Introduction

Vedāṅga Jyotiṣa is the oldest known mathematically codified calendric text of South Asia. The date of this text is, therefore, of crucial importance in the examination of history of mathematics and astronomy in South Asia. The first attempt to date Vedāṅga Jyotiṣa was made by Dīkṣit (1969) more than 100 years ago. Dīkṣit based his date of Vedāṅga Jyotiṣa on the interpretation of verses RJ.5-6 and YJ.6-7. The same approach was followed by Kuppanna Sastry (1984). The verses RJ.5 and YJ.6 state that “when the Sun and the Moon occupy the same region of the zodiac together with the asterism of Śraviṣṭhā at that time begins the yuga, and the (synodic) month of Māgha, the (solar seasonal) month called Tapas, the bright fortnight (of the synodic month, here Māgha), and their northward course (uttaram ayanam)” Kuppanna Sastry (1984). Both Dīkṣit and Kuppanna Sastry arrive at a date between 1500BCE and 1100BCE. Both these scholars assumed that the star β Delphini was the yogatārā of the nakṣatra Śraviṣṭhā. This identification of the yogatārā was from Burgess (1935), who identified yogatārās given in Sūryasiddhānta. This is a text of the Siddhānta period and the yogatārās identified during this period may not be the same as those identified during the Vedic period.

This date has been contested for over 100 years. The currently accepted date (particularly by western scholars) of Vedāṅga Jyotiṣa is the last half of first millennium BCE (Pingree, 1970, 1973). This date is based on the astronomy and language of Vedāṅga Jyotiṣa. There are similarities between aspects of Vedāṅga Jyotiṣa and Assyrian/late Babylonian astronomy. There was also a possible connection between these two astronomies (or accurately a connection between the cultures of Mesopotamia and South Asia) during the Achaemenid occupation of north-western South Asia from 513 BCE to 326BCE. The implication being that the mathematical astronomy of Vedāṅga Jyotiṣa was transmitted to South Asia from Mesopotamia and there is no original contribution by South Asians to Vedāṅga Jyotiṣa. This and such reasoning implicitly deny independent parallel or sequential developments of a subject at multiple centres. Moreover, the Achaemenid conduit is irrelevant since there was exchange of goods, ideas and people between South Asia and the Middle East long before and after the Achaemenid rule. The complete absence of any Mesopotamian words in Vedāṅga Jyotiṣa or in any Vedic text argues strongly against any Mesopotamian influence let alone borrowing by South Asians from Mesopotamian astronomy. The contention that Vedāṅga Jyotiṣa was transmitted to South Asia during Achaemenid occupation is just a restatement of the now discredited nineteenth and early twentieth century belief that conquest and subjection were the engines of change and progress.

The reconstructed evolution of Sanskrit literature from early Vedic to Classical places the linguistic form of Vedāṅga Jyotiṣa in the last half of first millennium BCE. It is possible that the text available now was composed in the last half of first millennium BCE. However, the Vedic texts were frequently reworked and the content of Vedāṅga Jyotiṣa may be much older, not unlike Euclid’s Elements or MULAPIN (Hunger & Pingree, 1989).

A re-evaluation of the date of Vedāṅga Jyotiṣa is essential given the large discrepancy in the date obtained from internal evidence and that inferred from circumstantial evidence.

Narahari Achar (2000) has re-examined the method of Dīkṣit and Kuppanna Sastry; he has correctly pointed out, as noted earlier, that the stars selected as yogatārās by the medieval astronomers my not be the same as those selected by the Vedic sky-watchers and secondly β Delphini (and about eleven other nakṣatras and their yogatārās) is quite far from the ecliptic. According to the Vedic texts the moon moves in the vicinity of the nakṣatras (e.g. RV. X.85.2); Narahari Achar, therefore, asserts that all nakṣatras should be within ± 10° of the ecliptic. This is a conjecture by Narahari Achar as he has provided no textual evidence. Narahari Achar has reinterpreted the passage “the Sun and the Moon occupy the same region of the zodiac together with the asterism of Śraviṣṭhā at winter solstice” to mean that at the epoch of Vedāṅga Jyotiṣa the asterism of Śraviṣṭhā should be at right ascension of about 18h (the right ascension of the Sun at winter solstice) and no more than ± 10° from the ecliptic. He has used the planetarium software SkyMap Pro to show that a 2.83m star, δ Capricorni (Ra:21°47m 02s.4; Dec: − 16°07m38s) satisfies these conditions around 1800BCE. He has proposed δ Cap as the yogatārā of nakṣatra Śraviṣṭhā and 1800BCE as the most likely epoch of Vedāṅga Jyotiṣa. This author has made the same mistake as that made repeatedly by almost all analysts over last almost 200 years in the interpretation of astronomical references in the Vedic text; namely, the interpretation is based entirely on comparison of coordinates (a concept that would not have been known to the Vedic sky-watchers) without addressing the issue of observations. The Vedic sky-watchers did not have the benefit of a list of stellar coordinates nor did they have access to planetarium software. They would have relied entirely on naked eye observations. This is particularly pertinent in the interpretation of verses RJ.5-6 and YJ.6-7 of Vedāṅga Jyotiṣa as these verses describe exactly the configuration of the Sun, Moon and the nakṣatra at the start of a yuga. Thus an attempt to identify the yogatārā of nakṣatra Śraviṣṭhā must ascertain that this star conforms to the sky configuration described in RJ.5-6 and YJ.6-7.

Stars around winter solstice

In this study the method of Narahari Achar using his criteria is extended to all stars and to a number of epochs in the Vedic Period. The study also examines if the Vedic sky-watchers would have been able to verify that the stars that satisfy these criteria were visible in the same region of the sky as the Sun at or around winter solstice, as described in verses RJ.5-6 and YJ.6-7. This is not an attempt to identify the yogatārā of nakṣatra Śraviṣṭhā or that of any other nakṣatra. Therefore, various methods for identifying yogatārā of nakṣatras have not been considered here.

In the present analysis four randomly selected epochs in the Vedic Period are considered and all stars that occupy the same region of the sky as the Sun at winter solstice at these four epochs, that is all stars around 18h and within ± 10° of the ecliptic, are identified. In the list of yogatārās most stars are brighter than 4m and the present study is limited to the 513 stars in the sky which are brighter than 4m. In Table 1 are given stars between 2000BCE (chosen arbitrarily) and 500BCE (the putative date of the end of the Vedic era) that satisfy the conditions specified by Narahari Achar i.e. right ascension of 18h ± 30m and ecliptic latitude of ± 10°. It can be seen from Table 1 that δ Cap is close to 18h from 2000BCE to 1500BCE in agreement with Narahari Achar’s analysis. At 1000BCE δ Cap will be at right ascension of 18.9h not very far from the position of the Sun at winter solstice, but at 500BCE it will be at right ascension of 19.4h, more than 1h away from the position of the Sun at winter solstice. There are a number of other bright stars, including β Aqr, the star proposed as a possible yogatārā of nakṣatra Śraviṣṭhā by Abhyanker (1991), also at 18h ± 30m and within ± 10° of the ecliptic at almost all epochs up to 500BCE. Although these stars are not as bright as δ Cap, their brightness is entirely within the range of brightness of stars currently accepted as yogatārās. By Narahari Achar’s criteria, any one of these stars could be the yogatārā of nakṣatra Śraviṣṭhā in the period from 2000BCE to 500BCE.

Table 1 Stars at right ascension 18h ± 30m (18 ± 0.5h) and ecliptic latitude of ±10°
Full size table

For corroboration of δ Cap as the yogatārā of nakṣatra Śraviṣṭhā, Narahari Achar has shown (with the aid of SkyMap Pro) that the first full moon after winter solstice of 1752BCE (his fiducial epoch) is in the nakṣatra Maghā (yogatārā α Leonis) as required by RJ.5-6 and YJ.6-7. Note that this yogatārā is from the same list that identified β Delphini as the yogatārā of nakṣatra Śraviṣṭhā i.e. this identification is made during the Siddhāntic Period and this may not be the identifications of the Vedic sky-watchers. For each epoch in Table 1 the location (in ecliptic longitude and latitude) of the first full moon after winter solstice is given in Table 2 along with the ecliptic coordinates of all bright stars (brighter than 4m) with ecliptic latitude of ± 10° and those separated from the Moon by no more than 10°. As can be seen from Table 2, α Leo (and some other stars) is within 10° of the first full moon after winter solstice at all epochs from 2000BCE to 1000BCE. At 500BCE α Leo is slightly further than 10° from the full Moon. Not all stars in Table 2 will be visible to a casual observer. In column six of Table 2 is given the limiting magnitude at the position of the star near a full Moon (Krisciunas & Schaefer, 1991). Only stars brighter than this limiting magnitude will be visible to a human observer. The stars that will be lost in the glare of the full Moon have been identified with an asterisk in Table 2. From 2000BCE to 500BCE the bright star α Leo will be the only star visible in the immediate vicinity of the first full Moon after winter solstice and the Moon can be considered to be in the nakṣatra Maghā at all epochs during the Vedic Period.

Table 2 Stars in the vicinity of the first full moon after winter solstice. Stars within ecliptic latitude ± 10° and within the 10° of the Moon
Full size table

As a further corroboration, Narahari Achar has shown that at 1752BCE the right ascension of star ζ Hydrae, the yogatārā of nakṣatra Āśleṣā (also selected from the list of yogatārās identified in Siddhāntic Period) is close to 6h (or ecliptic longitude of 90°), that is, it is in the same region of the sky as the Sun at summer solstice. In other words, at summer solstice the Sun is in the nakṣatra Āśleṣā; as required by RJ.5-6 and YJ.6-7. In Table 3 are shown all bright stars (brighter than 4m) at 6h ± 30m (or at ecliptic longitude of about 90°) and ecliptic latitude of ± 10 for four epochs between 2000BCE and 500BCE. Note that the stars close to the position of the Sun at summer solstice are similar to the stars close to the full moon after winter solstice; this is to be expected. The full moon at winter solstice or soon after winter solstice will occupy a region of the sky similar to that occupied by the Sun at summer solstice. At all epochs in Table 3 the star ζ Hya (yogatārā of nakṣatra Āśleṣā) is close to the position of the Sun at summer solstice, that is, the Sun is in the nakṣatra Āśleṣā during the entire Vedic Period. Narahari Achar has not address the question of how the Vedic sky watchers would have determined the stars in the vicinity of the Sun at summer solstice. One possibility is that they would have identified stars in the vicinity of the full Moon at winter solstice; these stars would be in the vicinity of the Sun at summer solstice for reasons described earlier. Only stars not lost in the glare of the full Moon would be visible.

Table 3 Stars around ecliptic longitude 90 ± 10° (right ascension 6h, Sun at summer solstice) and latitude 0 ± 10°
Full size table

Discussion

The verses RJ.5-6 and YJ.6-7 define the day of the start of a new yuga. This day was of crucial importance to the Vedic people for apart from its calendrical significance it was also the first day of the annual sacrificial cycle of Gavām ayana (cows’ walk/course). In the interpretation of Vedic texts, it is essential to trust the word of the Vaidīkas and the statement (in RJ.5-6 and YJ.6-7) “when the Sun and the Moon occupy the same region of the zodiac together with the asterism of Śraviṣṭhā at that time begins the yuga” suggests (certainly to the author) that the Vedic sky-watchers had observed the stars of asterism of Śraviṣṭhā in the vicinity of the Sun at the start of a yuga. The only time a star can be seen to occupy the same region of the sky as the Sun is at heliacal rising and setting of the star. The Vedic sky-watchers were familiar with heliacal raising and setting of stars (TB.1.5.2.1, Subbarayappa & Sarma, 1985). At astronomical twilight, the Sun is between 18° and 12° below the horizon and the sky is sufficiently dark for all bright stars to be visible. In this twilight, the position of the Sun in the sky is given by a faint glow on the horizon at the point of sunrise or sunset. A star close to this point can be considered to be in the same region of the sky as the Sun. The verses RJ.5-6 and YJ.6-7 also note that at the start of a yuga the asterism of Śraviṣṭhā is in the vicinity of the Sun at winter solstice. The Vedic sky-watchers would have determined the day of winter solstice by observing the apparent motion of the Sun; they were aware that at the solstices the ‘Sun stands still’ (KB.xix.3; Keith, 1920 and a number of other Vedic texts). However, the accuracy with which they would have determined the day when the ‘Sun stands still’ is not known.

In column six and seven of Table 1 are given the day after (+ ve) and the day before (− ve) the winter solstice when the respective star would have been seen to rise (column six) or set (column seven) helically. Consider the star δ Cap, around 2000BCE this star would have been first visible (under ideal seeing conditions) in the dawn astronomical twilight (the Sun 14° below the horizon) 22 days (column six) after winter solstice. At this first sighting the star would have been at about 4° above horizon (Schaefer, 1985). The essential point is that δ Cap would not have been visible before this day. On the days following this first sighting the star would have been seen at higher altitudes in the dawn astronomical twilight. Similarly, the star’s last sighting in dusk astronomical twilight (the Sun 14° below the horizon) would have been 26 days (column seven) before winter solstice. Again the essential point is that the star would not have been visible after this day. On earlier days the star would have been sighted at higher altitudes in the dusk astronomical twilight. The presence of the Sun in the dawn and dusk astronomical twilight would have been manifested by a faint glow on the horizon at the location of sunrise or sunset. Around 1500BCE the first sighting at dawn would have been 30 days after winter solstice and the last sighting at dusk would have been 18 days before winter solstice. Similarly, the star β Aqr proposed by Abhyanker as the possible yogatārā of nakṣatra Śraviṣṭhā would have been visible at dawn 16 days after winter solstice and 19 days before winter solstice in the dusk twilight, this is at (or around) 2000BCE. Around 1500BCE this star would have been visible at dawn 23 days after winter solstice and 11 days before winter solstice in the dusk twilight. The yogatārā proposed by Narahari Achar (δ Cap) or that proposed by Abhyanker (β Aqr) would not have been visible to a Vedic sky-watcher within about ± 20 days of winter solstice. This is also true of all bright stars in Table 1, all possible yogatārā of nakṣatra Śraviṣṭhā by Narahari Achar’s criteria. It is, of course, possible that the Vedic sky-watchers would have determined the stars in the vicinity of the Sun at winter solstice by observing the stars in the vicinity of the full moon at (or around) summer solstice 6 months earlier. However, would the Vedic ritualists have relied on observations made 6 months earlier or accepted an uncertainty of ± 20 days to start a yuga or start a new cycle of the annual sacrifice of Gavām ayana?

The identification of the star β Delphini as the yogatārā of the nakṣatra Śraviṣṭhā during the Vedic Period is questionable because of reasons given in the Introduction. However, this identification should not be dismissed lightly. At winter solstice, around 1500BCE this star (and the stars of the Delphinus constellation) is at the right ascension of 17.9h and would also have been visible in the astronomical twilight at dawn and dusk at winter solstice, as has been shown by Gondhalekar (2013). This star will be at right ascension of 18h ± 30m at winter solstice for few 100 years either side for 1500BCE. The star β Delphini is, of course, not within ± 10° of the ecliptic as prescribed by Narahari Achar. This prescription, however, is questionable; Narahari Achar does not provide any evidence and (to author’s knowledge) the Vedic texts are silent on the rational for the choice of the nakṣatras or their yogatārā. In the Yajurvedic texts nakṣatra Svāti is called Niṣṭhyā (MS II.13.20; KS 39.13; TB 1.5; TB 3.14-5), that is, ‘one kept far away’ (I am grateful to an anonymous reviewer for bringing this to my notice). Although this is not evidence for nakṣatras at a distance from the path of the Moon, it does suggest that the choice of nakṣatras was more nuanced than Narahari Achar would have us believe.

Conclusion

The proposed revision of the date of Vedāṅga Jyotiṣa to 1800BCE is not substantiated by detailed analysis. This analysis demonstrates that the star δ Cap and a number of bright stars including β Aqr satisfy the conditions prescribed by Narahari Achar that is, these stars are at right ascension around 18h or they are in the same region of the sky as the Sun at winter solstice and they are within ± 10° of the ecliptic at all epochs between 2000BCE and 500BCE. Moreover, nakṣatra Maghā (identified by yogatārā α Leo) and nakṣatra Āśleṣā (identified by yogatārā ζ Hya) do not provide corroboration as the full Moon after winter solstice is in nakṣatra Maghā and the Sun is in nakṣatra Āśleṣā at all epochs between 2000BCE and 500BCE. There is an uncertainty of almost 1000 years in the proposed revised date. Moreover, the proposed yogatārā of nakṣatra Śraviṣṭhā δ Cap (and also the star β Aqr proposed by Abhyanker) will not be visible for ± 20 days around winter solstice that is, the Vedic sky-watchers would not have been able to visually verify the configuration of the Sun (and the Moon) and nakṣatra Śraviṣṭhā at the start of a yuga described in verses RJ.5-6 and YJ.6-7 of Vedāṅga Jyotiṣa.