Time to think beyond the metonic cycle - the Vedic way

The 19 years metonic cycle is all about aligning the 19 tropical years to 235 synodic months as the period of both was found to be quite close. There are seven intercalary months (adhik maas) in the 19 years that are inserted at the interval of 3, 3, 2, 3, 3, 3 and 2 years respectively. Since the tropical year length used in the metonic cycle was not up to mark, the Calippic cycle and the Hipparchic cycle emerged that were of 76 years (equaling four metonic cycle) and 304 years (equaling four callipic cycles) respectively. The major difference in these, 76 and 304 years, cycles of course is in terms of the number of days that were better tuned to the observed tropical year length. The number of synodic months on the other hand remained the same like they were in case of the metonic cycle i.e. 235 synodic months in the 19 years resulting into 940 (235 x 4) for the callipic cycle and 3760 (235 x 16) synodic months for the Hipparchic cycle. This means the number of intercalary months in the Callipic and Hipparchic cycle are 28 (7x4) and 112 (28x4) respectively.

Let us take the exact tropical year length into consideration and see how the 19 years metonic cycle fares based on the J2000 data during a complete precession cycle:

Precession rate = 50.28792 secs per Julian year

Tropical year length = 365.2421904 days

Synodic period = 29.5305888 days

Precession cycle = 25772.148 tropical years (Based on the given precession rate)

Number of synodic months in this precession cycle =
25772.148 * 365.2421904/ 29.5305888 = 318756.79

Number of adhik maas (the intercalary months) for the tropical years in the given precession cycle = 318756.79 - 25772.148 * 12 = 9491.02

Number of metonic cycles in the same duration = 25772.148 /19 = 1356.43

Number of adhik maas as per metonic cycle = 1356.43 x 7 = 9495

Thus, there are four extra adhik maas (the intercalary months) for the tropical years in case of the metonic cycle even if the metonic cycle is modified to the exact J2000 tropical year length.

It is obvious that the metonic cycle will cease to work in the long run.

The Vedic idea on the other hand was to deal with the intercalary months in a natural fashion. They exploited the luni-solar months Chaitra etc. to address the issue of adhik maas (the intercalary months) for the tropical years. In my book “Resolving the Indian Calendar Anomalies”, I have given all the details of how it was being done in the Vedic times and on the basis of which a new framework has been devised that can take care of any cycle duration. When that method is adopted, the resulting number of adhik maas are found as desired i.e. 9491 for the precession cycle that is discussed above.

The beauty of the Vedic method is it takes care of the precession and varying precession cycle length automatically. Of course, the insertion of the intercalary months shall not be at the interval of 3, 3, 2, 3, 3, 3 and 2 years always as is specified in the case of the metonic cycle. The pattern shall undergo a natural change in line with the precession cycle, the synodic month duration and the tropical year length. When I tested it for the duration of 30 degree (i.e. one rashi) change in the ayanamsha or precession, I found 5 different patterns for the adhik maas in the 19 years cycle for the tropical years.

Certainly, it is time for the world to think beyond the metonic cycle and follow the Vedic way to align everything naturally.

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