Chapter on Mean Motion — 1

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...plus 161,841, placed below 161,841, divided by "Rama, Void, and Mountains" 703; in the reverse number system used in Sanskrit astronomy, the resulting quotient 230 is added to the upper 161,841 to get 162,071. This is divided by "Ages and Limbs" 64, and the resulting "omitted lunar days" avama; days dropped from the lunar calendar to sync with the solar cycle of 2,532 is subtracted from the upper 161,847. The resulting Ahargana the sum of days elapsed since the epoch is 159,316. When divided by seven, the remainder is 3. This indicates that the calculation was made for a Thursday, while Saturday has passed, and it is now Sunday sunrise. ॥ 2, 3 ॥

The Commentary of Sudhakara:
This is clear. Here is the rationale: Subtract the Saka year of the book’s commencement (which is 1105) from the desired Saka year to find the number of solar years elapsed since the book began. From there, the process of converting these into months is easy.

Then, the calculation of intercalary months adhimasa is explained through the rule "years elapsed in the Kali age multiplied by the Sun..." and so on. At the start of this work, the years elapsed in the current cosmic cycle Kalpa are 1,972,948,284. By dividing the years by "two and Ramas" and "void and Ramas" constants used to find remainders, the intercalary remainder in terms of months is 3/60. Since a full intercalary month does not fall exactly at the moment this book starts, the actual remainder is 1 + 3/60. By applying the inverse method to the number 65 and subtracting its parts, we find the number 66. Thus, the calculation of the intercalary months is established as stated. In this calculation, the value 908 was taken in place of "Serpents, Path, and Elephant" for the sake of simplicity.

Furthermore, by proportion, in every 703 $\times$ 64 lunar days, there are 704 omitted days ksayahah. From this, the omitted days for the desired lunar day are found by: $\frac{\text{Desired Lunar Day} \times 704}{703 \times 64}$. Thus, the calculation of omitted days is established. After subtracting the omitted remainder of 30 days, the actual omitted remainder is 3/60. This simple method of adjusting the lunar day via the inverse rule is very easy to follow. ॥ 2, 3 ॥

Starting Positions (Kshepakas):
The directions (10), the cows (9), the twins (2), and the universe (13) 10s 26° 12' 00" are for the Sun. For the Moon, they are the void (0), the twelve (12), the moon and moon (11), the limbs (6), and the twins (2) actually 10s 29° 05' 50"... for the Moon’s node, they are the elements (5), the mountains (7), the world (13), and the directions (10). ॥ 4 ॥
For Mars, they are the horses (7), the Earth’s parts (29), the Jinas (24), and the Earth (21). For Mercury, they are two (2), the eyes (2), the Earth (21), the Shakra (14), and the Ramas (30). ॥ 5 ॥
For Jupiter, the constant is two (2), the four (4), the void (0), and the arrows (51). For Venus, it is eight (8), the courage (18), the arrows (5), and the arrows (55). ॥ 6 ॥
For Saturn, they are the ages (4), the three (3), the four (4), and the mountains-moon (17-31). These are the positions in signs and so on. ॥ 7 ॥
The planet produced from the "day-heap" Ahargana should be added to its own starting constant. This gives the "mean" position at sunrise in Lanka the zero-meridian in Indian astronomy. ॥ 8 ॥

The Commentary of Sumatiharsha:

Sun: 10s 26° 12' 00", Moon: 10s 29° 05' 50", Moon’s Apogee: 4s 15° 12' 59", Moon’s Node: 9s 17° 25' 09", Mars: 7s 29° 24' 21", Mercury: 2s 21° 14' 30", Jupiter: 2s 04° 00' 51", Venus: 8s 18° 05' 55", Saturn: 4s 03° 04' 31" 07'''.

The phrase "planet produced from the day-heap" refers to the position calculated from the Ahargana. When this is added to its respective starting constant kshepaka, it results in the "Mean Planet" as it appears at mean sunrise on the equator Lanka. As it is said: "The mean planet is that which is at the horizon when the mean sun is in the city of the Ten-Headed One Ravana's Lanka." ॥ 4-6 ॥

Now, the calculation of the mean planets. First, what is meant by "mean-ness"? The passage of a planet through the twelve signs of the zodiac at its fixed, natural eastward speed is called a "revolution" bhagana. The number of times the Sun completes these twelve signs in a cosmic age Kalpa is the count of its revolutions. The portion of the current revolution that has been traveled, expressed in signs, degrees, etc., is called the Mean Planet.

The Commentary of Sudhakara:
This is clear. The rationale is that these starting constants kshepakas were created by taking the positions of the planets at the start of the book's epoch and adjusting them using the "seed-correction" bija methods, such as "multiply the years of the Kalpa by the void, void, void, and sun..." and so on. This is very easy to understand. ॥ 4-6 ॥

Calculating the Mean Sun, Mercury, and Venus:
Multiply the Ahargana by the "Universe" (13) and divide by the "Three, Void, and Path" (903). Subtract this quotient from the Ahargana; the result is the position in degrees, etc. These are the positions for the Sun, Mercury, and Venus. Then, subtract the minutes and seconds obtained by dividing the elapsed years by "Vedas and Limbs" (64). ॥ 7 ॥

The Commentary of Sumatiharsha:
Place the Ahargana in two places. Multiply one by "Universe" (13) and divide by "Three, Void, and Path" (903). Subtract the resulting degrees and minutes from the original Ahargana. This gives the degrees and so on for the Sun, Mercury, and Venus. In this calculation, specific corrections bija have been embedded within the divisors to simplify the process. To remove any remaining small errors, one must divide the elapsed years of this calculation system by "Vedas and Limbs" (64) and subtract the resulting minutes and seconds from the total.