The Jovian Years

Brhat Samhita 8.20–21. Multiply the number of years that have elapsed since the beginning of the Salivahana era by 44. Add 8589 to the product and divide the results by 3750. To the quotient thus obtained add the Saka Year. Divide this by 60 and its remainder by 5. The quotient represents the five year (yuga) period ruled by Vishnu and others, and the remainder denotes the number of years that have elapsed in the particular Yuga.
Brhat Samhita 8.23. Place the years of Jupiter obtained according to the previous verse in two places separately. Multiply the first by 9 and divide the other by 12. Add the product of the first and the quotient of the second. Divide the results by 4. The quotient would reveal the particular star counted from Dhanishtha. The remainder would indicate the particular Pada or Quarter of the next star that is occupied by Jupiter.

Explanations

• In a Mahayuga, there are 43,20,000 revolutions of Surya around the Sidereal Zodiac.
• In the same period, there are 3,64,224 revolutions of Jupiter. Please refer here. Considering 1 Jupiter’s revolution = 12 Jovian years, this is equivalent to 3,64,224 * 12 = 43,70,688 Jovian years.
• Solar years = 43,20,000 = 3,750 * 1152. Jovian years = 43,70,688 = 3,794 * 1152. This implies that in 3,750 years there are 3,794 Jovian years. Thus, 1 Solar year = [3,794 / 3,750] = 1 [44/3,750].
• The year elapsed (completed) from the beginning of Kali to the beginning of the Salivahana Saka is 3179 years. Thus Elapsed Year = Saka Year + 3179.
• Gregorian to Salivahana Saka conversion. Saka Year in period Jan 1st to Chaitra Shukla Pratipad = Gregorian year — 79. Saka Year in period Chaitra Shukla Pratipada to Dec 31st = Gregorian year — 78. Refer here for details.
• At the beginning of the Saka Year 3179, the Jovian year can be found as 3179 * [3,794 / 3,750]. = 3216.30
• The beginning of the Kali Yuga on January 22, -3101 coincided with #27 from Prabhava i.e., the Vijaya Year (as per 60 year Jovian cycle). This is different from Pramāthi that became operational as per the Saka Luni-Solar Calendar.
• This means that from the 26 Jovian years have elapsed at the start of the Kali Yuga. Hence, the figure 26 should be added to the Jovian years arrived at step above, to reset the Jovian calendar to the beginning of the cycle at Prabhava.
• So which year, the salivahana year started? It should be attained after adding 26 to 3216.30 Jovian years at the beginning of Salivahana Saka. It is 3242.30. The remainder after removing the cycles (multiples of 60) is 2.30 i.e., the 3rd Jovian Year i.e., Śukla.

Determine the Jovian year as on 2016 Chaitra Shukla Pratipada

• The Chaitra Shukla Pratipada, Saka 1938 coincides with 7th April 2016.
• Solar years = 1938 + 3179 = 5117
• Jovian years = 5117 * [3,794 / 3,750] = 5177.039 (5177 Jovian years elapsed and the 5178th year is is progress).
• 60 years cycle adjustment = 5177.039 + 26 = 5203.039

Jovian Year = Remainder of 5203.039 / 60 = 43.039 = 44th Year. The 44th year is Sādhāraṇ.

We note that as per the Saka calendar, this coincides with Durmukha (#32). But we should not confuse between the two as they are different measures of time. The difference between the two calendars years is about 12 years. This observation is endorsed by Pt. M. Ramakrshna Bhatt, the commentator of Brhat Samhita.

Determining the Nakshatra of Mean Jupiter (Moderate Accuracy)

• The Jovian Year elapsed is 43 from the beginning of Kali.
• Multiply 43 * 9 = 387
• Divide 43 / 12 = 3.58
• Add the multiplication and the division = 387 + 3.58 = 390.58
• Divide the result by 4 = 390.58 / 4 = 97.645
• This means Jupiter is in 98th Nakshatra from Dhanishtha.
• Divide 97.645 by 27 and get the remainder = 17.
• Dhanishtha is 23rd Nakshatra. Counting 17th Nakshatra from 23rd we get 23 + 17–1 = 39. 39–27 = 12 = Hasta Nakshatra.

Determining the Nakshatra of Mean Jupiter (Higher Accuracy)

• The Jovian Year elapsed is 43.039 from the beginning of Kali.
• Multiply 43.039 * 9 = 387.3510
• Divide 43.039 / 12 = 3.5865
• Add the multiplication and the division = 387.351 + 3.5865 = 390.9375
• Divide the result by 4 = 390.9375 / 4 = 97.7344
• This means Jupiter is in 98th Nakshatra from Dhanishtha.
• Divide 97.7344 by 27 and get the remainder = 16.7344.
• Dhanishtha is 23rd Nakshatra. Counting 16.7344 Nakshatra from 23rd we get 23 + 16.7344–1 = 38.7344. 38.7344–27 = 11.7344 = Uttarphalguni 3rd Pada.
• If we cast the actual horoscope on that day, Jupiter is in Purvaphalguni 3rd Pada. The result is very close to the mean Jupiter.

Conclusion

1. The Jovian Years are the mean years based on Jupiter’s movement in a Yuga.
2. The Jovian Years are different from the years reckoned based on the Solar or Soli-Lunar Calendar Year (Vikrama or Saka Samvat).
3. The Jovian year is nearly 12 years ahead of the Solar or Soli-Lunar Calendars Year reckoning, with respect to their names as per the 60 years cycle.
4. The mean Nakshatra position of Guru arrived based on the Jovian year is very close to the actual position of Jupiter. No doubt that the Nakshatra reckoning is as per Sidereal position and not Tropical Position. This debunks the claim of many that Varahamihira followed the Tropical Zodiac. This will be covered in another writeup.
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