Exact Match between Lunar & Solar Calendar

Shri Phadnis writes…

As far as I know, today’s system depends on Sun’s transit through Rashis. It is prevailing for the last 500 years at least. Is there a recognized cycle of years after which the Date of Chaitra Shuddha Pratipada repeats? If it does then only one can say that an exact match between lunar and solar year is achieved. Shri. Oak may like to verify.

I repeat that with ‘one lunar month’ as a correction unit, it is doubtful whether any system of Adhika Masas, will give an exact match between Lunar and solar years after a specific cycle of even several years.

Vedanga Jyotisha (Laghadha) employs 19 year cycle with use of ‘one lunar month’ as a correction unit that achieves exact match between ‘lunar’ and ‘solar’ year every 19 years.

The time of Vedanga Jyotisha, based on internal (and very intricate and thus precise) astronomy references can be estimated.

Do keep in mind, that Vedanga Jyotisha is a practical manual (calendar making) and thus updates are expected. Consequently, time estimated (by Shri P V Holay) is to be understood as that of the latest update, rather than its original composition).

Shri P V Holay estimated time of latest correction/update to Yajus Path (Vedanga Jyotisha) to be that of 2352 BCE and that of Rik path (Vedanga Jyotisha) to be much prior to (but definitely not later than) 2976 BCE.

One may refer to excellent and groundbreaking work ‘Vedic Astronomy (Vedanga Jyotisha)’ by Shri Prabhakar Vyankatesh Holay (published 1988?).

In Yajus cycle (Yajus-path of Vedanga Jyotisha), adhika masa appear at the interval of 2.5, 2.5, 3. 2.5, 3. 2.5, 3 years in a 19 year Yuga cycle.

In Rik cycle (Rik-path of Vedanga Jyotisha) adhik masa appear at he interval of 3, 2.5, 3, 2.5, 3, 2.5, 2.5 years in a 19 year Yuga cycle.

One may do a quick test of this exact match between Lunar and Solar calendar, for example, by noting down the Tithi/nakshatra of one’s birth date (per Julian calendar, e.g. 11 January 2016) and again, note down the Tithi/nakshatra for the same, 19 years afterwards.  Tithi and nakshatra (and lunar month) would match ‘exactly’ for this day.

Effects due to precession of equinoxes would enter the picture over a long period of time (~1000-3000 years) and appropriate corrections, especially in determining the beginning of new Luni-solar year, would need to be made.







4 thoughts on “Exact Match between Lunar & Solar Calendar

  1. The Jews also have a 19 year cycle to match Lunar and Solar year with an Adhika Masa in specified 7 years in those 19 years. If Vedang Jyotish follows the same cycle I am not aware. Question remains whether a Calendar based on the 19 year cycle was in use in India at any time, if so when it was introduced, by whom, how long it continued, when in went out of use and why. What was that Shaka called? The subject started with Mahabharata. Was the cycle of 19 years with 7 adhika masas in use in Mahabharata Times? Is any such reference available? If so why Bhishma said what he has said?

    • Yes, Jews also used a 19 year calendar. The usage is known since 4th century CE. What is not known is how far back, in antiquity, before 4th century CE, they used such calendar.

      Vedanga Jyotisha is nothing but a manual (siddhanta – similar to Surya Siddhanta and other Siddhanta) to create a calendar. It’s Yujus path in vogue since 2300 BCE and Rik path in vogue much earlier than (but at least as old as) ~3000 BCE.

      No information on how it was referred to (if it was referred to by any such reference..e.g.’Shaka’)

      Romaka Siddhanta or works of Varahamihir appear to be based on Vedanga Jyotisha with modifications.

      This shows that method of taking one adhika masa at a time existed at least as far as 3000 BCE.

      The evidence has nothing to say if Yuga of 19 years with 7 adhika masa were employed in Mahabharata times (neither in support nor against it).

      It is true that you (Shri Phadnis) have interpreted Bhishma’s reference as referring two “2 consecutive adhika masa”. No other Mahabharata researcher, as far as I am aware, has interpreted in your fashion. Of course, that is not the disqualification of your interpretation. I do not claim to know ‘sanskrit’ and interpretation as you see it is plausible.

      What I can assert is that such an interpretation can be falsified (and is been falsified by me) rather easily using (1) Mahabharata reference itself and (2) Calculations of Luni-solar calendar synchronization.

      (1) Bhishma’s next statement (after his statement of 2 adhika masa in 5 years) does not corroborate the method of taking ‘2 adhika masa consecutively’. If it was so, the count of Adhika masa would never amount to 5 months and 12 days (or 5 months and 6 nights).

      (2) A method of taking 2 consecutive adhika masa, after 58 consecutive regular masa (both lunar) amounts to a pure Lunar calendar. Adhika masa only comes in picture due to synchronization of Luni-solar calendar.

      (3) For this very reason (in (2)), while multiple methods (Jew, Vedanga Jyotisha with variations such as Yajus path or Rik path) exists for insertion of ONE adhika masa, there is no historically known/documented/workable method that employs insertion of ‘2 adhika masa consecutively’.

  2. I am glad to know that a 19 year cycle was known to our ancestors for so long in the past, maybe much earlier than the Jews. If it was in use in Mahabharata time, Bhishma would surely have explained it to Duryodhana. It is only logical to accept that a a reasonably correct method for taking extra months was in use at that time and the correct calculation became known eventually.
    Question of Adhika Masa had arisen because Arjun had appeared for fight earlier than the tithi of Dyuta in the 13th year. ( For whatever reason, Mahabharata does not state the month and tithi of Dyuta day or of Arjuna- Kourava battle) Duryodhana had immediately said that 13 years are not complete! He maintained that position all throughout. When Drona expressed wonder how Arjuna has appeared for war on that day, Bhishma explained, essentially, that ‘at the rate of 2 extra months over 58 regular months, Pandavas’ liability for observing extra period to compensate for difference between Lunar and Solar years over a period of 13 years ran to 5 months and 12 NIGHTS (kshapas, no ambiguity. For 13 x12= 156 months it works out 5 months and 11 1/2 days)). and considering that Dyuta ended in the evening and Vanavasa began same night, yesterday’s night was the 12th night, today morning the period is just over!’ In effect, Bhishma certified that Pandavas had completed 13 SOLAR years. The mention of ‘Panchame panchame varshe masadvayam’ is in this context. Accurate or not, it was clearly the method for adhika masas in use at that time. No one has contested Bhisma’s calculation. Pandavas had run short of 13th repetition of the Dyuta month-tithi by about 17-18 days. Duryodhana never accepted completion of Vanavasa-Adnyatvasa by Solar 13 years and he had a strong case as life was governed by lunar month and tithi. It remained a point of dispute. No one fully exonerated Pandavas but none clearly supported Duryodhana either. So war was inevitable. You can read my Marathi blog article on Adnyatavasa to see why Pandavas were compelled to take a chance.

  3. One curious fact can be noticed from the two sequences of 19 years quoted by Shri. Oak. Both are identical with a difference in only the starting point! If this system was in vogue, Pandavas would have been required to undergo only max. 5 Adhika Masas, during the 13 years’ period of Vanavas- Adnyatavas. E. G. If one assumes a worst case that just after first year of Vanavasa the first adhika masa occurred, the next 4 would be after next 2.5, 3, 2.5 and 3 years, or the 5th at the end of 12 years. There would have been no adhikamasa and less difficulty for them to reach the dyuta month/tithi in the 13th adnyatavasa year! With 2 after 58 months they were called upon to suffer 6 adhika masas. Their liability for matching 13 Solar years was 5 months and 11 1/2 days and according to Bhishma the met it!

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