Discovery of the Original Boundaries of Nakshatras

Zero Points of Vedic Astronomy

According to Vedāṅga Jyotiṣa there are 30 muhūrttas in a day and night (Ṛk Vedāṅga Jyotiṣa 16, Yajus Vedāṅga Jyotiṣa 38) and during the course of the year days and night increase or decrease by a maximum of 6 muhūrttas (Ṛk Vedāṅga Jyotiṣa 7, Yajus Vedāṅga Jyotiṣa 8). Thus the ratio of daylight duration to night duration was 1.5 (3:2) on summer solstice and the ratio of night duration to daylight duration was 1.5 (3:2) on winter solstice. The ratio of longest daylight duration to shortest night duration is a function of latitude, and this information can be used to locate the place where this observation was made.

Colonial era scholars were motivated to proclaim that Indians were borrowers either from Babylonians or from Greeks without providing any proof. Their opinions still continue to be the official position as described below:

Characteristic of the middle period is the fact that the longest day is considered independent of the geographic latitude and that the ratio of the longest day to the shortest day is taken to be 3:2. This ratio corresponds to a geographic latitude of almost 34°, too high for all parts of India except the northwestern corner. THIBAUT mentions that this ratio might be of Babylonian origin but considers this very unlikely because textual evidence was not available. In the meantime, however, KUGLER discovered that the ratio 3:2 occurs in Babylonian cuneiform texts of the Seleucid period. This, coupled with the fact that the ratio of 3:2 was considered in antiquity characteristic for the climate of Babylon, makes it very plausible that the ratio was taken over by the Hindus without correction. [1]

The ratio 3:2 used by the Indians, however, was commonly utilized in all Babylonian astronomical texts after ca 700 B.C. This tradition must surely be the source of the Sanskrit texts under discussion, and provide us with a terminus post quem for those texts. [2]

Based on the Nakṣatra positions given in the Vedāṅga Jyotiṣa, it is currently dated to 1150 BCE to 1400 BCE [3]. As shown in my previous article, the actual date of the composition of the Vedāṅga Jyotiṣa is much earlier, closer to 1830 BCE [4]. Since Vedāṅga Jyotiṣa is over 450 years older than Babylonian texts even by the most conservative estimate, it is more likely that the ratio of 1.5 was borrowed by Babylonians from Indians. The idea that this ratio was borrowed by Indians is based on the wrong assumption that there is no prominent place in India where this ratio is valid. Even in the quote above by Schmidt [1], it is said that this ratio is valid for north western part of the then united India. This fact is conveniently ignored to proclaim that the ratio of 3:2 was borrowed from Babylonian astronomers. Kuppanna Sastry in his translation of Vedāṅga Jyotiṣa has also noted that the ratio of 1.5 refers to 35 degrees latitude in the extreme north of India [3]. Sharma and Lishk have also argued against the foreign influence on Indian astronomy and proposed that the ratio 3:2 fits the region of Gandhāra as well and was discovered independently.

Besides, the simplicity of the relation between the ratio 3:2 and 183 days (half the annual course of the Sun) suggests that the Jainas might have searched for a standard place like Gandhāra where a simple relation of this order holds good. … Gandhāra had been a renowned seat of ancient Indian culture, and no abode of any mythological creatures. As Gandhāra and Babylon are situated on latitudes very close to each other, the ratio 3:2 might have been found independently in these two places. [5]

Gandhāra was a kingdom in ancient India. Its most important cities were Puruṣapura (current Peshawar), Puṣkalāvatī (current Charsadda) and Takṣaśilā (current Taxila). The identification of Gandhāra fits the ratio 3:2 well, however, Gandhāra was a wide region. Sharma and Lishk specify a ratio of 1.42 for Gandhāra, but do not specify exactly where in Gandhāra this ratio holds good. It can be shown using modern astronomical calculations that the ratio of 3:2 fits the location of Taxila exactly, which has a latitude of 33.74° and longitude of 72.80°.

The duration of daylight and night for any day of the year at any location in the world can be obtained from U.S. Naval Observatory website [6]. I have used this site to calculate the duration of daylight and night on the 21st day of each month at Taxila and calculated the ratios of the duration of daylight to night and vice-versa [7]. The data is shown graphically in Figures 1 and 2.

Figure 1: The ratio of daylight duration to night duration at Taxila
Figure 2: The ratio of night duration to daylight duration at Taxila

The choice of 21st day of each month is based on the fact that summer and winter solstices as well as spring and fall equinoxes take place around 21st of the respective months. Months 1 to 12 in these Figures refer to months January to December respectively.

From Figure 1, it can be seen that the ratio of daylight duration to night duration at Taxila on summer solstice is 1.5 and matches exactly with the ratio given in Vedāṅga Jyotiṣa. From Figure 2, it can be seen that the ratio of night duration to daylight duration on winter solstice at Taxila is 1.42 and close to the value of 1.5 given in Vedāṅga Jyotiṣa. Since the data has been obtained for the year 2017, it is natural to ask whether this data is applicable to the observations made during 2nd millennium BCE. The duration of daylight is a function of latitude and tilt of earth’s axis to the ecliptic. For fixed latitude, the duration over long time will only depend on earth’s tilt. Earth’s tilt is currently approximately 23.5 degrees. According to NASA Earth Observatory website [8], earth’s tilt changes from 22.1 to 24.5 degrees over a period of 40,000 years. Over a 40,000 year cycle, earth’s tilt changes by only 2.4 degrees. Thus the earth’s tilt could have differed by no more than 0.24 degrees from the present during the time of Vedāṅga Jyotiṣa and the duration of daylight would not have been significantly different from the values we have now.

From the discussion above, it is clear that there is a specific location in ancient India, namely Taxila, where the observations about the ratios of day and night durations are satisfied. Taxila was the most ancient centre of learning in India with the famous Takṣaśilā University located there. The discovery of Taxila as the location where Vedāṅga Jyotiṣa was composed shows that Taxila was the centre of Vedic astronomy. It is important to note that Taxila is located in the area where Indus Valley Civilization flourished. This discovery points to the continuity of ancient Indian Civilization. A date of 1830 BCE for the composition of the Vedāṅga Jyotiṣa also shows that the Vedāṅga Jyotiṣa was written when Indus Valley Civilization was coming to an end and refutes the Aryan Invasion Theory. It is important to understand that the Aryan Invasion Theory was invented to legitimize the rule of invaders and colonize the mind of the conquered. The purpose behind sliding the ancient Indian history forward by six and half centuries was to show that Indians were never advanced. It was to show that Indians lacked creativity and were borrowers from the Greeks. Currently, Purāṇas are considered to have been finalized during the reign of Imperial Guptas, who are dated to fourth century. If the Imperial Guptas started their reign in fourth century BCE, then the astronomical information contained in the Purāṇas was discovered by Indians over six centuries prior to the currently accepted date. Varāhamihira is currently dated to sixth century CE. I have shown in Part 5 of this series that the time of Varāhamihira was 2nd-1st century BCE [9]. This implies that his books were written prior to the writing of the Almagest by Ptolemy in 2nd century. This significantly alters the narrative of Indian astronomers borrowing information from Greeks. The truth is that ancient Indian civilization was a knowledge-based civilization and was far advanced than the contemporary civilizations. The flow of knowledge was from India to the west, but to establish it the correct chronological framework of history needs to be developed.

In my next article, I will show that that many passages from Vedic texts contain astronomical observations that can be dated to 3rd millennium BCE. This confirms that the Indus Valley Civilization was in fact Vedic Civilization.


1. Schmidt, O. H. (1944). The Computation of the Length of Daylight in Hindu Astronomy. Isis, 35(3): 205–211.

2. Pingree, D. (1973). The Mesopotamian origin of early Indian mathematical astronomy. Journal of the history of astronomy, 4: 1–12.

3. Kuppanna Sastry, T.S. (1985). Vedāṅga Jyotiṣa of Lagadha in its Ṛk and Yajus recensions. New Delhi: Indian National Science Academy, pp. 13–14.

4. Zero Points of Vedic Astronomy. Part 6 of 8 — The Dating of Vedanga… | by Dr. Raja Ram Mohan Roy | Feb, 2021 | Medium

5. Sharma, S.D. and Lishk, S.S. (1979). Length of the day in Jaina astronomy. Centaurus, 22(3):165–176.


7. Roy, R.R.M., 2020. Zero points of Vedic Astronomy. Mississauga, Ontario, Canada: Mount Meru Publishing.


9. Zero Points of Vedic Astronomy. Part 5 of 8 — The Dating of… | by Dr. Raja Ram Mohan Roy | Feb, 2021 | Medium

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 8 of 8- Indus Valley Civilization was Vedic Civilization



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