Bhishma Nirvana and the upper and lower limits to assigning Mahabharata date

Today is Magha Shukla Ashtami or Bhishma Ashtami day. Traditionally this day has been assigned to Bhishma nirvana. I have explained in previous posts why this is incorrect. I have also  shown that this was the day Yudhishtra met Bhishma after Rajyabishekam. Assigning Magha Shukla Ashtami to Bhishma nirvana will conflict with one or both of the following astronomical observations

1. Bhishma way lying on the bed of arrows for 58 days

2. Balarama arrived on Shravana nakshatra to witness the Gadha yudh between Duryodhana and Bheema.

This blogpost is not to prove these assertions again but to address a different point raised by this article. The article places a lower limit of 2241BCE. This article does not conflict with the 1504BCE date. But I would like to show why it is incorrect. I will then show what the actual lower and upper limit of dates would be if we take Bhishma Shukla Ashtami or Bhishma Krishna Ashtami to be the date of Bhishma Nirvana. 

-2240 or 2241BCE lower limit proposed in the article

The author states that -2240 should be the lower limit for dating the Mahabharata. His reason is that Magha is located at 60 Degrees from current solstice axis. Hence winter solstice at Magha should have happened 60 X 71 (years per degree of precession) or 4260 years ago or (4260-2020) -2240/2241BCE. 

The author seems to be confusing solstice axis at Magha versus Bhishma Nirvana in the Lunar month of Magha. Bhishma nirvana in the lunar month of Magha is the evidence from Mahabharata. Lunar month of Magha requires full moon near Magha not exactly on top of it. The year -2240BCE would not be the lower limit but a median year when winter solstice occurred in the lunar month of Magha. 

The author assumes 98 degrees difference in the position from full moon day to arrive at Magha Shukla Ashtami. He states that "precessionally" this corresponds to 568 years. Hence his lower limit moves from -2240 to -2240+568=-1672. Hence he argues that Mahabharata could not have happened prior to -1672BCE.

The 98Degree difference translates to 8.04solar days if we assume a lunar month has 29.53 days (98/360*29.53=8.04). The 8.04 solar days translates to 7.93 degrees in the motion of sun (8.04*360/365). Precession of 1 Degree for sun corresponds to 71.6 years, hence 7.93 degrees will result in 71.6*7.93 or 568year. Hence we can verify the author's assertion of 568 year adjustment to place solstice axis at Magha Shukla Ashtami.

But this does not change the fact that the year -1672 would be a median year for winter solstice at Magha Shukla Ashtami. It is not the lower limit. 

Finally for some unknown reason the author gives up -1672BCE lower limit assertion and says 2240BCE lower limit is non negotiable. Clearly it is not a well constructed argument.

Deriving the lower and upper limit for Winter solstice at Magha Purnima (-2940 and -864)

Let us derive the lower and upper limits for winter solstice if it happens at Magha Purnima. We can later adjust the limits using the 568 years correction derived above for winter solstice at Magha Shukla Ashtami.

Table 1 lists all 19 possible ecliptic longitude (J2000) for Magha Purnima. This sequence repeats every 19 years. Precession of equinox can change the ecliptic longitude for that year but J2000 values remains the same. 

Table 1: List of ecliptic longitude (J2000) for moon during Magha Purnima

Magha Purnima can happen between 159 to 130 Degree ecliptic longitude (J2000). This translates to 69(159-90) to 40(130-40) Degree from solstice axis for the year 2000AD. Assuming 71.6 years for precession of 1 Degree, winter solstice at Magha Purnima would have happened 4940 (69*71.6) to 2864 (40*71.6) years ago. The lower limit is the year -2940 and the upper limit is -864. This can be verified in the figure 1 and 2. The year 2940BCE has a winter solstice on Magha Purnima.

Figure 1: Magha Purnima in the year 2940BCE

Figure 2: Winter solstice (ecliptic longitude of 270Degrees) on Magha Purnima

Deriving the lower and upper limit for Winter solstice at Magha Shukla Ashtami (-2448 and -342)

We will use the quicker approach of adjusting the number of years for Magha Shukla Ashtami thithi precession derived above. We will use a definition of 90 Degrees instead of 98. This gives us 522 years instead of 568.

Let us subtract the 522 years to winter solstice at Magha Purnima limits to obtain the limits for Magha Shukla Ashtami. This gives us -2448 (-2970+522) and -342(-864+522). This can be verified by the figure 3 and 4. It shows a winter solstice on Magha Shukla Ashtami in the year 2346BCE. Clearly this breaches the lower limit of 2240BCE proposed by the author. 

Figure 3: Magha Shukla Ashtami Rohini Nakshatra in 2346BCE

Figure 4: Winter solstice on the Magha Shukla Ashtami date in 2346BCE

Deriving the lower/upper limit for Winter solstice at Magha Krishna Ashtami (-3492 and -1386)

We can use the above method to obtain the limits for Magha Krishna Ashtami Bhishma nirvana. We can add 522 years to winter solstice at Magha Purnima limits. We obtain the limits for Magha Krishna Ashtami Bhishma nirvana as -3492 (-2970-522) and -1386(-864-522).

Conclusion: This post provides a more rigorous proof for lower and upper limits for Mahabharata dates for the assumption of Magha Shukla Ashtami and Magha Krishna Ashtami dates for Bhishma nirvana. The lower limit for Magha Shukla Ashtami -2448 is close to the limit of -2240 proposed by the  article.

The post also concurs with the conclusion in the article that dates such as 3067BCE which propose Magha Shukla Ashtami for Bhishma Nirvana is not possible.