that the information given in Sūrya Siddhānta has been fudged by the interpretation of the given coordinates as polar coordinates. With the assumption of given coordinates as polar coordinates, the ecliptic longitude of the yogatārā of Śraviṣṭhā has been converted to 296⁰ 15′ from 290⁰ given in the text. This makes the yogatārā of Śraviṣṭhā nearly 3° inside the Śraviṣṭhā nakṣatra, while the evidence is clearly the opposite. Sūrya Siddhānta explicitly mentions that the yogatārā of Śraviṣṭhā nakṣatra was outside the Śraviṣṭhā nakṣatra. According to Sūrya Siddhānta (8.1–9), the yogatārā of Śraviṣṭhā nakṣatra was at the junction of 3rd and 4th quarter of Śravaṇa nakṣatra. The span of Śraviṣṭhā nakṣatra was between 293° 20′ to 306° 40′, while its yogatārā had the longitude of 290° 0′ . Thus when the beginning of Śraviṣṭhā nakṣatra had a longitude of 270°, its yogatārā had the longitude of 266° 40′. Figure 5 shows that the assumed yogatārā of Śraviṣṭhā, Rotanev (β Delphini), had a longitude of 266° 40′ in circa 1590 BCE. This is clearly outside the accepted dates of the composition of Vedāṅga Jyotiṣa. However the date of the composition of Vedāṅga Jyotiṣa was even earlier as discussed below.
Śraviṣṭhā nakṣatra has four stars as shown in Figure 6. The details of these stars are given in Table 1. Currently, Rotanev (β Del) is the accepted yogatārā of Śraviṣṭhā nakṣatra. However, the yogatārā of Śraviṣṭhā nakṣatra should be Al Salib (γ2 Del). The star Al Salib (γ2 Del) has relative longitude of 289° 57′ in the Aświnī-beginning Rohiṇī system, which is an excellent match with the 290° 0′ longitude given in Sūrya Siddhānta [5, 6]. Thus, Al Salib (γ2 Del) has a better claim of being the yogatārā of Dhaniṣṭhā than Rotanev (β Del).
The star Al Salib (γ2 Del) was at winter solstice in circa 1585 BCE as shown in Figure 7. The star Al Salib had ecliptic longitude of 266° 40′ in circa 1830 BCE as shown in Figure 8. As discussed earlier, when winter solstice was at the beginning of Śraviṣṭhā nakṣatra, its yogatārā had an ecliptic longitude of 266° 40′. Based on the identification of Al Salib (γ2 Del) as the yogatārā of Śraviṣṭhā nakṣatra, the winter solstice was at the beginning of Śraviṣṭhā nakṣatra in circa 1830 BCE. The date of the composition of the Vedāṅga Jyotiṣa is thus determined as circa 1830 BCE.
A date closer to this date for composition of the Vedāṅga Jyotiṣa has also been proposed by Narahari Achar, who has calculated the date of circa 1800 BCE based on the identification of Deneb Algedi (δ Cap) as the yogatārā of Śraviṣṭhā Nakṣatra . Deneb Algedi has J2000.0 ecliptic longitude of 323° 33′ and ecliptic latitude of -2° 36′. The yogatārā of Śraviṣṭhā Nakṣatra has the latitude of 36° according to Sūrya Siddhānta (8.1–9). Deneb Algedi is close to the ecliptic and south of the ecliptic, while the yogatārā of Śraviṣṭhā Nakṣatra is far north from the ecliptic according to Sūrya Siddhānta. Thus the identification of Deneb Algedi as the yogatārā of Śraviṣṭhā Nakṣatra is without merit.
The reason Narahari Achar has obtained a date close to 1800 BCE is due to the ecliptic longitude of Deneb Algedi being approximately 4° greater than the ecliptic longitude of Al Salib, the proposed yogatārā of Śraviṣṭhā nakṣatra. As discussed above, the ecliptic longitude of the beginning of Śraviṣṭhā nakṣatra is 3° 20′ greater than the ecliptic longitude of its yogatārā. This makes the ecliptic longitude of Deneb Algedi very close to the ecliptic longitude of the beginning of Śraviṣṭhā nakṣatra as specified in Sūrya Siddhānta (8.1–9). Thus the close matching of the date of composition of the Vedāṅga Jyotiṣa derived by Narahari Achar with my work is fortuitous and not based on in-depth analysis of the textual data.
To put things in perspective, the date of the composition of the Vedāṅga Jyotiṣa has been brought forward by up to 650 years based on two factors. First, the longitude of the yogatārā of Śraviṣṭhā nakṣatra has been increased from 290° to 296° 15′ by asserting that the coordinates given in the Sūrya Siddhānta are polar coordinates. Thus the yogatārā of Śraviṣṭhā nakṣatra has been artificially positioned inside the Śraviṣṭhā nakṣatra by 2° 55′. The actual position given in the Sūrya Siddhānta (8.1–9) is 3° 20′ outside the Śraviṣṭhā nakṣatra. This results in pushing forward the beginning of Śraviṣṭhā nakṣatra by 6° 15′. Second, Rotanev (β Del) has been selected as the yogatārā instead of Al Salib (γ2 Del). The difference in their ecliptic longitudes is approximately 3°. In effect, the beginning of Śraviṣṭhā nakṣatra has been pushed forward by 9° 15′. Each degree amounts to pushing forward the Indian history by 72 years. Thus 9° 15′ is equivalent to pushing Indian history forward by approximately 666 years. This is roughly the time difference between the beginnings of Mauryan era and Gupta era. This is also roughly the time difference between Cyrus Śaka era (550 BCE) and Śālivāhana Śaka era (78 CE). Thus we see that both historical information and astronomical information have been misinterpreted to give the impression that they corroborate each other.
1. Kuppanna Sastry, T.S. (1985). Vedāṅga Jyotiṣa of Lagadha in its Ṛk and Yajus recensions. New Delhi: Indian National Science Academy, pp. 13–15.
5. Roy, R.R.M. (2019). Sidereal Ecliptic Coordinate System of Sūrya Siddhānta, Indian Journal of History of Science, 54(3): 286–303.
6. Roy, R.R.M., 2020. Zero points of Vedic Astronomy. Mississauga, Ontario, Canada: Mount Meru Publishing.
7. Narahari Achar, B.N. (2000). A case for revisiting the date of Vedāṅga Jyotiṣa. Indian Journal of History of Science, 35(3): 173–183.
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.