Question

What is the technical name for the angular difference between the 'Manda-spashta' planet (partially corrected position) and the 'Madhyama' planet (mean position)?

• A. Bhujaphalam
• B. Deshantaram
• C. Mandaphalam
• D. Sheeghraphalam

Hint:

'Manda' means slow. This correction deals with the planet slowing down or speeding up due to its own orbit. Link the term 'Manda-spashta' directly to 'Mandaphalam'.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Planets do not move in perfect circles at constant speeds; they move in elliptical orbits. Consequently, their "true" position in the sky differs from their "mean" (average) position. In Indian astronomy, two main corrections (Phalas) are applied to the mean planet to find its true position: Manda Phala (Equation of Center) and Sheeghra Phala (Equation of Conjunction/Parallax).

Step 2: Key Formula or Approach:
The first correction applied is based on the eccentricity of the orbit.
\[ \text{Manda-spashta Graha} = \text{Madhyama Graha} \pm \text{Manda Phala} \]
Therefore:
\[ \text{Manda Phala} = \text{Manda-spashta Graha} - \text{Madhyama Graha} \]

Step 3: Detailed Explanation:
1. Madhyama Graha: The hypothetical position if the planet moved at a constant speed in a circular orbit around the Earth.
2. Mandaphalam: This correction accounts for the planet's elliptical path. It depends on the 'Manda Kendra' (the angular distance of the planet from its apogee/perigee).
3. Manda-spashta Graha: The position of the planet after the Manda Phala has been applied. For the Sun and Moon, this is the "True" (Spashta) position. For other planets, a further 'Sheeghra' correction is needed.
- Bhujaphalam: A general term for a sine-based result.
- Deshantaram: The correction for the difference in terrestrial longitude between the observer and the prime meridian (Ujjain).
- Sheeghraphalam: The second major correction representing the relative position of the Earth and the planet.

Step 4: Final Answer:
The difference between the Manda-spashta and Madhyama positions is called the Mandaphalam.