Jyotişa : Tropical or Sidereal?
Over the past few years there has been a lot of talk about whether the tropical or the sidereal zodiac is valid for use in jyotiṣa, especially for horoscopy. Here I try to go over the oldest source texts to explain how both zodiacs are found in them, but are meant for different purposes.
The best known system of dividing the ecliptic from ancient India is that of the twenty-seven nakṣatras, which originated as a means to study the movement of the Moon, Sun and planets across a fixed backdrop of the stars in the night sky. The tradition of reckoning the nakṣatras as twenty-seven equal divisions of the ecliptic seems to originate in the Vedic Saṃhitās where Soma (the Moon) is said to be married to asterisms and spends equal time with each of them. The Maitrāyaṇīya Āraṇyaka Upaniṣad (also known as the Maitri Upaniṣad) divides the circle of the zodiac into two equal halves along the initial point of Magha and the middle point of the Śraviṣṭhā nakṣatra (assignable to 1800 BCE), implying the use of twenty-seven equal nakṣatras -
सूर्यो योनिः कालस्य तस्यैतद्रूपं यन् निमेषादिकालात्सम्भृतं द्वादशात्मकं वत्सरमेतस्याग्नेयमर्धमर्धं वारुणं मघाद्यं श्रविष्ठार्धमाग्नेयं क्रमेणोत्क्रमेण सार्पाद्यं श्रविष्ठार्धान्तं सौम्यम् तत्रैकैकमात्मनो नवांशकं सचारकविधम् सौक्ष्म्यत्वादेतत्प्रमाणमनेनैव प्रमीयते हि कालः
“… Sun is the birth place of Time. The form of Time is the year, consisting of twelve (months), made up of nimeṣa and other measures. Of the year one half is āgneya and the other half vāruṇa. The āgneya half begins with the asterism of Magha, and ends with the half of Śraviṣṭhā; this being Sun’s southern travel. That which is saumya, in the reverse order, is from āśleṣā, to the half-end of Śraviṣṭhā; this is the northern course. And then, there is (the month), one by one, belonging to the year, each consisting of nine-amśa (quarter) of asterisms, each determined by the Sun moving (with the asterisms). Because Time is too subtle (for sensory perception) this progress of the Sun is its evidence (or proof), and by it alone is Time cognized…”
- Maitrāyaṇīya Āraṇyaka Upaniṣad 6.14
The nakṣatras as twenty-seven equal divisions of the ecliptic identified with a specific star or constellation are found both in Lagadha’s Vedāṅgajyotiṣa and the Parāśara Tantra, where six seasons are measured through the motion the sun across equal segments of the zodiac, each measuring four and a half nakṣatra.
There are references to the celestial wheel being divided into twelve parts in the Ṛgveda, as a possible reference to both the wheel of time (a year of twelve months), as well as to a twelve-fold division of the ecliptic -
द्वादशारं नहि तज्जराय वर्वर्ति चक्रं परि द्यामृतस्य।
आ पुत्रा अग्ने मिथुनासो अत्र सप्त शतानि विंशतिश्च तस्थुः ॥1.164.11॥
“The twelve-spoked wheel of the true (Sun) revolves round the heavens, and never (tends) to decay : seven hundred and twenty children in pairs, Agni, abide in it.”
द्वादश प्रधयश्चक्रमेकं त्रीणि नभ्यानि क उ तच्चिकेत।
तस्मिन्त्साकं त्रिशता न शङ्कवोऽर्पिताः षष्टिर्न चलाचलास: ॥1.164.48॥
“The fellies are twelve; the wheel is one; three are the axle; but who knows it?
Within it are collected 360 (spokes), which are, as it were, both moveable and immovable.”
The twelve fellies of the wheel can be taken as the twelve months of a civil year with thirty days each, consisting of a total of 360 days, or 720 days and nights. The three axles could be the three different interpretations of the wheel, which is explained in the Śatapatha Brāhmaṇa (SB) of the Śukla Yajurveda. The first interpretation is as a circle divided into 360 equal parts (SB 10:5:4:4) -
“But, indeed, that Fire-altar also is the sun: — the regions are its enclosing-stones, and there are three hundred and sixty of these, because three hundred and sixty regions encircle the sun on all sides;”
The second is as a circle of the 27 equal naksatras, and the 27 equal subdivisions (upanakṣatra) of each (SB 10:5:4:5) -
“But, indeed, that Fire-altar also is the Nakṣatras: — for there are twenty-seven of these Nakṣatras, and twenty-seven secondary stars accompany each Nakṣatra, — this makes seven hundred and twenty, and thirty-six in addition thereto.”
The third is as a civil year of 360 days and nights (SB 10:5:4:10) -
“But, indeed, that Fire-altar also is the Year, — the nights are its enclosing-stones, and there are three hundred and sixty of these, because there are three hundred and sixty nights in the year; and the days are its Yagushmatî bricks, for there are three hundred and sixty of these, and three hundred and sixty days in the year;”
Therefore the wheel is conceptualised in essentially two ways — temporally (as the year) and spatially (as a zodiac). The circle of the zodiac is divided into equal parts corresponding to the measure of the Sun’s motion in various divisions of the year — 12 parts for each of the 12 months, 360 parts for each day, 720 parts for each day and night and so on. These smaller partitions of the zodiac are made using various subdivisions of the 27 equal nakṣatras, e.g. 27 equal sub portions (upanakṣatra) makes a total 729 divisions, a good approximation for 720. We see the use of aṁśa (¼) i.e. quarter part of a nakṣatra in the previously quoted section of the Maitri Upaniṣad [6.14], which divides the ecliptic into 108 equal parts. It can also be argued that because the original list of 27 nakṣatras contain only 24 distinct names, each representing the 24 half months of the year and hence 24 equal divisions of the ecliptic. Further, a day is divided into 60 nāḍikās in Lagadha’s Vedāṅgajyotiṣa, this means that the degree (representing the Sun’s motion in one day) can further be divided into 60 parts (i.e. minutes). Thus we see that the ecliptic has various smaller subdivisions (24, 108, 360, 720 and so on) corresponding to equal partitions of the nakṣatras. The twelfth division of the ecliptic can be conceptualised as a grouping or sum (rāśi) of these nakṣatra segments — each of the 24 nakṣatras as the rāśi’s half (hora), aṁśa/quarters as the ninth part (navāṁśa), upanakṣatras as the sixtieth part (ṣaṣṭiāṁśa) etc. This is how a zodiac sign as a rāśi is described in Yavanajātaka [1.44] :
“They call (a sign) a “collection” (rāśi) in order to distinguish the activities of these corresponding (parts); this is immeasurable like the waters of the sea because of doubts as to the variety of their mutual interrelationships.”
Since the nakṣatras and their subdivisions are sidereal by definition, so too are the twelve rāśis.
The year on the other hand was measured tropically, beginning with the winter solstice and divided into two ayana (halves), three cāturmāsya (four month periods), six ṛtu (seasons) and twelve solar months. Parāśara Tantra contains a passage describing the six seasons equalized in time and space to each be of 4½ nakṣatra span, starting with the śiśira ṛtu at the beginning of śraviṣṭha (which was the point of winter solstice for his time) -
तस्य श्रविष्टाद्यात् पौष्णान्तम् चरतः शिशिरः । वसन्तः पौष्णार्धातु रोहिण्यान्तम् । सौम्यात् सर्पार्धम् ग्रीष्मः । प्रावृट् सर्पार्धात् हस्तान्तम् । चित्राद्यात् ऐन्द्रार्धं शरत् । मन्त ज्येष्टार्थात् वैष्णवान्तम् इति ।।
“Śiśira (cold season) is when he (Sun) transits from beginning of Dhaniṣṭhā till middle of Revati. Vasanta (spring) is from middle of Revatī till end of Rohiņi. Grīşma (summer) is from beginning of Mṛgaśirā till middle of Āśleṣā. Varṣā (rainy season) is from middle of Aśleṣā to end of Hastā. Śarat season is from Citra to middle of Jyeṣṭhā. Hemanta (dewy season) is from middle of Jyeṣṭhā to end of Śravana.”
This seasonal measurement across four and a half nakṣatras was adopted by Lagadha in his Vedāṅga-jyotiṣa [Rg-VJ 9]. In the Taittirīya Saṃhitā [4.4.11.1] each of the six seasons are associated with the two Vedic solar months (Tapa and Tapasya with Śiśira, Madhu and Mādhava with Vasanta, and so on), and each solar month is associated with a solar deity (Āditya) in the Śatapatha Brāhmaṇa [11.6.3.8].
Parāśara’s six fold seasonal zodiac (“Parāśaratantra”, R.N. Iyengar, p. 76)
In the Maitri Upaniṣad [6.14] we find that the winter solstice is placed in the middle of the asterism Śraviṣṭhā (śraviṣṭhārdha), but some 400–500 years later Parāśara (~1350 BCE) shifts it to the beginning to Śraviṣṭhā (śraviṣṭhādi) to account for the effects of precession. Another verse quoted by Bhattotpala attributed to Parāśara describes the effects of the Sun not reaching the Śravaṇa nakṣatra on winter solstice instead of Śraviṣṭhā, valid for 400–300 BCE.
Thus we have evidence that the point of the winter solstice was understood to be drifting backwards with time, and beginning of the year and the seasons were being updated accordingly.
The beginning of the Vedic tropical year was marked by the sun’s position in the Dhaniṣṭha nakṣatra on the winter solstice day, and the counting of the nakṣatras began from Kṛttikā since the vernal equinox was located in it. The following statements by Vṛddha-garga explain this tradition for his times :
तेषां च सर्वेषां नक्षत्राणां कर्मसु कृत्तिकाः प्रथममाचक्षते । श्रविष्ठा तु सङ्ख्यायाः पूर्वा लग्नानाम् ।
“The first of all those nakṣatras in sacrificial actions is Krittika. Śraviṣṭhā is the first of the count of the ascendants (lagnas).”
Kṛttikā was chosen as the first nakṣatra for sacrificial purposes due to its attribution to the spring equinox, and therefore all the oldest Vedic texts begin the list of nakṣatras with it. The count of the sidereal ascendants (lagnas) in a five year yuga begins with Dhaniṣṭha, the rising nakṣatra at sunrise on the winter solstice at the beginning of the year (also found in Lagadha’s Vedāṅgajyotiṣa — R-VJ 19). Both the nakṣatras (Kṛttikā, Dhaniṣṭha) were hence useful for marking the cardinal points of the year for timing various rituals. However, due to the effects of precession, they were not thought to be suitable to mark the fixed zero point of the sidereal zodiac. Instead a more appropriate choice for a fixed beginning of the nakṣatras is found in a version of the Puruṣa Sūkta, a prayer to the cosmic being (Puruṣa), in the Śukla Yajurveda [Vājasaneyisaṃhitā 31.22]. Here the nakṣatras are said to be the form (rūpa) of the macrocosmic man with the Aśvins as his open mouth, as a reference to the beginning of nakṣatras -
अहोरात्रे पार्श्वे । नक्षत्राणि रूपमश्विनौ व्यात्तम् ।
“each side of thee are Day and Night.
The constellations are thy form: the Aśvins are thine open jaws.”
Since the Aśvins are associated with the break of dawn, and are seen as uniting the day with night, and the earth with the sky, it makes sense to associate them with the fixed ascendant of the cosmic being, and to begin counting the signs and constellations from them i.e. the Aśvinī nakṣatra.
Another reference to the Aśvins being the first is found in Yāska’s Nirukta [12.1] (~700 BCE) -
अथातो द्युस्थानाः देवताः । तासामश्विनौ प्रथमागामिनौ भवतः ।
“Next in order are the deities whose dwell in the sky.
Among them the Aśvins are the first to arrive.”
Following this tradition, the Yavanajātaka places Aśvini at the beginning of zodiac, which is called the body of kāla (time) made up of the nakṣatras and the twelve rāśis starting from Aries [79.56–57,59] -
प्रजाः सिसृक्षुः किल विश्वधाता प्रजापतिः प्राग्व्रतमाचचार ।
स द्वादशाङ्गप्रभवं स्वदेहम् सृष्ट्वा आदितः वै भगणं ससर्ज ॥56॥
तेभ्यः स मेषादिगणान् प्रजज्ञे तेभ्यः च तद्भेदविकल्पतः अन्यान् ।
अतः भवर्गस्य विभुः प्रणेता प्रजाभवाभावविधीश्वरत्वम् ॥57॥
तपोभिरुगैर्विदुरश्विनौ तु प्रजापतेः शास्त्रमिदं यतोऽर्कः।
अतोऽश्वयुग्मं विदधौ विधाता शीर्षादि कालर्क्षशरीरचक्रे ॥59॥
“56. The creator of all things, Prajāpati, desiring to create people, carried out his previous vow; he created the constellations from his own body, beginning with the head — his body which is the source of parts which are like all things.
57. From these he produced the group which begins with Aries; and from these (zodiacal signs) are there distinction and differentiation between those (material objects). Hence the lord (īśvara) who knows the origin (bhavā) and the existence (bhāva) of people, knew the rule of the zodiacal signs (i.e., astrology).
59. By terrible feats of asceticism the two Aśvins learned this science from Prajāpati, and the Sun learned it from them; hence the Creator placed the pair of horses (Aśvinī) at the beginning of his head in the circle of signs which is the body of Kāla.”
The cosmic man is therefore referred to as the kālapuruṣa in astrological texts [Bṛhat Saṃhitā 2.4] or simply as kāla [Yavanajātaka 1.14, Vṛddhayavanajātaka 1.4]. Various body parts of the creator [Prajāpati] in the form of the kāla(puruṣa) starting from the head till the feet are allotted to the signs beginning from Aries and Aśvinī nakṣatra.
The 360 spokes of the celestial wheel are therefore called both movable and immovable in Ṛgveda 1.164.48 as a description of the movable nature of the tropical year and the fixed nature of the sidereal zodiac respectively.
The Yavanajātaka [1.34–37] specifies various subdivisions of a zodiac sign like the horā, drekāṇa, saptāṁśa, navāṁśa, dvādaśāṁśa and triṁśāṁśa which are described as being useful for the purpose of genethlialogy (making predictions, determining longevity etc.). In addition to them there are descriptions of the saura (sixty solar portions), cūḍāpada (72nd part of a navamsa) and liptika (60th part of a degree), which have to be divided on a separate zodiac (bhamaṇḍala) [Yavanajātaka 1.43] -
सौराः सचूडापदलिप्तिकाख्या भाज्यास्तदान्येन भमण्डलेन ।
“The sauras, cūḍāpadas, and liptikas are to be distributed through another zodiacal circle;”
The cūḍāpadas and liptikas are mentioned in one curious verse that appears in Mīnarāja’s Vṛddhayavanajātaka [1.24] (300–325 CE) -
चूडापदं द्विस्वरसप्तलिप्तमाद्यं पुराणा गृहलिप्तिकानाम् ।
“The first cūḍāpada of the liptikas of the zodiac signs of the ancients is (located at) 772 liptas.”
A lipta is one sixtieth of a degree, hence 772 liptas correspond to a measure of 12°52’, which could be the position of the vernal equinox for the beginning of an ancient epoch known to the Yavanas. Ancient Greek astronomers like Hipparchus (second century BCE) followed an era that began with the first year of the reign of the Babylonian king Nabonassar on February 26, 747 BCE, a system that was adopted from Chaldean astronomers. The zero point of the sidereal ecliptic according to Hipparchus’s star catalogue coincided with the vernal equinox (i.e. tropical zero point) for the year 540 CE and the rate of precession was determined by him to be 1° for every 100 years. Using his model of precession, the equinoctial point for the beginning of Nabonassar era [747 BCE] would be at 12°51’40” of Aries, nearly equal to the value found in the Vṛddhayavanajātaka verse. This implies that the Yavana authors were aware of Hipparchus’s model of precession and used it to determine the position of the vernal equinox to mark the first cūḍāpada on a separate zodiacal circle. These tropical subdivisions (cūḍāpada, liptika, saura) should have existed for the purpose of tracking the months and the seasons (the measure of one cūḍāpada roughly corresponds to the motion of the Sun in 45 minutes, close to the measure of a muhūrta of 48 minutes), while the other sidereal ones (horā, drekāṇa, saptāṁśa, navāṁśa etc.) for horoscopy. It’s also worth noting that the cūḍāpadas are never used in astrological texts (except for once in the quoted Vṛddhayavanajātaka verse), and the sixtieth portions (ṣaṣṭyāṁśaka) used by Parāśara and later authors like Vaidyanātha (Jātaka Pārijāta 1.38–43) and Mantreśvara (Phaladīpikā 3.5) are quite different. By asking for the tropical and sidereal divisions to be made on two different zodiacs, the Yavanajātaka subscribes to the view of the Ṛgveda regarding the two-fold interpretation of the celestial wheel — the fixed sidereal circle of signs with its subdivisions and the tropical one for timekeeping (calendrics, measuring seasons etc.), the only difference being that the latter begins with the vernal equinox in the Yavanajātaka instead of the winter solstice.
The use of this twelvefold sidereal zodiac continued after the arrival of hellenistic astrology to India sometime around the start of the common era, albeit with new Sanskrit names and symbolism for each of the twelve signs derived from the their Greek counterparts. Evidence with respect to the use of the twelvefold sidereal zodiac from this period is found in two early Sanskrit astronomical sources — the Romakasiddhānta and the last chapter of the Yavanajātaka.
Romakasiddhānta (“astronomical theory of the Romans”) is one of the five ancient treatises on astronomy summarised by Varāhamihira in his Pañcasiddhāntikā, containing several elements of ancient Greek astronomy (the Hipparchan solar year, metonic cycle etc.). K. Chandra Hari identifies the original epoch of the text as the Sunday sunset at Yavanapura (Alexandria) on 19 March 52 CE, which was recast by Lāṭadeva (a student of Aryabhatta, fl. c. 499 CE) to the sunset at Alexandria on Monday, 21st March, 505 CE in a later recension used by Varāhamihira in the Pañcasiddhāntikā [1.8]. The text’s algorithms for the calculations of the mean positions of Sun, Moon and Rāhu should give zero degree longitude for the original epoch. The values obtained are, however, nearly 2.5° west of the vernal equinox. But when using the Babylonian sidereal zodiac, Sun, Moon and Rāhu very nearly coincide the sidereal zero point, which in 52 CE was 2.5 degree west of the vernal point. Hence it is likely that the original Romakasiddhānta was based on the sidereal zodiac that prevailed in Alexandria in the pre-Ptolemaic period. To quote the conclusion of his paper -
“On the basis of the computational features of Romakasiddhānta available in Pañcasiddhāntikā, the original epoch of Romakasiddhānta is identified as Sunday sunset at Yavanapura on 19 March 52 AD. Longitudes of luminaries and Rāhu for the above epoch (357°28’) suggest that the original Romakasiddhānta was based on the Babylonian sidereal zodiac and zero point having a three-degree norm for the vernal equinox. True sun of the epoch suggests an ayanāmśa of 2.5 degree to be added and therefore the vernal point coincided Romaka zero point in 233 AD.”
The ayanāmśa derived by Chandra Hari is indeed very close to the other Babylonian ayanāmśas of Fagan-Bradley (221 CE) and Huber (229 CE), each lying within less than ten arc-minutes of the other. The last chapter of the Yavanajātaka (called Horāvidhi — “rules for calculating horoscope”) is an exposition on mathematical astronomy dealing with the synodic motion of planets and luni-solar astronomy based on a novel astronomical cycle (yuga) of 165 years. The astronomical configuration of the conjunction of Sun and Moon at the beginning of the very first yuga is described in the following verse from the chapter [79.4] -
तदाद्यतिथ्यादि युगादि सौरं मेषादिभागस्थितयो रवीन्द्वोः ।
मेषोदये प्रागृतुचैत्रशुक्ले प्रवृत्तिते मानगतिक्रमेण ॥
“That solar yuga begins on the first tithi in the Śukla pakṣa of Caitra in the first season (spring), when the Sun and the Moon in their courses are in conjunction in the first degree of Aries and when Aries is in the ascendant (i.e., at dawn).”
The beginning of the yuga of the Yavanajātaka can be fixed to the sunrise of 21st March, 22 CE at Ujjain, India, when the longitude of the Sun and Moon conjunction should lie in the first degree of Aries.
The various ayanāmśas and the longitudes of the Sun/Moon found for this epoch are listed in table 1. The tropical ayanāmśa can be ruled out since the longitude of the conjunction falls in Pisces instead of Aries. Among the remaining choices, only the Fagan-Bradley and Huber ayanāmśa fall in the first degree of Aries, followed by the Chandra Hari ayanāmśa which is less than one arc-minute out of range. This again points to the use of the Babylonian sidereal zodiac among the earliest western authors (Yavanas) who brought hellenistic astral sciences to India.
Therefore, we find that two ancient Sanskrit texts are in agreement over their choice of the Babylonian sidereal zodiac. The transmission of western ideas found in both texts should have taken place independently, by the Romakas (Romans) in the mid-first century CE, and the Yavanas (Indo-greeks) possibly about a century earlier, predating the Roman conquest of Alexandria in 30 BCE. Quoting from Harry Falk’s paper on the yuga of Sphujidhvaja -
“The beginning of the yuga of the Yavanajātaka was corrected from AD 126, emended by Pingree to AD 136, to AD 22. This new starting point is important since it gives us a date when people from the West (yavana) spread their astronomical knowledge in South Asia. Since their yuga lasts for 165 years the starting point in AD 22 could not have been defined through experiences of a single human life-time. There must have been generations before, watching the stars and noting remarkable constellations.”
The Babylonians in the fifth century BCE defined a sidereal zodiac with twelve equal signs in such a way that the two first magnitude stars Aldebaran and Antares fell exactly at the midpoint (15°) of their respective sign (Taurus and Scorpio). Starting from 300 BCE, this sidereal zodiac was transmitted to Greece, Egypt, Rome, and since it is present in Sanskrit texts, to India. We do however find earlier evidence for the use of these two stars as the central axis of the zodiac in the Taittiriya Saṃhitā 4.4.10, which names two Rohiṇīs — Rohiṇī as Aldebaran and Rohiṇī as Antares — which were thought to be equivalent because of their position at diametrical ends of the zodiac and their association with the two equinoxes in around 3200 BCE (Rohiṇī was accorded a special status among the nakṣatras as the Moon’s favourite wife [Mahābhārata 9.34.38–70] because of its connection to the spring equinox). The use of this pair of stars as the fiducial axis for fixing the zodiac could have been transmitted westward to Babylon with the Persian conquests of northwestern India in 514 BCE.
Indian astronomers starting from the 5th-6th century CE favoured the use of Revatī naksatra (ζ piscium) to define the sidereal zodiac, fixing the zero point at 0°10′ east of Revatī (according to the 359°50′ longitude in the Sūrya Siddhānta [8.1–9]) or at Revatī itself (0° longitude in the Paitāmahasiddhanta). It’s possible that this association of the sidereal zero point with Revatī is rooted in an older tradition found in the Taittiriya Brāhmaṇa 1.5.4.2 -
प्रजापतिः पशूनसृजत । ते नक्षत्रं नक्षत्रमुपातिष्ठन्त । ते समावन्त एवाभवन् । ते रेवतीमुपातिष्ठन्त । ते रेवत्यां प्राभवन् । तस्माद्रेवत्यां पशूनां कुर्वीत । यत्किं चार्वाचीन सोमात् । प्रैव भवन्ति । सलिलं वा इदमन्तरासीत् । यदतरन् । तत्तारकाणां तारकत्वम् ।
“Prajāpati created the cattle. They went from nakṣatra to nakṣatra. They became possessed of the years. They went to Revatī. They were born in Revatī. From that (rituals) of the cattle should be performed in Revatī. Whatever should be below the Moon. Water was situated in this place. Those (stars) swam (across it). That is the quality of the stars.”
This passage can be interpreted in an astronomical context, with the cattle representing the planets and their grazing being symbolic of the planets moving from one nakṣatra to the next (which could be why the Sanskrit word for planetary transits is gocara, which also means “pasture ground for cattle”). The planets becoming possessed of the years means that their motion became cyclical with each planet having a fixed number of years or months in its orbital period, and that of being born in Revatī is that the starting point of the cycles was assumed to be at Revatī, similar to Sūrya Siddhānta’s assumption of a grand conjunction of all the planets at zero degrees of Aries in 3102 BCE. The region below the Moon is said to have been occupied in the past by water (Salila) which is the primordial medium out of which all creation including the celestial bodies emerged, referenced to in the ṚgVeda [10.129.3, 72.6] and the Vṛddhagarga-saṃhitā. This is further proof for the creationist nature of this passage (all the planets emerge from the primordial waters at the end of sidereal Pisces in Revatī). Additionally, planetary rituals (navagraha rites etc.) are prescribed to be done when the Moon is in Revatī.
The vernal point coincided with the zero point of the Revatī sidereal zodiac for 562/63 CE, but in 499 CE according to ancient Indian astronomers like Aryabhatta and Maṇindha (4th/5th century CE). Therefore most of the astronomical texts (Sūrya Siddhanta, Pañcasiddhāntikā etc.) and the purāṇas, composed or consolidated around 500 CE, take the vernal equinox at the beginning of Aries. In the Yavanajātaka [79.30] too we find that the solstices are at the beginning of Capricorn and Cancer and the equinoxes at the beginning of Aries and Libra. This is because the second yuga cycle in 187–352 CE was current during the times of Sphujidhvaja (Yavanajātaka 79.15), and the zero year of the Babylonian zodiac (~220 CE) alluded in his text falls in this period, which should be the year in or around when he wrote his text. It’s a matter of coincidence that the tropical and sidereal zodiacs were aligned during the times of both the siddhantic astronomers like Varāhamihira (~530 CE) and of Sphujidhvaja (~220 CE), owing to the different ayanāmśas they used. This is again proven by the fact that most purāṇas too place the vernal point at the beginning of Aries, only because they were composed sometime around 4th-6th centuries CE i.e. when both the zodiacs coincided, while preserving more ancient observations e.g. the Brahmāṇḍa Purāṇa [21.143–149] places the equinoxes at the end of Aries and Libra with the equinoctial full Moon in Viśākhā and Kṛttikā respectively, valid for ~1600-1800 BCE -
śaradvasantayormadhye madhyamāṁ gatimāsthitaḥ ।
atastulyamahorātraṁ karoti timirāpahaḥ ॥
haritāśca hayādivyāḥ tasya yuktā mahārathe ।
anuliptā ivābhānti padmaraktairgabhastibhiḥ॥
meṣānte ca tulānte ca bhāskarodayataḥ smrt̥āḥ ।
muhūrttā daśa pañcaiva ahorātriśca tāvatī ॥
kṛttikānāṁ yadā sūryaḥ prathamāṁśagato bhavet।
viśākhānāṁ tathā jñeyaścaturthāṁśe niśākaraḥ॥
viśākhāyāṁ yadā sūrya carateṁ’śaṁ tṛtīyakam।
tadā candraṁ vijānīyāt kṛttikāśirasi sthitam ॥
viṣuvaṁ taṁ vijānīyādevamāhurmaharṣayaḥ।
sūryeṇa viṣuvaṁ vidyāt kālaṁ somena lakṣayet ॥
samā rātrirahaścaiva yadā tadviṣuvadbhavet।
tadā dānāni deyāni pitṛbhyo viṣuveṣuca॥
Sun being in normal (medium) speed at the middle of śarat (autumn) and vasanta (spring) makes the day and night to be equal. The yellowish divine horses of his chariot shine as if painted by lotus-red coloured rays. At the end of meṣa and tulā rāśi from sunrise, the day is fifteen muhūrta long; so is the night. When the sun is in the first aṁśa (quarter) of kṛttikā, it has to be understood that the moon is in the fourth aṁśa of viśākhā. When the sun moves in the third aṁśa (quarter) of viśākhā, then moon has to be known to be at the head (beginning) of kṛttikā. This has to be understood as the equinox day; so it has been said by the sages. From the sun one should know the viṣuva (day) and the time observed from the moon. When the viṣuvat happens, day and night are of the same duration. Then charities are to be offered for (pleasing) the manes.
