Question

What is the name for the difference between the true longitude (Spashta) and mean longitude (Madhyama) of a planet?

• A. Madhyamantaram
• B. Bhujantaram
• C. Charantaram
• D. Udayantaram

Hint:

Think of 'Bhuja' (Arm). The difference between where the Sun "should" be and where it "is" is like an angular reach or arm (Bhuja). Bhujantara is the primary "Equation of Center" time correction.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
As discussed in previous questions, the mean planet (Madhyama) moves at a constant speed, while the true planet (Spashta) moves at a variable speed. The difference between these two is generally caused by the eccentricity of the orbit. In the context of time correction (Equation of Time), this difference has a specific technical name.

Step 2: Detailed Explanation of Corrections:
1. Equation of Time: To convert mean time (clock time) to true solar time (sundial time), two corrections are applied.
2. Bhujantaram: This is the correction due to the unequal motion of the Sun in its elliptical orbit. It is the difference between the mean Sun and the Sun corrected for eccentricity (Manda-spashta Sun). It is also known as the "equation of center" correction for time.
3. Udayantaram: This is the correction due to the obliquity of the ecliptic (the Sun's path being tilted relative to the Earth's equator).

Step 3: Analyzing the Options:
- Bhujantaram: Correctly describes the "Spashta-Madhyama-antaram" (True-Mean difference) of the Sun applied to the length of the day.
- Charantaram: Difference in ascensional difference (Chara), used for finding the length of the day at different latitudes.
- Madhyamantaram: A redundant term not used technically.

Step 4: Final Answer:
The difference between the true and mean longitude as a correction is Bhujantaram.