Mathematical proof for why the Julian date of the astronomy software can never corroborate the Vedic date of Mahabharata (Supplement to Mahabharata date series -3)

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Recap:

·         The use of astronomy software to date a long past event such as Mahabharata is unreliable. The main reason is the mismatch between the zodiacal system used in the astronomy simulators and the fixed zodiac of the Indic society for all times in the past.

·         The astronomy softwares use the tropical zodiac or the shifting zodiac along with the moving vernal equinox. This causes the solstices to shift accordingly.

·         This concept is absent in Indic astronomy in which the ayanamsa is calculated and deducted from the tropical degrees to align with the fixed zodiac at zero degree Aries. 

·         At this stage itself the dating research using ANY astronomy simulator is rendered useless.

·         A case study of the year 3067 BCE proposed by Dr. Achar and Dr. Manish Pandit is taken up to show a flawed reference to the vernal equinox at Taurus during Mahabharata, displayed by the astronomy simulator, while it should have been close to the zero point of Aries as per the Indic calendar system.

·         The use of the astrology software simulated with Drik Siddhanta – Lahiri ayanamsa combination to identify the sidereal positions for the various planetary locations picked out from the astronomy simulator for the year 3067 BCE is proved to be a case of flawed methodology with Adhika Masa appearing in the most inappropriate month of Magha around that time. 

From this let me proceed further to show that the date system of the astronomy software doesn’t match with the Indic system of time keeping. Similarly any attempt to deduce the sidereal positions for the dates of the astronomy simulator in the astrology simulator for the Hindu calendar dates cannot produce the correct results.

The calendar system used in the astronomy simulators.

The calendar system used in astronomy and in the astronomy software is different. Unlike the historians, the astronomers depend on arithmetic calculations to arrive at the dates. The date should be easily computable and not requiring counting the number of days of the months and the years and adjustment of the leap years. It should be helpful in simple addition or subtraction in calculating, say, the duration of the cycle of a variable star. For these purposes, the Julian day is found to be helpful and therefore universally used in astronomy applications and in the astronomy softwares.[1]

This day is given as a number with decimal places for the fraction of hours, minutes and seconds remaining in a day, counted from noon to noon in Universal Time or from midnight in Modified Julian days. For civil purposes, the calendric date of the Julian days is given in Julian year. The Julian year was in vogue in the western countries until the Gregorian year was introduced to replace it, though the Julian day system is retained for astronomy purpose. We must know the background of this replacement to understand important features related to the reliability of the astronomy software for dating Mahabharata.

In the western societies, the year was counted from one vernal equinox to another vernal equinox. This is known as a Tropical year. Around 46 BCE, Julius Caesar introduced a calendar named after him as ‘Julian’ that followed the tropical year. It was found out that this year was not of the exact duration of the tropical year and overshot by 11 minutes and 14 seconds.[2]  This resulted in the mismatch of the true tropical position with the calendric tropical year. The Julian calendar accumulated 12.7 days by the time of 1582 CE.

To correct this, the Gregorian calendar was introduced after expunging the accumulated days of the Julian calendar. Ten days were removed but the week day continuity was maintained. From October 4^th on Thursday, the next day became October 15 on Friday!  Ten days in the Julian calendar were lost and the sequence of the week days was adjusted arbitrarily from the previous to the next week day to match with the new calendar. This is the first anomaly that one faces while using the Julian calendar system for dating Mahabharata. A number of researches have gone into matching the Julian date with the Gregorian date, but the bottom line is that the loss of week days in the Julian calendar remains. The conversion between the two looks as follows.

For the current time, there is a gap of 12 to 13 days. The week day is synced in both the calendars and synced at all times in past and in future, but we should remember that the natural sequence of the Julian week day is disrupted during the change-over. Two anomalies arise here, (1) the day begins at noon in Universal Time in the Julian calendar but at midnight in the Gregorian calendar at each zone. In the Modified Julian Day System the Julian day starts at midnight at UT. This is in contrast to the Vedic day that starts at local sunrise in India. (2) These calendar dates are just numbers and have no connection to the star positions as in the Vedic system. In all, there are three anomalies if we include the loss of 10 week days.

The Julian days are extrapolated to the past, to the year 4713 BCE (proleptic Julian calendar) which is derived by matching three cycles in use in Europe in the past- the solar cycle, the lunar cycle and the Indiction cycle– each with varying length but synced on Monday noon, January 1 of 4713 BCE. [3] The corresponding date in the Gregorian date was 24^th November, 4714 BCE. The week day was the same. It was Monday. The difference was 37 days at that time. 

The conversion between the dates of Gregorian and Julian calendars are perfectly laid now. However the Julian day continues to be the favored system of the astronomers. The reason for this preference is expressed by the International Astronomical Union as follows:  

“Although there are several different kinds of year, the IAU regards a year as a Julian year of 365.25 days (31.5576 million seconds) unless otherwise specified. The IAU also recognises a Julian century of 36,525 days in the fundamental formulas for precession. Other measurements of time such as sidereal, solar and universal time are not suitable for measuring precise intervals of time, since the rate of rotation of Earth, on which they ultimately depend, is variable with respect to the second.” [4] This offers the best explanation for why we cannot take the Julian date for dating Mahabharata.

The Julian year is tropical and it is matched with the tropical year of another calendar, namely Gregorian. Experts have worked on equalizing them by conversion, but where is the research for conversion of the Julian year into the Vedic year which is sidereal?

Sidereal year being longer than the tropical year, how is it possible to claim that the planetary combinations picked out for a Julian date in the astronomy software was the same expressed in Mahabharata that used the sidereal calendar?

It may be argued that the Mahabharata calendar was not sidereal because it used Uttarayana (winter solstice) position for calculating a year. If so, why did Vayu Purana that existed before Mahabharata and which was quoted in Mahabharata for Time computations, express the four units of time of which sidereal is one?[5] The sidereal year was computed even before Mahabharata times and it continued for all times till today.

The Uttarayana computation was for ritual purpose just as the lunar Caitra is taken as year beginning in the current times for rituals. Burgess in his translation of Surya Siddhanta has provided a list of sidereal year duration given in six Siddhantas by giving the difference with the current time.[6]

The error column is not actually errors in computation, as he thinks, but fluctuations in the sidereal year. These fluctuations cause the difference in the length of the year that would further upset the direct match between the Julian tropical and the Vedic sidereal year. These computations must put at rest any doubt on what constituted a year for computation. It was the sidereal year.

Let me take up the more recent text on sidereal year, known as “Veemanatha Pancanga Vākya” in Tamil, written in Kali Year 4968, corresponding to 1867 CE.[7] The length of the year given in this Tamil text is 365 days, 15 Nazhigai (नाडी), 31 Vinadi and 15 Tatparai.

The conversion for this:

Using the conversion, and further converting the into present time scale, the length of the Vedic sidereal year is 365.2586806 days……..(A)

Compare this with the length of the tropical year of the Gregorian and Julian dates.

Gregorian (Tropical)    365.24219878 days …….. (B)[8]

Julian (Tropical) is 11 minutes 14 seconds longer than B = 365.24999971days ………. (C )[9]

The difference between C and B = 0.00780093 days.

The difference of 0.00780093 days per year had caused the Julian year advance by 12.7 days in 1629 years (between 46 BCE and 1582 CE)

It caused a gap of 24 days between now and 3067 BCE promoted as the year of Mahabharata. The gap was 13 days between 4713 BCE and 3067 BCE.  However these differences are just numbers. This is not the case with the Vedic date which is linked with a star and a sign to mark the year beginning.

Now let us compare between Vedic sidereal and Julian tropical that is in use in the simulator.

Vedic Sidereal (A) – Julian Tropical (C) = 0.00868089 days.

Vedic year is longer by 0.00868089 days than the Julian Tropical year.

In how many years, this difference would become 1 day?

115.1955077   Years =1 day

So every 115 to 116 years one Julian day is lagging behind the Vedic year. It must be added to the Julian year to be on par with the Vedic year. 

Calculate the number of days drifted in this way for 3067 BCE (in 5087 years from now)

5087 Years =44.157971 days

The Julian days in the astronomy simulator would be behind the Vedic sidereal day by little more than 44 days for the date 3067 BCE promoted as the date of Mahabharata. 

The drift is higher than this for Mr. Nikesh Oak’s date, 5561BCE that is publicised as scientific. Any date derived from the astronomy simulator suffers from the defect of drifting Julian days.

What I have shown is simple arithmetic.

Only experts can do the conversion accurately by taking into account the noon and mid night beginning of the Julian day and the sunrise time of the Vedic sidereal day.

But what I have shown is that,

·         The planetary combinations in the astronomy software supposed to have been corroborated with the Mahabharata text for the year 3067 BCE cannot match with the true positions in the Vedic year corresponding to that date.

·         The application of the Julian year in Jhora astrology software to generate the sidereal positions of the Vedic Year cannot produce the true positions because in the absence of the conversion of the Julian to Vedic sidereal, the day and the planetary combinations shown in the simulator is not the true date corresponding to the Julian date.

To cross-check this mismatch between the Vedic sidereal year and the Julian date of the astronomy software, let me take up the 1^st day of the Julian period, i.e. January 1, 4713 BCE that occurred on Monday. The astrology simulator must show Monday on that date for noon at Universal Time. I checked it for the year 4713 BCE and also 4712 BCE (one year less) as was done by the 3067 researchers. Drik- Lahiri is taken up as done by them.

Figure 26: First day of the Julian calendar

Figure 26 shows Friday, NOT Monday. The solar and lunar calendars were supposed to have begun on that date. They don’t appear so. Figure 27 shows the features for one year less.

Figure 27: Julian Calendar with one day less

The week day and the solar- lunar calendars do not match with the proleptic Julian first year.

Now let me also show how it appears for the Gregorian settings. The conversion is as follows:

The simulation for 24^th November, 4714 BCE is as follows:

Figure 28: First day of the Julian calendar in Gregorian settings

It was Friday and the solar and lunar months did not begin on this date.

The following Figure is generated for one year less.

Figure 29: One day less for the first day in Gregorian calendar

Once again mismatch in all respects.

This makes it very clear that the Julian date taken up from the astronomy software does not tally with the Vedic year of the astrology software.

Conversion is a very basic requirement when we pick out a date from one calendar and try to match it with another calendar.

This major defect started from Prof. K. Srinivasa Raghavan whose work was embraced without any critical study. He used Julian days for calculating the dates of Mahabharata. He overlooked the fact that the Vedic day is not of the same length as the Julian day - a crucial point and a game- changer in the search for the true date of Mahabharata war. This was similar to Dr. S. Balakrishnan’s failure to recognize that a tithi is different from a solar day. The entire research group of today followed these two persons and lost their way to reach the goal.

In any research in science or engineering, the veracity of the methods and methodology (use of software) would be meticulously tested and assessed before embarking on the research. Here in dating research of Mahabharata (and Ramayana too) this minimum requirement is not at all adhered to. Without even knowing whether the astronomy software is suitable for testing the planetary positions given in the Itihasas, too many people are just picking out an astronomy software and are claiming that they have “found out” the date!! Without knowing this major limitation of the softwares, people are picking out some date – none of which tally with the traditional date of Mahabharata at 3136 BCE! The reading public should know this limitation of every dating research done using the astronomy software. 

With this we are moving on to the 3^rd issue on how the calculation of the position of the planets and the stars in the astronomy software is not the same as in Vedic astrology by taking up the year 5561 BCE proposed by Mr.Nilesh Oak.  

(To be continued)

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[1] https://en.wikipedia.org/wiki/Julian_day

[2] https://www.grc.nasa.gov/www/k-12/Numbers/Math/Mathematical_Thinking/calendar_calculations.htm

[3] https://en.wikipedia.org/wiki/Julian_day

[4] https://www.iau.org/public/themes/measuring/

[5] Vayu Purana: Ch. 50 – 188.

[6] E.Burgess, “Translation of the Surya Siddhanta” University of Calcutta, 1935, p. 26

[7] Periya Varushadhi Nool” (Tamil) p. 6

[8] http://www.public.asu.edu/~mjwhite/Sidereal%20and%20tropical%20years.pdf

[9] https://www.grc.nasa.gov/www/k-12/Numbers/Math/Mathematical_Thinking/calendar_calculations.htm