Question

In the calculation of the Sun's longitude using the Ahargana (cumulative day count) method in 'Grahalaghava', arrange the following computational steps in their correct functional sequence:
A. Ahargana 150 = Phalam (result in minutes)
B. Finding the total Ahargana (Day count)
C. Ahargana 70 = Phalam
D. Summation of results to find the Sun's position
E. Ahargana 70 = Phalam (result in degrees)

• A. C, B, A, E, D
• B. D, E, A, B, C
• C. A, E, D, B, C
• D. B, E, C, A, D

Hint:

In 'Karana' math, the denominator 70 is specifically used for the Sun's degree correction. Remember: Ahargana is ALWAYS step 1. Final Summation is ALWAYS the last step. This helps eliminate options (1), (2), and (3) immediately.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The Grahalaghava, authored by Ganesh Daivajna, is a 'Karana' text designed to simplify astronomical calculations. One of its primary simplifications is the method of finding the Sun's longitude (Surya-spashtikarana) without using complex trigonometry. Instead of the standard Siddhantic method involving sine tables, it uses a series of simple arithmetic ratios applied to the Ahargana (the count of days since the epoch). The goal is to calculate the angular distance the Sun has traveled since its position at the start of the current year (the epoch).

Step 2: Detailed Explanation of Steps:
1. Finding the Ahargana (B): The first and most critical step in any Karana calculation is to determine the Ahargana. This is the total number of terrestrial days that have elapsed from the start of the specific epoch year (which for Grahalaghava is Saka 1442/1443) to the target date. All subsequent movements are based on this day-count.
2. Calculation of Degrees (E): The Sun's daily motion is approximately $0^\circ 59' 08''$. This is nearly $1^\circ$ per day. In the simplified method, the astronomer first takes the Ahargana itself as the base degree. However, since the Sun moves slightly less than $1^\circ$, a correction is needed. Dividing the Ahargana by 70 gives a quotient that represents a primary corrective factor in degrees.
3. Refining the Factor (C): After obtaining the primary degree-based correction, the text involves further operations with the factor of 70 (or 60 depending on the specific planetary dhruva being calculated) to align the mean motion with the true elliptical path observed from Earth.
4. Calculation of Minutes (A): Further precision is added by dividing the Ahargana by 150. This result is in 'Kalas' (minutes of arc). This factor compensates for the finer fractional parts of the Sun's motion that accumulate over several days.
5. Synthesis (D): Finally, all these components—the base Ahargana, the degree-corrections from the factor 70, and the minute-corrections from the factor 150—are combined (added or subtracted according to the rules) to find the final longitude of the Sun.

Step 3: Verification with Options:
The sequence starts with finding the base value (B), then calculating the large degree-correction (E), followed by its refinement (C), then the fine-tuning minute correction (A), and finally the summation (D). This matches the sequence B, E, C, A, D.

Step 4: Final Answer:
The logical sequence for Sun's computation in Grahalaghava is B, E, C, A, D.