Discovery of the Original Boundaries of Nakshatras

Zero Points of Vedic Astronomy

Part 5 of 8 — The Dating of Varāhamihira to 123 BCE

According to the Indian tradition, Varāhamihira was one of the nine gems in the court of Emperor Vikramāditya. Vikrama era named after Emperor Vikramāditya has its zero point in 57 BCE. Modern history denies the existence of Emperor Vikramāditya in 57 BCE and has placed Varāhamihira in sixth century CE, whose time was in 1st century BCE if Indian tradition is to be believed. The reason for this disagreement lies in the interpretation of Śaka era used by Varāhamihira.

1. A tale of two eras

Varāhamihira has himself given his date by saying that he wrote Pañchasiddhāntikā in 427 Śaka [1]. Based on the zero point of Śaka era in 78 CE, Varāhamihira wrote Pañchasiddhāntikā in 505 CE. However, Varāhamihira has defined the Śaka era used by him in Bṛhat Saṃhitā, which is reproduced below [2]:

āsanmaghāsu munayaḥ śāsati pṛithvīn yudhiṣṭhire nṛipatau

ṣaḍdvikapañcadviyutaḥ śakakālastasya rājyasya.

English translation of this verse has been provided by Alexander Cunningham in 1883 CE as follows [3]:

The seven seers were in Maghā when king Yudhiṣṭhira ruled the earth, and the period of that king is 2526 years before the Śaka era.

The verse gives the information that the difference between the zero points of Yudhiṣṭhira era and Śaka era was 2,526 years. This information can have two different interpretations. Alexander Cunningham interpreted this verse as defining the time of King Yudhiṣṭhira and calculated the time of Yudhiṣṭhira as 2448 BCE, which is 2526 years before 78 CE. Second interpretation is that Varāhamihira has defined Śaka era which is 2,526 years after Yudhiṣṭhira. Indian tradition places the time of Yudhiṣṭhira close to 3102 BCE, the traditionally accepted date of the beginning of Kaliyuga. This places the Śaka era specified by Varāhamihira in sixth century BCE. The question is which interpretation is correct?

Venkatachelam calculated that Varāhamihira used the Śaka era with zero point in 550 BCE and proposed that Cyrus the Great was the Śaka king after whom Varāhamihira has named his Śaka era [4]:

So the Śaka Era related in the Sloka is neither Vikrama nor Salivahana Era and this fact is approved by all the historians. That is the age of the Persian Emperor, Cyrus, which began in 550 B.C.

The difference between these two Śaka eras is 628 years. It is a long time period and astronomical observations reported by Varāhamihira can be used to decide which interpretation is correct.

2. Precession of the solstices

Varāhamihira has made the following astronomical observation in Bṛhat Saṃhitā about his time period [5]:

Currently Sun turns southward from the beginning of Karkaṭaka and turns other way from the beginning of Makara. If in the future there is deviation from this, then this should be ascertained by direct observation.

From the wordings of the verse, it is clear that Varāhamihira was using sidereal zodiac and not tropical zodiac. In a tropical zodiac, the statement will always be valid. To fix the time period of Varāhamihira, we need to fix the time when the Sun turned southward from the beginning of Karkaṭaka. Karka or Karkaṭaka is same as Cancer. The question then is — when did the Sun turn southward from the beginning of Karkaṭaka (Cancer)?

The answer lies in the phenomenon of the “Precession of the Equinoxes”, which is the wobbling of the earth’s axis. Due to precession, the position of sun among the background of the stars during equinoxes keeps changing. The Sun returns to the same position in about 26,000 years. As the zodiac has 12 signs, it takes approximately 2160 years to transit through one zodiac sign. The time when the Sun turned southward from the beginning of Karkaṭaka (Cancer) can be calculated by knowing the position of the summer solstice at some other time. Professor James B. Kaler of the University of Illinois has given the following date for the transition of the summer solstice from Gemini to Taurus [6]:

As a result of precession, around 1990 the Summer Solstice crossed the modern boundary from Gemini to Taurus, which now technically holds the point. Because the Summer Solstice is closer to the classic figure of Gemini than it is to that of Taurus, and since Gemini (along with Pisces, Libra, and Sagittarius) quarters the ecliptic, Gemini is still traditionally taken as the Solstice’s celestial home.

Since the Sun turned southward from the beginning of Gemini around 1990 CE and it takes about 2160 years to transit through one zodiac sign, we can calculate backwards and get the approximate dates for previous transitions as shown in Figure 1. Thus it was around 170 BCE that the Sun turned southward from the beginning of Karkaṭaka (Cancer). This matches well with the traditional date of Varāhamihira. Placing Varāhamihira in sixth century CE essentially means that the boundaries of sidereal Hindu and western zodiacs do not match and have a difference of about 10° as shown in Figure 2. It is currently believed that the concept of zodiac signs was borrowed by Hindus from Greeks. Then it begs the question as to why the boundaries do not match between Hindu and Western zodiac signs. In fact, the boundaries of sidereal Hindu and Western zodiac signs match very well in the Rohiṇī system as described in my previous articles [7, 8]. With the determination of rāśi boundaries and their correspondence with nakṣatra boundaries, precise dates of the position of summer solstice at rāśi and nakṣatra boundaries can be determined as shown in Figure 3.

Figure 1: The transition of summer solstice into new Zodiac due to precession
Figure 2: Current understanding of the transition of summer solstice into new Zodiac due to precession
Figure 3: The date of summer solstice at nakshatra and rāśi boundaries

Varāhamihira has also stated that the Sun changed its course from the middle of Āśleṣā earlier, but now that takes place in Punarvasu [9]. If we look at Figure 3, we find that the beginning of Cancer falls in Punarvasu (3/4 th from the beginning of Punarvasu), so Varāhamihira’s statements are consistent. From Figure 3, it is clear that the astronomical observation made by Varāhamihira took place around 140 BCE. Varāhamihira should be dated using the Cyrus Śaka era of 550 BCE. Varāhamihira wrote Pañchasiddhāntikā in 427 Śaka or 123 BCE. One major problem needs to be resolved before Varāhamihira could be dated to 2nd to 1st century BCE. This is the problem of Varāhamihira quoting Āryabhaṭa in Pañchasiddhāntikā [10].

3. Āryabhaṭa I or Āryabhaṭa II

Āryabhaṭa has given information about his birth in Āryabhaṭīya [11]. The information has been translated to mean that Āryabhaṭa was 23 years old in the year 3600 of the Kali era. Counting Kali era from the zero point in 3102 BCE, it is claimed that Āryabhaṭa wrote the book Āryabhaṭīya in 499 CE and was born in 476 CE. Varāhamihira could not have lived in 2nd to 1st century BCE, if he has quoted Āryabhaṭa who lived in 5th to 6th century CE. First of all, there is doubt whether Āryabhaṭa was born in 476 CE, 499 CE or 522 CE. Haridatta in 689 CE has interpreted the verse to mean that Āryabhaṭa was born in 499 CE and wrote Āryabhaṭīya in 522 CE, when he was 23 years old [12]. Commentator Someśvara (11th century CE) has interpreted the verse to mean that Āryabhaṭa was born 23 years after 3600 years of Kali era had passed [13].

Strange to say, commentator Someśvara understands the verse to mean that 3623 years had elapsed of the Kali Yuga at the birth of Āryabhaṭa.

If this interpretation is correct, then Varāhamihira could not have referred to the Āryabhaṭa of sixth century CE born after he wrote Pañchasiddhāntikā in 505 CE. Even if Āryabhaṭa wrote his famous book Āryabhaṭīya in 499 CE, it is unlikely that he would have been referred by Varāhamihira. Āryabhaṭa lived in Kusumpura, which modern historians identify with Patna in Bihar, while Varāhamihira wrote his treatise in far away Ujjain. It is unlikely that Āryabhaṭa would have become so famous in a mere six years to be quoted by Varāhamihira in an age 1500 years ago, when information travelled much more slowly and it took much longer to build one’s reputation. Varāhamihira was referring to an earlier Āryabhaṭa, and not the author of Āryabhaṭīya. It becomes clear from the two quotes by Al-Biruni (11th century):

In the book of Āryabhaṭa of Kusumapura we read that the mountain Meru is in Himavant, the cold zone, not higher than a yojana. In the translation, however, it has been rendered so as to express that it is not higher than Himavant by more than a yojana. This author is not identical with the elder Āryabhaṭa, but he belongs to his followers, for he quotes him and follows his example. I do not know which of these two namesakes is meant by Balabhadra. [14]

I have not been able to find anything of the books of Āryabhaṭa. All I know of him I know through the quotations from him given by Brahmagupta. The latter says in a treatise called Critical Research on the Basis of the Canons, that according to Āryabhaṭa the sum of the days of a caturyuga is 1377,917,500, i.e. 300 days less than according to Pulisa. Therefore Āryabhaṭa would give to a kalpa 1,590,540,840,000 days. According to Āryabhaṭa and Pulisa, the kalpa and caturyuga begin with midnight which follows after the day the beginning of which is the beginning of the kalpa, according to Brahmagupta. Āryabhaṭa of Kusumapura, who belongs to the school of the elder Āryabhaṭa, says in a small book of his on Al-ntf (?), that ‘1008 caturyugas are one day of Brahman. The first half of 504 caturyugas is called utsarpini, during which the sun is ascending, and the second half is called avasarpini, during which the sun is descending. The midst of this period is called sama, i.e. equality, for it is the midst of the day, and the two ends are called durtama (?).’ [15]

These two statements clearly show that there was another Āryabhaṭa before the Āryabhaṭa of Kusumapura born in 476 CE or 499 CE. Varāhamihira has referred to an earlier Āryabhaṭa about whom not much is known at this point. Also, Varāhamihira could not be contemporary of Āryabhaṭa of six century as that Āryabhaṭa had fixed the date of the beginning of Kaliyuga in 3102 BCE and thus Mahābharata war in 3138 BCE. Being his contemporary and quoting him, Varāhamihira could not have fixed the date of Mahābhārata war around 2448 BCE.

To put things in perspective, the date of the Varāhamihira has been brought forward by over six centuries based on calculating the date of Varāhamihira from Śaka era with zero point in 78 CE instead of the Cyrus Śaka era with zero point in 550 BCE. But why would Varāhamihira use an era based on the reign of a Persian emperor?

4. From Persia with love

Sometimes a name says a lot, and in the case of Varāhamihira it indeed does so. Varāhamihira is a combination of two words — “Varāha” and “Mihira”. Varāha meaning wild boar is an incarnation of Lord Viṣṇu. Mihira is a corrupted form of Mithra, an ancient Persian God equivalent to the Vedic God Mitra. As the word Mihira is of Persian origin, it points to Varāhamihira’s forefathers coming to India from Persia. Varāhamihira being called a “Śākadwīpī Brāhmaṇa” by commentator Bhaṭṭotpala. According to Agnipurāṇa, Śakadwīpa or island of Śakas is inhabited by Maga Brahmins, who are sun-worshippers [16]. Varāhamihira has instructed that idols of the Sun should be installed by Maga Brahmins [17]. Varāhamihira has also told us that he was the son of Ādityadāsa, born in Kapitthaka and living in Avanti [18]. As the kingdom of Avanti had its capital at Ujjayinī (Ujjain), Varāhamihira lived in the place from where the Emperor Vikramāditya ruled. Ujjain was also the most important place for astronomical learning in ancient India, and so it was natural for the most celebrated astronomer of his time to live there. His father’s name Ādityadāsa means servant of the Sun, and his own name has the Sun (Mihira) as part of it. This lends credence to the belief that he was from the family of Sun worshippers.

According to Indian tradition, Maga Brahimns came from Persia. The equivalent term Magi priests are well known from Persian history. The Magi were official priests of Achaemenid kings. The question then is why did the ancestors of Varāhamihira migrate to India? Throughout history, wars have been a major cause of migration. I consider the invasion of Persia by Alexander the Great as the most likely cause of this migration. We now have an explanation of why Varāhamihira would introduce the Śaka era instituted in the name of Cyrus the Great, ruler of Persia. Of all the kings that have been given the coveted title of “The Great”, I consider Cyrus the Great to be the most worthy of this title. Some kings have been given this title for being great conquerors, but I don’t consider the wanton pursuit of self-glory and bringing unwanted bloodshed of epic proportions to innocent people as signs of greatness. Here was a king who really cared about his people, and his subjects adored him. He is credited with instituting the first charter of human rights. When he conquered Babylon in 539 BCE, his first actions were to free the slaves and declare that everyone had the right to choose their religion. Cyrus succeeded to the throne in 559 BCE. He was not an independent ruler, and was subordinate to Media. In 550 BCE he conquered Media, declared himself an independent king, and founded the Achaemenid Empire. Here is a quote describing the timeline of ancient Persian empires [19]:

The Median Empire (728–550 BC) controlled the northern shore of the Persian Gulf and the Gulf of Oman, but did not extend west of the Tigris; the Achaemenid Empire (550–330 BC) included Mesopotamia and its access to the sea and the Parthian Empire (247 BC-224 AD) dominated the Arabian coast right up to Qatar.

We now know that the Śaka era referred to by Varāhamihira was instituted to celebrate the founding of the Achaemenid Empire. It is also of critical importance to know that Varāhamihira defines the era as that of the Śaka king, while the later Śaka era is invariably described as starting with the end of the Śakas. Varāhamihira’s Śaka king is a good king, while the Śaka king of Śālivāhana Śaka era is an enemy king who needed to be eliminated. We can work out the Cyrus Śaka era from the description given by Varāhamihira as follows.

The time of Yudhiṣṭhira was well established in Varāhamihira’s mind. As Yudhiṣṭhira participated in the Mahābhārata war and the Kali age followed shortly after the Mahābhārata war, the time of Yudhiṣṭhira will be close to 3102 BCE — the traditionally accepted date of the start of the Kali age. If we count 2526 years from 3102 BCE as Varāhamihira has specified, then we get 576 BCE as the date of Śaka era as defined by Varāhamihira. There is need for a correction here as follows. Yudhiṣṭhira is supposed to have lived for 25 years after the start of the Kali age and the era named after him, Yudhiṣṭhira era, starts from the date Yudhiṣṭhira left this world. Thus the Yudhiṣṭhira era starts from 3077 BCE, 25 years after the start of Kali era. If we count from this date for Yudhiṣṭhira, 2526 years from 3077 BCE comes to 551 BCE as the date of Śaka era as defined by Varāhamihira. This is within a year of 550 BCE and the difference can be due to different beginnings of the year. As Varāhamihira wrote Pañchasiddhāntikā in 427 Śaka, his time was 123 BCE instead of sixth century. This also makes him the senior contemporary of Emperor Vikramāditya in whose name the Vikrama era of 57 BCE was established. This Vikramāditya was of course different from Chandragupta II Vikramāditya of Imperial Gupta dynasty.


1. Pañchasiddhāntikā 1.8.

2. Bṛhat Saṃhitā 13.3.

3. Cunningham, A. (1883). Book of Indian Eras, with Tables for calculating Indian Dates. London, UK: Thacker, Spink and Co., page 9.

4. Venkatachelam, K. (1953). The plot in Indian Chronology. Ghandhinagara/Vijayawada, India: Bharata Charitra Bhaskara, page 50.

5. Bṛhat Saṃhitā 3.2.


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

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

9. Pañchasiddhāntikā 3.20–22.

10. Pañchasiddhāntikā 15.20.

11. Āryabhaṭīya, Kālakriyāpāda, Verse 10.

12. Sarma, K.V. (2001). Āryabhaṭa: His name, time and provenance. Indian Journal of History of Science, 36(3–4): 105–115.

13. Dāji, B. (1865). Brief notes on the age and authenticity of the work of Āryabhaṭa, Varāhamihira, Brahmagupta, Bhaṭṭotpala, and Bhāskarāchārya. Journal of the Royal Asiatic Society of Great Britain & Ireland, New Series, Volume the First: 392–418. Quote on page 406.

14. Sachau, E. C. (1910). Alberuni’s India. Vol. 1. London, UK: Kegan Paul, Trench, Trubner & Co. Ltd., page 246.

15. Sachau (1910): 370–371.

16. Agnipurāṇa 119.15–22.

17. Bṛhat Saṃhitā 60.19.

18. Bṛhat Jataka 28.9.

19. Cadene, P. and Dumortier, B. (2013). Atlas of the Gulf States. Boston, Massachusetts, USA: Brill, page 10.

More about the author

I am a seeker in search of the true history and heritage of India. I have strong scientific background (B.Tech. in Metallurgical Engineering from Indian Institute of Technology, Kanpur and Ph.D. in Materials Science and Engineering from The Ohio State University, USA) and a deep interest in ancient Indian texts. My work on Indology spans three different fields: cosmology, astronomy, and history.


Next: Zero Points of Vedic Astronomy: Part 6 of 8 — The Dating of Vedanga Jyotisha to ~1830 BCE

Vedic Scholar, Materials Scientist, Author of books on Vedic Astronomy, Jain Astronomy, and Ancient Indian History