Transit of sun through the seasonal nakṣatra cycle in the Vṛddha-Gārgīya Jyotiṣa

Abstract

Vṛddha-Gārgiya-Jyotiṣa (VGJ) is an important text of Indian astral sciences before the astronomy texts of the Common Era. Only a few of the chapters of this text have been edited and published so far. The present paper reports an important study of two sections of this text which describe the transit of Sun along the 27 asterisms (nakṣatra) during the six seasons beginning with winter. The first section called Ādityacāra describes each season to be covered by Sun travelling 4½ asterisms starting from śraviṣṭhā nakṣatra at the beginning of śiśira ṛtu reckoned as the winter solstice day. The seasons are stated in terms of Sun transiting the beginning, middle and end of nine asterisms some of which are made of more than one star. The second section of the text known as Ṛtusvabhāva starts with the vasanta ṛtu and names twelve asterisms through which Sun transits in the 12 months of the tropical year. It is shown that the solar transit information in the Ādityacāra and the Ṛtusvabhāva chapters of VGJ can be dated, for minimum observational error, to c 1300 BCE and c 500 BCE respectively.

1 Introduction

Vṛddha-gārgīya Jyotiṣa (VGJ) is an ancient encyclopedic text, originating several centuries before the more popular saṃhitā text, the Bṛhatsaṃhitā (BS) of Varāhamihira (sixth century CE). Several manuscripts attributed to Garga, Vṛddha-garga, Gārgya, Gārgīya and other variant names are available to differing levels of accuracy and readability. Such manuscripts are yet to be edited and published in readable form to properly understand and appreciate the contribution of the Vṛddha-garga or Garga School of Indic astronomy before the proliferation of Siddhānta texts of mathematical astronomy from around the beginning of the Common Era (CE).

Existence of the school of Vṛddha-Garga (VG) and/or Garga has been known for a long time. Dikshit (1896) and Sudhākara Dvivedi (1908) drew the attention of modern scholars to the text of Garga quoted by Somākara (7th century?) in his commentary on the calendar text of Lagadha in support of sun being with śraviṣṭhā nakṣatra on the winter solstice day. This observation of śraviṣṭhā (later known as dhaniṣṭhā) epoch of winter solstice seems to have been transmitted over centuries as a memorized standard. Varāhamihira in BS writes that as per ancient treatises the winter solstice occurred once upon a time with sun in dhaniṣṭhā asterism.¹ Varāhamihira refers to both Parāśara and Vṛddha-garga by name in several places, but not specifically to their winter solstice data. Bhaṭṭotpala (9th–10th century) the commentator of BS quotes extensively from Vṛddha-Garga and Garga, but attributes the above dhaniṣṭhā observation to Parāśara, further adding that it must have been an utpāta or an unprecedented anomaly.² He quotes from the prose text of Parāśaratantra (PT) to the effect that the transit of sun started from śraviṣṭhā at the beginning of the winter season, taken as the winter solstice day, to pass through the six seasons at the rate of 4½ nakṣatra (asterisms) per season. It is interesting to note that VGJ the text under study in the present paper, contains the same seasonal transit in versified form in one place, but towards the end of the compilation describes a different transit for each month of the solar year. VGJ states matter-of-fact invisibility day numbers for planets and realistic periods for eclipses and description of a sequence of comet appearances with details of rise and transit in the background of the stars. The present study is limited to a brief review of sun’s transit as given in two sections of VGJ named Ādityacāra and Ṛtusvabhāva. Analysis of this information helps one in estimating the historical origin of the School of Vṛddha-Garga, known as Vṛddha-gārgīya or just the Gārgīya tradition, before the Common Era (BCE).

2 Manuscripts of VGJ

The manuscripts of VGJ referred to by some as Gārgīya-jyotiṣa, are heavily layered with the most ancient and the relatively later parts mixed up. Since the available manuscripts are reproductions of previous versions, scribal errors are quite large in some copies. Additionally, some of the chapters in whole or in part seem to be added by the followers of the tradition of VG in the early centuries of the Common Era. Notwithstanding such difficulties a timeline of development of observational astronomy can be deciphered in VGJ. Pingree (1971) lists more than ten versions of VGJ, popularly known as Vṛddha-garga-saṁhitā, available in the manuscript libraries in India and abroad. Previously Mankad (1951), Mitchener (1986), Geslani et al (2017), Mak (2019), Iyengar et al (2019) have reviewed these manuscripts from differing perspectives and in varying details. At present only certain select chapters extracted from the manuscripts have been edited and published. Broadly, it is known that the astral sciences part of VGJ contains ideas and theories of ancient Vedic thinkers, generally followed by later astronomers. Thus, the importance of VGJ for tracing history of science in general and of Hindu astral sciences in particular can never be over emphasized.

3 Ādityacāra: sun’s transit

The astral science tradition expounded in VGJ is organized in 24 aṅga (section) and 40 upāṇga (sub-section), each such section having one or more adhyāya (chapter). Sun’s transit among the 27 nakṣatra circle forms the 11th section with a single chapter. There are 135 verses in this chapter, as narrated by Garga to Nārada, largely devoted to qualitative description of sun’s orb, shape, colour, weather changes, characteristics of seasons and portents for good and deficient rainfall. Among these are six verses, one each for the six seasons that state the position of sun among the nakṣatra starting from the beginning of the śiśira-ṛtu, which is winter. This implies that the Vedic Year started on the winter solstice day with the sun starting to move north, from its extreme southern declination. Each season is stated to cover 4½ nakṣatra stretches starting from śraviṣṭhā. One could easily see that this is same as the seasonal solar zodiac stated in the Parāśara Tantra (PT). The difference between the two is only in the style and not in the content. Parāśara’s statement is in prose known to us through quotations by later authors (Iyengar, 2013). VGJ gives the same information in versified form. The six verses are as follows:

श्रविष्ठादीनि चत्वारि पौष्णार्धञ्च दिवाकरः ।

वर्धयन् सरसस्तिक्तं मासौ तपति शैशिरे ॥

रोहिण्यन्तानि विचरन् पौष्णार्धाद्याच्च भानुमान् ।

मासौ तपति वासन्तौ कषायं वर्धयन् रसम् ॥

सार्पार्धान्तानि विचरन् सौम्याद्यानि तु भानुमान् ।

ग्रैष्मिकौ तपते मासौ कटुकं वर्धयन् रसम् ॥

सावित्रान्तानि विचरन् सार्पार्धाद्यानि भास्करः ।

वार्षिकौ तपते मासौ रसमम्लं विवर्धयन् ॥

चित्रादीन्यथ चत्वारि ज्येष्ठार्धञ्च दिवाकरः ।

शारदौ लवणाख्यं च तपत्याप्याययन् रसम् ॥

ज्येष्ठार्धादीनि चत्वारि वैष्णवान्तानि भास्करः ।

हेमन्ते तपते मासौ मधुरं वर्धयन् रसम् ॥ ( Ādityacāra; v. 47, 48, 52, 53, 54, 55)³

The text is more detailed about the environmental features and changes that occur in the seasons but the sun’s positions are stated crisply with only the starting and ending parts of the respective nakṣatra. In the above six verses the astronomical content is limited to the first half of each verse. The second half states the name of the season of 2-month duration. The month names are not mentioned. The gist of the text is as follows.

Sun’s transit starting from śraviṣṭhā nakṣatra till half-revatī is the śiśira-ṛtu; from half-revatī to end of rohiṇī is the vasanta-ṛtu. Sun’s course from the beginning of mṛgaśiras till half-āśleṣā is the grīṣma-ṛtu; from half-āśleṣā till end of hasta is the varṣa-ṛtu. Sun’s travel from the beginning of citrā till half-jyeṣṭhā is the śarad-ṛtu; from half-jyeṣṭhā ending with śravaṇa is the hemanta-ṛtu.

Here, as in the Parāśara Tantra, the seasons are linked to the position of sun with respect to stars visible in the background. This is in contrast to later siddhānta astronomers defining seasons in terms of the twelve signs or rāśi.

In VGJ the winter starts with sun in the asterism śraviṣṭhā denoted as dhaniṣṭhā in later texts. Each of the seasons is 61 days long, equal to one-sixth of the year of 366 days. The three seasons of śiśira, grīṣma and śarat start with sun respectively in śraviṣṭhā, saumya (mṛgaśiras) and citrā, to extend up to the middle/half of pauṣṇa (revatī), sārpa (āśleṣā), and jyeṣṭhā respectively. The subsequent seasons vasanta, varṣa, and hemanta are stated to continue from the same half-points of the above three asterisms, but are said to end with sun in rohiṇī, hasta and śravaṇa respectively.

Vedic astronomers had long recognized that seasons follow the sun and had qualitatively characterized them in terms of annual periodicity of felt weather, sky features, environmental conditions and social behaviour.⁴ Observation of the early morning rise of auspicious nakṣatra for performance of house hold rites as enjoined in the Taittirīya Brāhmaṇa (TB)⁵ and the recognition of maghā, śraviṣṭhā and sārpa as the background nakṣatra for defining the southern and northern transit of sun in the Maitrāyaṇīya Āraṇyaka Upaniṣat (MAU) are the easily traceable beginnings of the formation of the Vedic solar zodiac.⁶MAU says that the fiery southern transit of sun is in direct order from beginning of maghā till śraviṣṭhārdha and the milder northern transit is in the reverse order from beginning of sārpa to śraviṣthārdha. Taken in the direct order the mid-śraviṣṭhā (śraviṣṭārdha) boundary is common to both the transits. But curiously, the beginning of the southern and the end point of the northern sojourn of sun which should be temporally identical are stated in terms of two spatially distinct but consecutive asterisms. The mention of the beginning and ending nakṣatra exhibits a peculiarity that is common to MAU, PT and VGJ. To find the position of sun in a nakṣatra with several constituent stars by observation is a difficult task. By observing the star that is just above the horizon before sunrise and similarly noting the same star that is just visible in the west after sun set, one can form an idea about sun’s station in a nakṣatra. The ending and starting of the seasons are in reality seamless, but here expressed in terms of two different asterisms. We can only speculate that this may be an attempt to relate the end and start of a ṛtu with the set and rise of consecutive boundary stars. These texts are the very early specimens of observational astronomy and formation of the Indic solar zodiac, developed over the already existing lunar zodiac. The statements in VGJ are verbal expressions for technically equating the temporal extent of 183 days in one ayana and 61 days in one ṛtu on earth, counted in terms of sun rises, to the visible spatial transit of sun in the sky as a matter-of- fact observation.

Rohiṇī asterism is made of five stars, looking like the Vedic Soma-cart with a triangular plank. The bright star α Tau (Aldebaran) is located at the western end of this figure. The distance between this and the next nakṣatra namely, mṛgaśiras with three (or five) stars, usually recognized by the middle star λ Ori is about 14°. If the end of spring, when Sun is at 30° longitude, were to be recognized by the early morning rise of rohiṇī, it might take another 10–15 days for parts of mṛgasiras to be seen in the morning. Thus, when PT and VGJ declare vasanta (spring) ends in rohiṇī and grīṣma (summer) begins with mṛgasiras, a diffuse boundary is implicitly recognized between the above two asterisms. Since śiśira-ṛtu by convention started on the day of the winter solstice, sun would have been with the asterism śraviṣṭhā (dhaniṣṭhā in later texts) theoretically at 270° longitude. Based on this, all the 27 nakṣatra sectors, each taken to be 13° 20ʹ wide, can be figured out and named in their traditional order which has remained unchanged since the Vedic past. The textual statements on the seasons can be taken to be meaningful if the relative positions of the 27 nakṣatra sequence remain internally consistent. However, since the VGJ text uses phrases such as rohiṇyanta and saumyādi, without equating the two in space, this internal consistency condition of the 27 nakṣatra that are made up of more than eighty stars can be verified only in a statistical sense using a suitable error criterion. Even if the consistency condition gets satisfied, the VGJ verses can be taken to be observationally realistic if the named nine asterisms remained coevally visible on yearly basis at or near the season boundaries for a few years in the past. If such a period can be found, it would be a historical bench mark in the practice of astronomy in ancient India.

4 Nakṣatra identification

There is considerable literature on the identification of the 27–28 nakṣatra, the names of which along with interesting astral lore have come down to us from antiquity. A standard reference for the names of traditional stars and their possible identification with the help of siddhānta texts of the Common Era is the Report of the Calendar Reform Committee (Saha & Lahiri, 1955). Some of the nakṣatra are star groups and consequently several works exist on the relation between the bright stars with which moon comes in conjunction (yogatārā) of the ancient asterisms, their given longitudes in the astronomical texts of the Common Era and attempts at backward projection of such results to the ancient period. There is difficulty in correctly identifying the nirayana nakṣatra zodiac of c 285 CE, in terms of the Vedic asterisms, which if successful would have helped in knowing the ancient system of Parāśara and Vṛddha-Garga more accurately (Dikshit, 1969; Sen & Shukla, 2000). The sequential order of the nakṣatra names starting with kṛttikā has remained unchanged, except for the elision of abhijit from the original list of 28 asterisms and postulation of average travel time of nearly 13½ days for sun in each nakṣatra. As a corollary the stellar circle got divided into 27 equal divisions of 13° 20ʹ with each nakṣatra assigned to its corresponding sector.

Some of the famous nakṣatras such as kṛttikā, rohiṇi, maghā, hasta, citrā, svāti, viśākhe, jyeṣṭhā are identifiable reasonably well in terms of their modern names due to the number of member stars, their geometry and shape as stated in PT and other ancient texts. However, the same cannot be said about others such as aśvayuk (aśvini), bharaṇi, uttarāṣāḍhā, and revatī. The sequential organization of the nakṣatra system, though stable by itself, might have suffered disturbances in the assigned eponymous older divisions, due to effect of precession. This introduces uncertainty particularly in the identification of uttarāṣāḍhā, śravaṇa and śraviṣṭhā asterisms near the eliminated abhijit nakṣatra, with possibility of positional errors propagating further.

In effect, identification of the winter solstice nakṣatra of Lagadha’s Vedic calendar (Sastry, 1984) with the star α- or β-delphini and consequent dating of his work to c 1300 BCE is not as straight forward as it is generally presumed. Abhyankar (1991) pointed out this problem and also suggested corrections to the identification of some traditional stars, which will be discussed later. Previously while analysing the seasonal zodiac of Parāśara, the above difficulty of fixing the origin of the circle of seasons, was circumvented by considering only the well-known six nakṣatras namely, kṛttikā, rohiṇī, maghā, citrā, viśākhe and jyeṣṭhā represented by their constituent bright stars further identified in terms of their modern names, for verifying whether their positions as understood from the yet unidentified śraviṣṭhā at 270° remain internally compatible. Even though this does not address the textual star statements directly, visibility of the above six stars within their sectors in a year, constrain the possible epoch of PT and subsequently of VGJ to a narrow band of 1350–1130 BCE (Iyengar, 2014). For this period, it is natural to take the winter solstice star to have been in the Delphinius constellation as demonstrated by Gondalekhar (2013). Now, it remains to verify whether the star boundaries given in our text are consistent with β Del as a proxy for the śraviṣṭhā nakṣatra of the seasonal zodiac of VGJ.

Here, we face a new difficulty. Both PT and VGJ characterize the seasons by the ādi (beginning), ardha (half/middle) and anta (end) of the asterisms which have to be some type of limits associated with particular seasons and visible asterisms. Since the nakṣatras are groups made of one to six stars of varying geometrical forms, the boundaries are not at all obvious. We can only surmise that there must have been naked eye spatial markers visualized on the sky by means of an imaginary figure or astrograph made by the particular nakṣatra and nearby stars. In any case, for further analysis, it is useful to collect available data on the nakṣatras from VGJ and a few other ancient texts fixed in the centuries before the beginning of the Common Era. Apart from PT, the Atharvaveda-pariśiṣṭa (AVP), the Śardūlakarṇāvadāna (SKA) and the Sūrya-candra-prajñapti (SCP) discuss ancient astral topics including the star list. The three texts PT, VGJ and AVP are in the Vedic tradition; SKA and SCP are from the Bauddha and Jaina tradition respectively. Information available in the above texts on the number of stars, their objectivised shape and nearest possible modern star names is presented in Table 1. The visual figure of the asterism or astrograph is collected as stated in the texts, given therein as an aid for identification of the nakṣatra. In some cases, the Vedic name and its synonym indicates the shape, like the name hasta refers to the Corvus constellation looking like a hand or palm with five (fingers) constituent stars. Āśleṣā called sārpa resembles a snake-head. However, SCP sees here the shape of a dhvaja or a flag, which is equally possible.

Table 1 Nakṣatra list with star count, shape, catalogue names, proxy star and yogatārā

The Nakṣatropasarga (occultation and affliction of asterisms) chapter of the Parāśara Tantra gives the relative directions of the stars in a nakṣatra. This helps in understanding how rohiṇī with five stars is figured as śakaṭa (cart) and maghā with six stars is mapped as koṣṭāgāra (enclosure/room). SKA and SCP also give the star count and the shape of all the 28 nakṣatras of their list which is broadly same as in the Vedic tradition with a few exceptions. Some of the picturesque names given to the nakṣatra shapes are indicative of the astrograph of such asterisms. For example, in SCP the shape of jyeṣṭhā with stars α Sco, σ Sco, ε Sco, is named gajadanta or elephant tusk which is apt for the bent profile of this asterism. When a nakṣatra has only one member, SKA and SCP denote the figure as tilaka, bindu or flower. The astrographs listed in the table are as per the Vedic, PT and VGJ texts wherever available, otherwise they are taken from SCP (marked by a star) which is in some places different from the shapes meant by the Vedic tradition.

It is to be noted that the primary objective of the present study is not identification of the ancient asterisms, but finding the period when the nakṣatra of VGJ were visibly stationed in their seasonal positions. This in turn depends on how closely we are able to equate the 27 nakṣatra of VGJ with corresponding star names in current astronomical tables. As a first step the constituent stars of the asterisms with their star catalogue names can be sourced from the works of past authors. These are shown in Table 1, with a few significant differences. The total number of stars making up the twenty-seven nakṣatra as per VGJ is eighty-three; a system inherited from antecedent sources for tracking the moon.⁷ In fact, VGJ assigns unequal time for moon to transit the nakṣatra stretches. But in describing the six season solar transit, each season is equalized in time and space to be of 4½ nakṣatra span. We may infer that for lunar transit of a shorter period, unequal dwell time was more realistic, whereas when sun arrived nearly to the same nakṣatra at the solstices, equal division was a natural choice for demarcating the two ayana and the six seasons. Such a view is quite explicit in the Sāmavedic Nidāna Sūtra which takes sun to spend equal time of 13 and (5/9) days in each of the 27 asterisms.⁸ The year is 366 days long as in our text and hence expectation of the stated season boundary to be in the specified nakṣatra division of 13° 20ʹ arc is logical. However due to the extended shape of some asterisms with two to six stars, the member stars may creep into neighbouring sectors. In the literature, including astronomical siddhānta texts, the difficulty of multiple stars is handled by defining a junction star (yogatāra) usually the brightest member in the asterism. But, when mid-points of the nakṣatra form the seasonal limits, it will be convenient to have a representative proxy star that can be followed over time. Accordingly, a few comments on the selection of the proxy stars, particularly those mentioned by VGJ as seasonal boundaries, would be appropriate.

The first two nakṣatra namely, kṛttikā and rohiṇī have stood the test of time since their Vedic antiquity and are identifiable easily. The nakṣatra mṛgaśiras (saumyaṃ) with three (or five) stars is in the Orion constellation. The astrograph as deer’s head gets well defined with the α, λ, γ stars of Orion, the first and the third being brighter than the second, but λ Ori forming a vertex joining the other two. The vertex star λ Ori with two nearby dim stars is sometimes called invakā. The Yajurvedic Maitrāyaṇīya Saṃhitā (MS) gives the name invakā (invagam) for what others call mṛgaśiras and states the regent deities as maruts and not as soma. VGJ in the nakṣatra-karma-guṇa chapter describes mṛgaśiras as tritāraṁ adhikā saumyam. Even though the text is not very clear, this may mean one with three surplus stars. The famous lexicon Amarakośa characterizes mṛgaśiras as that asterism at the head of which invakā are stationed.⁹ Kṣīraswāmin the commentator of the above lexicon is clear not only about the Vedic name and the deities, but also says invakā or mṛgaśiras is made of five stars.¹⁰ Hence λ Ori near about the centre of the figure, as the proxy star for mṛgaśiras is reasonable. Abhyankar (1991) arrived at the same conclusion through different arguments. This discussion on the ancient asterism mṛgaśiras indicates that the identification of the next asterism ārdrā with α Ori (Betelgeuse) in the more ancient periods is not tenable. In the MS we read bāhuḥ nakṣatram rudro devatā in the place of ārdra. This means, the single star ārdra was located on the arm-like part of a constellation next to Orion, which is Gemini. Hence we have taken this to be the bright star γ Gem, which is same as the revised identification of ārdrā by Abhyankar following different arguments. In the case of interpreting the half-limit sārpārdha, jyeṣṭhārdha, and pauṣṇārdha in the absence of any other clarifications available, we have to select a star near the central part of the asterism figure as the proxy. The representation of the first and the second above with ζ Hya and ε Sco is straightforward since the astrograph with multiple stars is stated in the texts. The selection of ε Psc needs some explanation. Revatī is called pauṣṇaṃ since Pūṣan is the deity of this asterism. All the ancient texts mention only one star for this nakṣatra. But, the spatial extent of Pisces constellation, figured as a fish, is large and texts like SCP and BS mention 32 stars forming the figure of a canoe. Even though this location for revatī is an inherited tradition, there is a tenuous link for the fish astrograph in the Vedic texts. In the Taittirīya Saṃhitā the Vedic deity of revatī namely, Pūṣan the leader of animals is characterized as toothless and hence flour balls are prescribed as food offering in rituals.¹¹ This seemingly harmonizes with the celestial figure of toothless Pūṣan to be like fish. In the past literature revatī has been identified variously as α Psc, ζ Psc and other stars. Since, there is no mention of separation of stars in terms of angular or other distances in VGJ, we take pauṣṇārdha as the visible star ε Psc in the middle region of the Pisces constellation.

For sake of comparison, the 27-yogatārā identified by Abhyankar for the vedāṅga period is listed in the last column of Table 1.

5 Error analysis

The analysis we have to carry out is to check how closely a given nakṣatra is located in its predetermined interval corresponding to the VGJ seasonal stars. As a first step in this direction the ecliptic longitudes of each of the eighty-three stars constituting the twenty-seven nakṣatras are found for a long period with the help of the Stellarium software. Some stars will satisfy the internal location condition for some years, while many others may not do so over long time periods. To capture this information an error function E is defined as follows. Let, the desired interval of the ith asterism be (J_i to J_i+1) and its longitude in a given year y be L_i (i = 1, 2, …27). The error of location will be zero, if a nakṣatra with single star, is found to be in its division; otherwise the lesser of the absolute difference between L_i and the two boundary values J_i and J_i+1 is the error E_i. That is,

$${\text{E}}_{{\text{i}}} = \, 0\,if\,\left( {{\text{J}}_{{\text{i}}} < {\text{ L}}_{{\text{i}}} < {\text{ J}}_{{{}{\text{i}} + {1}}} } \right)\;else\;{\text{E}}_{{\text{i}}} = {\text{ min }}\left[ {{\text{abs }}\left( {{\text{L}}_{{\text{i}}} - {\text{ J}}_{{\text{i}}} } \right),{\text{ abs }}\left( {{\text{L}}_{{\text{i}}} - {\text{ J}}_{{{}{\text{i}} + {1}}} } \right)} \right]$$

For a nakṣatra with multiple stars there will be more than one sample error value which will be smoothened over the constituent stars to get the mean location error Ei (i = 1, 2…27) in any year. The location error E_y in a given year y is the average of E_i over all the 27 nakṣatra. This quantity is plotted (green broken line) in Fig. 1 for the period of (2500–250) BCE at intervals of 50 years. It is seen that the error curve is smooth and reaches its minimum around 1250 BCE. The mean positional error of consistency for any nakṣatra is about 1° during (1500–1000) BCE which is acceptable for the ancient epoch, considering that the correspondence shown in Table 1 is not perfect. One more result of consistency is shown in Fig. 1 (green full line) by considering only the 27 proxy stars. This result is not very different from the previous one, indicating the sufficiency of considering the proxy stars for further verification of the visibility condition for the nine seasonal boundary stars of VGJ. The internal consistency with minimum error exhibited by the 27 proxy and 83 constituent stars, when the winter solstice was in śraviṣṭhā, identified with β Del, upholds that the six equal division tropical zodiac was formalized in middle 2nd millennium BCE. This is still a broad picture, since seasonal dependence is inherent in the sequencing of the stars.

Fig. 1

Yearly variation of the nakṣatra location error E_y in the seasonal solar zodiac of VGJ. The green curves (.83 stars; 27 proxy stars; 9 seasonal nakṣatra) refer to the Ādityacāra data of the 11th Section of VGJ. The 83 constituent and the 27 proxy stars are as per Table 1. Errors for the nine seasonal nakṣatra boundaries remain zero during 1210–1150 BCE. The red curves refer to the 12 month solar nakṣatra data available in the 59th section titled Ṛtusvabhāva

Several older Vedic texts mention the names of the six felt seasons and 12 months of the tropical year, implying that from the extreme southern declination day of sun the onset of the seasons was estimated in terms of multiples of 61 sun rises. The texts of Parāśara and Vṛddha-Garga exhibit more sophistication in that they connect the seasons with the position of sun with visible stars.

For declaring sun’s position among the nakṣatra, which should have been useful in predicting the onset of a season in advance, careful observation of the morning and evening stars nearer to sun should have taken place over a prolonged period. Existence or otherwise of such an effort can be verified by considering the nine named asterisms (2-rohiṇī, 3-mṛgaśira, 7-āśleṣā, 11-hasta, 12-citrā, 16-jyeṣṭhā, 20-śravaṇa, 21-śraviṣṭhā, 25-revatī) as border points through which the transition from season to season was said to be taking place. This amounts to verification of coeval yearly visibility of the above nine specific nakṣatra in their respective divisions. This can be done by finding the error E_y for these nine stars separately. This result is also shown in Fig. 1 (green dot & dash line) where it is found that during 1210–1150 BCE the error of location of all the nine seasonal asterisms was precisely zero. There could be minor variations in the above result if small errors due to vague star boundaries are considered. Nevertheless, the core statement of Ādityacāra originating with the śraviṣṭhādi (dhaniṣṭhādi) scheme, cannot be more recent than 1150 BCE, from when the errors start steadily increasing.

At this stage one may question, due to the omission of abhijit from the original 28 Vedic nakṣatra system, whether our identification of the stars corresponding to śravaṇānta and śraviṣṭhādi for the start of the śiśira season needs a relook. How sensitive is our result for possible errors in identifying the Vedic śraviṣṭhā as β Del? Another question would be how sensitive are the results, if Abhyankar’s list is used for checking the positional error.

6 Abhijit, Śravaṇa, Śraviṣṭhā/Dhaniṣṭhā

Vedic texts use the nomenclature śraviṣṭhā for the 21st nakṣatra and this is followed by VGJ in 13 out of 15 places. Atharva Pariṣiṣṭa knows only the name śraviṣṭhā which is cited 19 times. Atharvaveda Saṃhitā refers to śraviṣṭāḥ in the Nakṣatrasūkta and in the Rātrisūkta.¹² The nomenclature dhaniṣṭhā is found once in the Bodhāyana Śrauta Sūtra text. The Buddhist SKA, knows only dhaniṣṭhā mentioned 22 times. These are perhaps the BCE texts to use the name dhaniṣṭhā in the place of the older śraviṣṭhā. The Mahābhārata in one place uses the nomenclature śraviṣṭhā,¹³ otherwise dhaniṣṭhā appears in four instances. The epic has the famous legend of abhijit going away to do penance when Time was made to begin with dhaniṣṭhā by Brahma.¹⁴ This makes a case for arguing that, at some time in the past the winter solstice was occurring with sun in a nakṣatra part called śraviṣṭhārdha (MAU) and still later it fell back to the beginning parts called śraviṣṭhādi (PT, VGJ). With passage of time, winter solstice was observed to be shifting towards abhijit. This changed winter solstice nakṣatra was called dhaniṣṭhā sounding similar to śraviṣṭhā and for equalizing the length of each season to 61 days covering 4½ nakṣatra, abhijit was eliminated. This must have affected visual identification of three nearby asterisms since the name of the nakṣatra and the order could not be violated. Abhyankar’s (1991) line of argument on misidentification by later authors of these three Vedic nakṣatras is different, but the conclusions are same. He worked on this issue to demonstrate that there is good ground to show that the ancient abhijit, with cow-horn as the astrograph in SCP and a small sky sector allocated between U. āṣāḍha and śravaṇa, was what is now called Aquila. Śravaṇa with the astrograph resembling an Ear was in Vedic times the constellation Delphinius, but due to the elision of abhijit, śravaṇa got identified with the constellation Aquila with three stars. This argument leads one to infer that in the older 28-nakṣatra list, śraviṣṭhā nakṣatra with five constituent stars should have been in the Aquarius constellation. After the solar equal nakṣatra system came into vogue, śraviṣṭhā with a new name dhaniṣṭhā became the winter solstice nakṣatra visualized as α, or β Del. This line of argument postulates a transition period between the 28-nakṣatra cycle year and the 27-nakṣatra tropical year divided equally into six seasons. In such a transition period, abhijit was ignored when śiśira ṛtu started with sun in Aquarius and śraviṣṭhā approximately identifiable as β Aqr and śravaṇa as β Del. The reality or otherwise of this transition period can be verified by the same methods as discussed above.

The error E_y for the 27 asterisms and also for the nine seasonal stars with the above two readjustments is shown in Fig. 2. On the same figure the error variation of Abhyankar’s 27- yogatāra list is superposed. It is observed that the overall error for the 27 asterisms, taken either as the proxy stars or as the yogatāra of Table 1, reaches its minimum still around 1250 BCE. But the interesting fact is that all the stated nine nakṣatra season boundaries would have remained visible in their respective longitudinal divisions within a year for a long period of 1700–1350 BCE. This indicates that the prose PT textual tradition of Parāśara which knew abhijit with three stars and also the śraviṣṭhādi scheme of 4½ nakṣatra per season must be more ancient than 1350 BCE. This helps us to surmise that the six-part zodiac stated in the Parāśaratantra starting with the śisira-ṛtu originated first in terms of day numbers counted from the winter solstice day. Thus, errors notwithstanding, the theoretical six division tropical zodiac was fully developed and in use by the Vedic schools of astronomy already by 1500 BCE. This stability got disturbed around 1300 BCE and observed to be so, when two new asterism identities but with old names, as discussed previously were introduced most likely by Vṛddha-Garga or his followers.

Fig. 2

Error sensitivity for possible identification of Vedic star śraviṣṭhā as β Aquari and śravaṇa as β Delphini. The readjusted 27 proxy stars and the yogatāras of Abhyankar lead to almost the same result of c 1250 BCE for the error minimum. Errors for the nine seasonal nakṣatra boundaries remain zero during 1700–1350 BCE

Once again the seasons remained true with the original nakṣatra nomenclature during a short span of 1210–1150 BCE. But this order could not remain unchanged and had to be reorganized. How this was done is not clear. But VGJ which is like a compendium of the Vṛddha-Garga tradition takes us further in time by a few centuries to the monthly transit of sun through twelve nakṣatra in the Ṛtusvabhāva section.

7 Continuity of observations

The Ādityacāra chapter with 135 verses, as it is available now, can only be quoting the above seasonal transit of sun (v. 47, 48, 52–55) from some ancient text or tradition followed by the VG School. This follows easily, once we recognise that a later verse¹⁵ (v. 125) in the same chapter mentions “sun turning north without reaching the śraviṣṭhā asterism and not reaching āśleṣā on return is cause of fear”. This is clearly an observation of the effect of precession with passage of time and taken as a bad omen due to change of the śraviṣṭhā epoch. Such an observation seems to have happened towards the beginning of the 1st millennium BCE. This follows from the 59th section (upāṅga) of VGJ known as Ṛtusvabhāvaḥ. This section has six chapters, one each for the six seasons starting with the vasanta. All the chapters are a mix of prose and poetry. Interestingly in each chapter the nakṣatra through which sun transits in the 2 months of the season is stated along with the name of the month. Thus, here for the first time in Hindu astronomy we come across the 12-month solar zodiac, not in terms of the Rāśi signs (meṣa, vṛṣabha etc.), but in terms of the names of months starting with the Vedic month madhu equated in civil calendar reckoning with caitra. The chapters have varying number of verses totalling seventy-five, increased further with archaic prose sections that describe the seasons qualitatively in terms of weather, flora, fauna and social behaviour. Here only the text of interest containing information on sun’s transit is presented followed by a gist for further analysis.

वसन्तघर्मौ जलदागमश्च विद्याच्छरद्धैमतशैशिरौ च ।

ऋतून् पृथग्लक्षणतः प्रवक्ष्ये संवत्सरं ये परिवर्तयन्ति ॥

तेषामुदग्दक्षिणतश्च गच्छेद्यावान् विवस्वान् प्रचिनोति तावान् ।

तांस्तान् प्रवक्ष्यामि तथैव सर्वान्यथा च वै लौकिकवैदिकानि ॥

यद्रेवती ऋक्षमुपैति भानुश्चैत्रः स मासो मधुसंज्ञकश्च ।

वैशाखमासोऽपि च माधवश्च तदा हि भानुर्भरणीगतः स्यात् ॥

एतैर्वसन्तः समयैर्विदध्याद्द्वौ द्वौ च पक्षौ भवतीह मासः । (VGJ Aṅga 59; Ch.1)

I shall explain individually the character of the seasons; vasanta, grīṣma, varṣa, śarat, hemanta, śiśira that cyclically change the year. Also, I will explain, as sun goes from north and from south, his access to the civil and the Vedic months. When sun attains revati asterism, that month is caitra also known as madhu. Vaiśākha is also the mādhava month. Then sun would have reached bharaṇi. By this vasanta ṛtu is recognized and each month is made of two fortnights.

शुचिशुक्रौ मृगशिरो गच्छत्कुर्यात्तु भानुमान् ।

तथा पुनर्वसू चैव ज्यैष्ठाषाढौ तु तौ स्मृतौ ॥

एतौ मासौ विजानीयाद्ग्रैष्मिकौ कालवित्तमः । (VGJ Aṅga 59; Ch.2)

Sun in mṛgaśiras is the month śuci known also as jyeṣṭha. Sun in punarvasū is the śukra month same as āṣāḍha. These two months are to be known as the grīṣma ṛtu.

नभस्तु कुर्तयादुपसर्प्यमाणो रविर्मघाश्रावणजातसञ्ज्ञा ।

तत् प्रोष्ठदं च तथा नभस्यं गत्वा विदध्याद्भगदैवतर्क्षम् ॥

एतौ तु वार्षिकौ मासौ विद्यात्कालविशारदः । (VGJ Aṅga 59; Ch.3)

When sun approaches maghā, the month is nabhaḥ known as śrāvaṇa. Next, having gone to pūrva-phalguni sun makes the nabhasya month same as bhādrapada. These two are the rainy months (vārṣikau māsau).

इषुमाश्वयुजं विद्याद्भानुश्चित्रागतस्तदा ।

कार्तिकं जनयत्यूर्जमैन्द्राग्न्यं प्राप्यरश्मिवान् ॥ (VGJ Aṅga 59; Ch.4)

Month iṣu equivalently āśvayuja is when sun has reached the citrā asterism. Sun generates kārtika month also known as ūrja having reached the viśākhe asterism.

ऐन्द्रं समासाद्य तथोष्णरश्मिः स मार्गशीर्षं सहसं करोति ।

अब्दैवते त्वेव गतः सहस्यं पौषं विदध्यात् प्रचिनोति मासम् ॥(VGJ Aṅga 59; Ch.5)

Sun in jyeṣṭhā nakṣatra makes the mārgaśira month same as sahas. When sun goes to pūrvāṣāḍha, it is the month of pauṣa or sahasya.

गतश्रविष्ठासमयं तु माघस्तपोविधत्ते भगवान् विवस्वान् ।

सफाल्गुनं चापि तथा तपस्यं पूवां रतप्रोष्ठपदां करोति ॥

ऋतुं तु विद्याच्छिशिरं विचार्य तस्यैव भावावयवं च सम्यक् । (VGJ Aṅga 59; Ch.6)

The month of māgha or tapas is when the time for śraviṣṭhā is past. Sun makes the month phālguna or tapasya having attained the pūrvābhādrā nakṣatra. This should be understood as the siśira ṛtu with is parts and features.

The above solar transit is different from the previous one, not only in the star positions but more so in the way it is organized and stated. The description is still about the seasons, but here it begins with the vasanta (spring) and not the śiśira (winter). The older ādityacāra was only about the seasons with no mention of the months. Here the stress is on the months for which their Vedic and laukika (civil/popular) names are given. Seasons are mentioned only in terms of the months and not as per any nakṣatra boundaries. For each month starting from madhu/caitra, the prominent nakṣatra through which sun passes is mentioned. This way there are 12 months and correspondingly twelve nakṣatra, each spanning 30° in longitude. The equinox is here reckoned in the middle of the vasanta ṛtu, and the starting of the mādhava/vaiśākha month, with sun passing through the asterism bharaṇi. The implication is that this month started on the equinox day. The text does not name aśvini after revatī, through which sun had to transit before arriving at bharaṇi. Similarly, kṛttikā, rohiṇī are not mentioned before sun is said to be in the mṛgaśiras nakṣatra in the month jyeṣṭhā. The text is in line with the older tradition of reckoning the winter solstice as the start of the śiśira ṛtu. But, in the month of māgha, asterism śraviṣṭhā is mentioned not as with sun, but having past its time. The text just narrates the stars that were visible in the months that are named and counted starting from the vernal equinox or nearby full moon or new moon. This seems to be the origin of the solar calendar of twelve months, without any need for intercalation.

We can get an idea of the period in which the above 12-month solar zodiac was organized by finding the location error for the twenty-seven asterisms starting with the first named bharaṇi sector stretching from zero to 13° 20ʹ longitude as done previously. The result is shown in Fig. 1 (red lines) side by side with the results of the earlier seasonal zodiac. Clearly in the VGJ text there are two different observations of sun’s position among the nakṣatra, separated by 700 to 800 years. One can further find an interval in which the twelve stated asterisms would have been visible in a given year in the specified months. This turns out to be (620–160) BCE. Since the text is silent on the visibility of adjacent nakṣatra in the named months, the above interval cannot be further refined. However, beyond reasonable doubt, we can say that the observational data available in the Ṛtusvabhāva section of VGJ belongs to the epoch of 600–500 BCE. As a demonstration of this, for the year 500 BCE the ecliptic coordinates of the eighty-three stars making up the twenty-seven nakṣatra are plotted in Fig. 3. The points are joined smoothly for better visualization with markings for the seasons and the months. It can be verified that all the twelve nakṣatra named in the VGJ text would have been visible sometime in the specified months.

Fig. 3

Twelve month (madhu-tapasya) or (caitra-phālguna) Sun’s transit in 500 BCE as per the Ṛtusvabhāva (59th aṅga) of VGJ

8 Discussion

In popular parlance nakṣatras are taken as twenty-seven stars with which moon comes in contact. However, since Vedic antiquity several nakṣatras are composed of multiple stars. All the five ancient texts shown in Table 1 state the number of stars for each of the nakṣatra, obviously due to some special importance attached to that number. We guess by hindsight, that multiple stars might have helped the ancient observers to follow the wavy path of moon, by recognizing some of the nakṣatra to have more than one star, for clarity in visual perception and memory. This was before aṁśa (1/4) and ardha (1/2) nakṣatra parts as in MAU came into vogue among particular groups of sky observers. VGJ in its chapters on the transit of moon postulates the conjunction of moon with a nakṣatra as being of three types; leading, following and at same level. It also states three groups of nakṣatra with which moon spends 15, 30 or 45 muhūrta of time in its sidereal month cycle of about 27 1/3 days. Such an observational model directly leads to vague spatial domains and unequal longitudinal intervals for the visible asterisms. Investigation of the unequal nakṣatra system is beyond the scope of the present paper, but it suffices to point out that the sequence of 28 nakṣatra with augmented star counts as background points for observing and remembering moon’s spatial position should have existed from very ancient times. Gradually associating nakṣatra with sun arose once the seasons were differentiated, named and recognized as six in a year. The nakṣatrasūkta of the Atharvaveda (19.7) hints that one of the two north–south-north transit of sun happened in the asterism maghā.¹⁶ This must have been the southern sojourn (dakṣiṇāyana) of sun when some stars of the maghā asterism such as α, η-Leo were at around 90° longitude. The Yajurvedic MAU specifically differentiates the felt weather for sun’s north to south transit from maghā to half-śraviṣṭhā for 6 months as hot and the 6 month return from south to north as mild. Starting with such formulations in the Vedas proper, astronomy emerged as an ancillary to the Vedas by the middle of the second millennium BCE, to be aptly called Vedāṅga Jyotiṣa.

Three textual traditions of Jyotiṣa attributed to Parāśara, Vṛddha-Garga and Lagadha, have come down to us from this period. Among these three, the first called the Parāśaratantra (PT) being largely in prose stands in stark contrast with the other two. This is the first text to give the six seasonal solar zodiac; conditions for the rise and set of the southern star Agastya (Canopus); visibility day numbers for Venus, Mercury, Jupiter, and Saturn. This is also the first text to list twenty-six comets with names, their transit among the stars and arrival intervals in years. The second text denoted here as VGJ contains archaic prose parts and also long versified chapters on varied topics added at later dates. The text seems to have had an original nucleus in the 24th section named the Mahāsalilaṁ over which later layers have been deposited in differing order. It is plausible that PT and VGJ originated as independent traditions, but over time VGJ seems to have inherited the astral content of the Ādityacāra, some parts of Rāhucāra and large parts of Ketucāra from PT. VGJ is more detailed about moon, the sidereal and synodic months and the unequal time spent by moon with the asterisms. Both the texts present matter-of-fact sky observations. VGJ is more detailed, repetitive and with texts of several other authors interpolated by the manuscript copyists. While PT is purely observational, VGJ recommends combination of observation and computation in the context of moon’s conjunction with the stars.¹⁷VGJ has long chapters devoted to each of the five planets, with quantitative information on visibility and retrograde movement of Mars, which is absent in PT. Lagadha’s work on finding the position of sun and moon in the 5-year cycle is short and terse but more sophisticated than the other two being entirely computational. The common factor of all the three is their Vedic origin, absence of week days and Rāśi (Sign) notation and starting of the yearly cycle at the winter solstice point, even if the determination of this were to be approximate. If we take the general view that sky observations precede computational approaches, the chronological order of the three Vedāṅga Jyotiṣa tradition has to be first PT, next VGJ, followed by the Ārca-yājuṣa-jyotiṣa of Lagadha. All the three have Vedic precedents as well as later interpolations, but interestingly in VGJ we get a verifiable temporal separation of eight centuries (c1300 to 500 BCE) between two chapters on the transit of sun through the nakṣatra circle.

9 Conclusion

The nakṣatra system for tracking moon in the background of stars has been in vogue since very ancient times. As interest in understanding the relation between seasons and the position of sun grew, identifying some special nakṣatra for heralding important seasons came into practice. Naked eye observation of rise of sun in the extreme south position of the horizon was the starting of the śiśira ṛtu, harmonized as the winter solstice day. Probably in the early days when observation of sun’s position with a nakṣatra was not yet practiced, the onset of the seasons was counted in number of days starting from the vague winter solstice day. With evidence for observing early morning Vedic nakṣatra before sunrise as in the Taittirīya Brāhmaṇa and the northern and southern sojourn of sun correlated with visible nakṣatras as in MAU, we can say that a primitive solar zodiac was theoretically conceptualized in the core Vedic period with two ayana, three cāturmāsya and six ṛtu (seasons). This background work got empirically formalized in PT and VGJ by observing the seasonal boundary nakṣatras in the early morning sky, by which the onset of the seasons could be forecast. Such seasonal nakṣatra information available in VGJ, in two different sections, is analyzed in the present study. Sun’s transit through the six seasons mentioned in terms of nine nakṣatra names forms part of the earlier Ādityacāra section. This can be shown to belong to c 1300 BCE. The Ṛtusvabhāva section wherein prominent twelve nakṣatras through which sun transits in the 12 months of the year are stated can be dated to c 500 BCE. This by itself should be of interest in following how the original Vṛddha-Garga school has contributed to the development of astral literature in India before the Common Era.