Refutation of Nilesh Oak’s Astronomical Dating of Mahabharata to 5561 BCE
Part 7 of 18 — Was there an epoch of Arundhatī?
In the previous article, it was shown that the distance between Arundhatī and Vasiṣṭha is currently 11.8 arcminutes and has only changed by 0.62 arcminute over last 14,000 years according to Stellarium 0.20.4 software. Thus, the maximum value of the distance between Arundhatī and Vasiṣṭha has been only 12.43 arcminute over last 14,000 years. However, the right ascension (RA) difference between Arundhatī and Vasiṣṭha was as high as 48.94 arcminutes in 2500 BCE. This means that RA difference presents an exaggeration and does not truly represent the phenomenon of Arundhatī walking ahead of Vasiṣṭha. What is the cause of this overestimation and how does this affect our understanding of this phenomenon? Let’s delve deeper into these issues.
7.1: Software calculated epoch of Arundhatī
The Epoch of Arundhatī is a term coined by Oak, based on the Right Ascension of Arundhatī becoming smaller than Right Ascension of Vasiṣṭha from 11091 BCE to 4508 BCE [1]. During this period, the maximum difference between the right ascensions of Arundhatī and Vasiṣṭha was only 8.6 arcminutes, as provided by Oak and verified by me using Voyager 4.5. The details have been provided in Article 5 of this series. The relevant data is shown in Table 7.1 and graphically presented in Figure 7.1.
Now, Right Ascension is measured on celestial equator, but Arundhatī and Vasiṣṭha are not on celestial equator. They are far away from the celestial equator. This has very important implications for the claim of the Epoch of Arundhatī.
7.2: Distance along declination
Right Ascension (RA) and declination are equivalents of longitude and latitude respectively. As the RA difference is measured along the celestial equator, it can be a much larger than the actual distance between the stars, which are closer to the celestial poles. Let’s illustrate this point using Figure 7.2.
In this Figure,
CD = RA difference, which is measured on Celestial Equator.
AB = distance between two stars along their declinations (effective RA difference)
[picture courtesy https://pages.uoregon.edu/jschombe/ast121/lectures/lec03.html]
As can be seen from Figure 7.2, effective RA difference AB can be much lower than RA difference CD, if the stars are very close to North Celestial Pole, P, which is the case for Arundhatī and Vasiṣṭha. If we know the RAs and declinations of both stars, it is straight forward to calculate the effective RA difference AB [2].
AB = CD * cos (declination)
7.3: Effective RA difference
The RA difference and effective RA difference between Arundhatī and Vasiṣṭha over past 14.000 years are shown in Table 7.2 and graphically presented in Figure 7.3. The data shows that RA difference between Arundhatī and Vasiṣṭha was 46 arcminutes in 2000 BCE and 3000 BCE, but they were separated by only 12 arcminutes in 2000 BCE and 3000 BCE. Thus, RA difference represents a distorted picture of actual star separation. The absolute maximum effective RA difference between Arundhatī and Vasiṣṭha was only 3.5 arcminutes between 4508 BCE and 11091 BCE. This has important implications for the observation of Arundhatī being ahead of Vasiṣṭha.
[Data Source: Stellarium 0.20.4 software, calculations performed using MS Excel]
7.4: Visual observation of Arundhatī being ahead of Vasiṣṭha
If the effective RA difference between Arundhatī and Vasiṣṭha was only 3.5 arcminutes between 4508 BCE and 11091 BCE, then could it be distinguished by naked eye?
In an article on naked eye resolution of visually close stars, Sarnecki writes [3]:
“Everyone knows how to split the famous double star Mizar (mag 2.4) and Alcor (mag 4.0) in the handle of the Big Dipper. With a separation of 11.8 arcmins this is “easy.” Most everyone I have ever pointed the pair out at a star party can “split” this famous pair with naked eye observing (except the most visually challenged). … Another pair that will test your observing skills is up at zenith this time of year. Omicron 1 Cygni (mag 3.8) and 30 Cygni (mag 5) are separated by 5.5 arcmins (338”). You will need to look with determination to split this pair, but it can be done on a night of steady seeing.”
Thus human eye can barely separate two stars less than 5.5 arcminutes apart. Even if Arundhatī was ahead of Vasiṣṭha during the epoch of Arundhatī, no one could observe this phenomenon by naked eye as the absolute maximum effective RA difference between Arundhatī and Vasiṣṭha was only 3.5 arcminutes between 4508 BCE and 11091 BCE. Another major problem with the claim of Arundhatī being ahead of Vasiṣṭha during Mahabharata time is the accuracy of astronomy software.
7.5: The accuracy of astronomy software
Oak’s claim of Arundhatī being ahead of Vasiṣṭha during Mahabharata time is based on astronomy software. Do astronomy software have that kind of accuracy? Here are critical comments by Elio Antonello, who has served as the President of the Italian Society for Archeoastronomy [4]:
“The eccentricity of the ecliptic, the obliquity or inclination of the Earth rotation axis with respect to the axis of the orbit, the intersection between the ecliptic and the equatorial plane, the longitude of the perihelion, and the inclination and longitude of the nodes of the ecliptic with respect to the solar system reference plane change with time. We used trigonometric expressions with amplitudes, frequencies and phase terms derived by Berger (1976) for these various parameters. The adopted epoch by that author was 1850.0, and we made a check of the results with those collected and published by him referred to 1950.0. Moreover, we made a comparison of the obliquity and general precession with those obtained with an accurate expansion in time (Laskar 1986), for a time interval of 10,000 years. We estimate an accuracy of some arcminutes, and the corresponding uncertainty in time of the given coordinates of a star in the sky is of several centuries. However, we remark that the evaluation of the precision of the results of the computation requires a comparison with real observations, and that means a time interval of just few centuries. Therefore, in principle the validity of the results very far in time cannot be assessed for any model of the Earth dynamics.”
Thus the uncertainty in the software calculated RA difference between Arundhatī and Vasiṣṭha over 7,500 years ago can be very high. In Voyager 4.5 simulation run by Oak, Arundhatī was ahead of Vasiṣṭha by a maximum value of 8.6 arcminutes only between 4508 BCE and 11091 BCE. In Stellarium 0.20.4 simulation run by me, the absolute maximum effective RA difference between Arundhatī and Vasiṣṭha was only 3.5 arcminutes between 4508 BCE and 11091 BCE. Oak has made a claim without considering the accuracy of astronomy software Voyager 4.5. Astronomy software do not have the kind of accuracy to determine the “The Epoch of Arundhatī”. So, Oak’s claim of Arundhatī being ahead of Vasiṣṭha between 4508 BCE and 11091 BCE cannot be validated.
Let’s illustrate it further by comparing star positions in Voyager 4.5 and Stellarium 0.20.4. Table 7.3 compares the right ascensions of Arundhatī in Voyager 4.5 and Stellarium 0.20.4 software and Table 7.4 compares the right ascensions of Vasiṣṭha in Voyager 4.5 and Stellarium 0.20.4 software. Comparison of right ascensions in Voyager 4.5 and Stellarium 0.20.4 shows that right ascension in 5500 BCE differed by 13 to 14 arcminutes for Arundhatī as well as Vasiṣṭha between the two software. SINCE THE ERROR IN RIGHT ASCENSIONS OF ARUNDHATĪ AND VASIṢṬHA IS HIGHER THAN WHAT IS BEING MEASURED, “THE EPOCH OF ARUNDHATĪ” CANNOT BE DETERMINED USING ASTRONOMY SOFTWARE.
7.6: Conclusions
Mr. Nilesh N. Oak has claimed that Mahābhārata could not have taken place outside of 11091 BCE and 4508 BCE as this was the period when Arundhatī was ahead of Vasiṣṭha. The claim is based on Mahābhārata 6.2.31, which describes Arundhatī moving ahead of Vasiṣṭha. However, the event is described as an omen and occurs among a number of omens that are out of ordinary, which means that Arundhatī was actually behind Vasiṣṭha.
Based on Oak’s dating of Mahabharata War to 5561 BCE, Arundhatī was ahead of Vasiṣṭha for 5,530 years before the Mahābhārata war and for 1,053 years after the Mahābhārata war. Still, Arundhatī is not shown walking ahead of Vasiṣṭha anywhere else in Mahābhārata.
The right ascension difference between Arundhatī and Vasiṣṭha was 46 arcminutes in 2000 BCE and 3000 BCE, but they were separated by only 12 arcminutes in 2000 BCE and 3000 BCE. The absolute maximum effective right ascension difference between Arundhatī and Vasiṣṭha was only 3.5 arcminutes between 4508 BCE and 11091 BCE. Human eye cannot separate two stars less than 5.5 arcminutes apart. Thus, the observation could not have been made even if Arundhatī was ahead of Vasiṣṭha. Furthermore, Oak has made a claim without considering the accuracy of astronomy software Voyager 4.5. Astronomy software do not have the accuracy to determine the “The Epoch of Arundhatī”. Comparison of right ascensions in Voyager 4.5 and Stellarium 0.20.4 shows that right ascension in 5500 BCE differed by 13 to 14 arcminutes for Arundhatī as well as Vasiṣṭha. As the error in star positions is higher than the maximum value of difference in right ascensions between them, “The Epoch of Arundhatī” cannot be determined.
References
1. Oak, N.N., “When did the Mahabharata War Happen?”, Bhim USA, 2011, page 222 (not numbered, counted from last numbered page).
2. Detailed derivation at: https://astronavigationdemystified.com/2015/10/14/calculating-the-distance-between-meridians-of-longitude-along-a-parallel-of-latitude/.
3. Christopher Sarnecki, “Observing naked (or I got 5.5 arcminutes resolution)”, http://websites.umich.edu/~lowbrows/reflections/1999/csarnecki.6.html
4. Elio Antonello, “The Palaeolithic Sky”, in A. Orlando (ed.), The Light, The Stones and The Sacred, Astrophysics and Space Science Proceedings 48, pp. 159–164, 2017.
Note: The content of this series of articles is based on the three-part presentation author made on Sangam Talks on the refutation of the 5561 BCE dating of the Mahābhārata War. Here are the links to these presentations.
1. Refutation of the 5561 BCE dating of the Mahabharata War, Part 1: https://www.youtube.com/watch?v=W2YuGQRmZ9c
2. Refutation of the 5561 BCE dating of the Mahabharata War, Part 2: https://www.youtube.com/watch?v=7DiLSUFrTx8
3. Refutation of the 5561 BCE dating of the Mahabharata War, Part 3: https://www.youtube.com/watch?v=eop31blDa2c
Here are three other presentations refuting Mr. Nilesh Oak’s dating of Surya Siddhanta to 12000 BCE and Ramayana to 12209 BCE.
1. Dating the Surya Siddhanta: https://www.youtube.com/watch?v=55pvrTUWi94
2. Dating the Ramayana — Part 1: https://www.youtube.com/watch?v=2S0PO3SzqBc&t=5s
3. Dating the Ramayana — Part 2: https://www.youtube.com/watch?v=AKNkrgm1Tu0
More about the author
I am a seeker of historical truths and am deeply interested in the heritage of India. I have earned a B.Tech. in Metallurgical Engineering from the Indian Institute of Technology, Kanpur and a Ph.D. in Materials Science and Engineering from The Ohio State University, USA. I have a deep interest in ancient Indian texts. My research besides Materials Science covers several different areas: Vedic cosmology, Vedic astronomy, Jain astronomy, and ancient Indian history.
Email: rajarammohanroy108@gmail.com
Twitter: https://twitter.com/RamMohanRoy108
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