Jyotishkarandak Ek Adhyayan

Here's a comprehensive summary of the provided Jain text, "Jyotishkarandak: Ek Adhyayan" by Dr. Vidyadhar Johrapurkar, based on the given pages:

The article is an analytical study of the Jyotishkarandak, a Jain text comprising 176 verses (gathas). It was published in 1928 by the Shri Rishabhdev Keshrimal Shwetamber Sanstha in Ratlam as part of a larger compilation. The author states that the Jyotishkarandak is attributed to ancient, unnamed Jain acharyas who predated the Valabhi recension (5th century CE). The text itself claims to be based on the Suryapannatti. There's a mention of a commentary by Acharya Padalipta (2nd century CE), but the author has not had the opportunity to examine it.

The author posits that the Jyotishkarandak represents a significant aspect of Jain astrological mathematics and provides a glimpse into the astronomical understanding prior to the common era. This is evidenced by the absence of mentions of the twelve zodiac signs, seven days of the week, and specific planets like Mercury and Venus. Only the total number of planets is stated as 88. The study then proceeds to compare the descriptions related to the Sun, Moon, and constellations in the Jyotishkarandak with contemporary astronomical observations and calculations.

Here's a breakdown of the comparisons made:

1. Solar Year (Saur Varsha):

   • Jyotishkarandak: The solar year is described as 366 days and nights (Gatha 40), with 10,980 Muhurtas (Gatha 43). A Muhurta is defined as 2 Ghadi or 48 minutes.
   • Current Calculation: The solar year is approximately 365 days and 5.8 hours.
   • Lunar Year (Chandra Varsha): The Jyotishkarandak states a lunar year of 354.33 days (Gatha 41), while current calculations place it at 354.36 days.

2. Adhikamas (Extra Month):

   • Jyotishkarandak: To reconcile the solar and lunar years, an extra month was inserted after every thirty lunar months. Over five solar years, there were sixty-two lunar months (Gathas 93 and 62). This five-year cycle began on the first day of the dark fortnight of Shravana (Gatha 55). The first, second, and fourth years of this cycle were considered "lunar" (chandra), while the third and fifth were "augmented" (abhivardhit) (Gatha 50).
   • Current Calculation: The intercalation of extra months is not as regular. An extra month is added in a lunar month where the Sun does not transit from one sign to another. A "decay month" (kshaya masa) occurs when the Sun transits a sign twice within a lunar month. Over 19 years, seven extra months are added.

3. Tithi Calculation (Tithi Ganana):

   • Jyotishkarandak: Each Tithi (lunar day) has an duration of 293.3 Muhurtas (Gatha 105). To align days and nights with Tithis, during each of the four months of the rainy, snowy, and summer seasons, the third and seventh fortnight had fourteen days, while the rest had fifteen (Gatha 112). This applied to the bright fortnight of Bhadrapada, Kartik, Paush, Phalguna, Vaishakha, and Ashadha.
   • Current Calculation: Tithi calculation is not as precise. A Tithi is defined by the 12-degree difference in the apparent positions of the Moon and Sun. Due to the elliptical orbits of the Moon and Earth, this duration can sometimes exceed one day and night, leading to a "Tithi growth" (tithi vriddhi) where a Tithi spans two calendar days. Conversely, if a Tithi begins after sunrise and ends before the next sunrise, it's a "Tithi decay" (tithi kshaya).

4. Moon and Sun Diameter:

   • Jyotishkarandak: The Moon's diameter (vishkambha) is stated as 5661 Yojanas, and the Sun's as 48/61 Yojanas (Gatha 144).
   • Current Calculation: Based on goniometric instruments and trigonometry, the Moon's diameter is approximately 2,059.9 miles, and the Sun's is 864,000 miles. The author notes a significant difference.

5. Sun's Motion:

   • Jyotishkarandak: The Sun's circular path of revolution is described as having a minimum circumference of 3150.89 Yojanas and a maximum of 3183.50 Yojanas (Gatha 196). The Sun completes a circumambulation of Mount Meru in sixty Muhurtas. Therefore, the Sun's speed per Muhurta is estimated to be between 525.105 and 530.68 Yojanas.
   • Modern Understanding: What was historically considered the Sun's daily motion is now understood as the Earth's daily rotation on its axis. The equatorial speed is estimated at about 1,000 miles per hour (approximately 800 miles per Muhurta). The East-West extent of present-day India is about 2,000 miles (250 Yojanas). According to ancient calculations, the difference in sunrise time between the eastern and western borders of India should be only 1/20th of a Muhurta (about 2.5 minutes). However, current observations show a difference of approximately two hours.

6. Conjunction of Moon and Constellations:

   • Jyotishkarandak: The text describes the duration of the Moon's conjunction with the 28 visible constellations. For Shatabhisha, Bharani, Ardra, Ashlesha, Swati, and Jyeshtha, the Moon stays for 15 Muhurtas. For Uttara Phalguni, Uttara Ashadha, Uttara Bhadrapada, Punarvasu, and Vishakha, it stays for 45 Muhurtas. For the remaining 15 constellations, the Moon's presence is for 30 Muhurtas. The shortest duration is with Abhijit, described as 1/67th of a day and night (Gathas 150-153).
   • Current Calculation: While modern calculations also show variations in the Moon's conjunction time with constellations, the differences are not as extreme. The celestial sphere is divided into 27 equal parts called Nakshatras. Abhijit is no longer considered a constellation. Even with equal distribution of constellations, the Moon's elliptical orbit causes variations in its time with each constellation. For example, in September 1979, the minimum time with Dhaniṣṭhā was 20 hours 53 minutes (approx. 26.25 Muhurtas), and the maximum time with Magha was 27 hours 2 minutes (approx. 33.75 Muhurtas).

7. Increase and Decrease of Day Length:

   • Jyotishkarandak: According to Gathas 305-310, within the thirty Muhurtas of a day and night, the sequence of changes in day and night duration indicates a minimum day and night of twelve Muhurtas and a maximum of eighteen Muhurtas.
   • Modern Measurement: This corresponds to 9 hours 36 minutes and 14 hours 24 minutes respectively. The author notes that this difference varies with latitude. The described difference is accurate for a latitude of 35 degrees North, the approximate latitude of Taxila, a historical center of learning. In Jabalpur, located in central India, the minimum and maximum day and night durations are 10 hours 35 minutes and 13 hours 25 minutes. South of this, the difference decreases, becoming zero at the equator where day and night are equal. Further north, the difference increases, reaching 24 hours at 66.6 degrees latitude, with a 24-hour day on January 22nd and a 24-hour night on December 22nd. At the North and South Poles, this difference extends to six months of day and six months of night.
   • Sun's Path and Solstices: Gathas 194-195 suggest the Sun's path of revolution is 180 Yojanas inside the circumference of Jambudvipa and 330 Yojanas outside its maximum circumference. This implies that sunlight can fall perpendicularly within this zone. Current calculations indicate that the region where the Sun's rays fall perpendicularly is bounded by the Tropic of Cancer in the north and the Tropic of Capricorn in the south. The Tropic of Cancer passes through the approximate middle of India, about 1,000 miles (125 Yojanas) from the southern coast. The Tropic of Capricorn is about 2,000 miles (250 Yojanas) south of this coast. The author connects the perpendicular incidence of the Sun's rays on the Tropic of Cancer with the start of "Dakshinayana" (southern solstice) and on the Tropic of Capricorn with the start of "Uttarayan" (northern solstice).

In conclusion, the article by Dr. Vidyadhar Johrapurkar provides a scholarly examination of the Jyotishkarandak, highlighting its significant astronomical data and comparing it with modern scientific understanding. It demonstrates the Jain tradition's early engagement with and sophisticated calculations in the field of astronomy, even though some of its conclusions differ from contemporary scientific models.