Delight of Mathematicians

The Joy of Calculation

Explanation: Place the total elapsed days Dyugana in two separate positions. Multiply the bottom position by 3 and divide the result by 503. Subtract the resulting degrees and minutes from the top position of elapsed days. This gives the degrees for the Sun, as well as for the mean positions of Mercury, Venus, and other planets. Add the previous epoch constants Dhruva fixed values representing the position of planets at the start of the current era of 11-15-22-3. Multiply the elapsed years of the era Sharanabda by 3 and divide by 15; subtract the resulting minutes. Furthermore, multiply the distance by 80 and divide by 50; subtract the resulting seconds to arrive at the Mean Sun Madhya Surya.

For the Moon

original: "Chandrasya"

Verse: Multiply the total elapsed days by thirteen original: "Vishwa-Aditya," referencing the 13 deities or solar forms and place it in two positions; divide the second by twenty-eight (28). Add the resulting degrees to the elapsed days. Then, divide the elapsed days by 1522 original: "shaila-adri-yuga-rupa-nagara" and add those degrees. Thus, the Mean Moon is always found. Always add the epoch constant of 11-8-46-33 original: "rudra-ashta-anga-arnava-sura". Multiply the elapsed years of the era by three, divide by eight, and subtract those minutes. Subtract the seconds derived from the regional distance to find the Moon.

Explanation: Multiply the total elapsed days Dyugana by 13 and place the result in two positions. Divide the bottom position by 28. Also, divide the total elapsed days by 1522. Add both these resulting degrees and minutes to the 13-times elapsed days calculated initially to find the Moon's position in degrees and minutes Amshadi. Add the previous epoch constant of 11-8-46-33. Multiply the elapsed years of the era Sharanabda by 3 and divide by 8; subtract the resulting minutes Liptas. Since the regional distance for this location is 80 yojanas a traditional unit of distance, roughly 8-15 kilometers, multiply by 80 and divide by 50. Subtract the resulting seconds Viliptas to obtain the Mean Moon Madhya Chandra.

For the Moon's Apogee

original: "Chandrocchaku"

Verse: The sum of the degrees and minutes obtained by dividing the total elapsed days by one hundred and sixty-nine original: "nandaih-hutashaih," 9 and 3 squared/combined is the apogee. Always add the epoch constant 9-16-16-19 original: "dwisapta-indu-tara-rashmi". Multiply the elapsed years by 3 and divide by 96; subtract those minutes to find the apogee. Subtract the seconds calculated from the regional distance.

Explanation: The prose for this section follows the verse's logic To find the Moon's Apogee Chandroccha the point where the Moon is farthest from the Earth, divide the total elapsed days by 169. Add the epoch constant of 9-16-16-19. Multiply the elapsed years by 3 and divide by 96, then subtract those minutes. Finally, subtract the correction for the regional distance in seconds to determine the precise position of the Moon's apogee.