Question

What is the maximum celestial latitude (Parama-shara) of the Moon as defined in classical Indian astronomical texts?

• A. 10'
• B. 270'
• C. 90'
• D. 120'

Hint:

Think of the number 27. The 27 Nakshatras are the Moon's home. The max latitude is 10 times that number: 270 minutes ($4.5^\circ$).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The 'Shara' refers to the celestial latitude of a planet, which is its angular distance North or South of the Ecliptic. This occurs because the orbits of the planets (including the Moon) are tilted relative to the Earth's orbital plane (the Ecliptic). The point where the Moon's path crosses the Ecliptic is called a node (Rahu or Ketu). The maximum distance the Moon reaches from the Ecliptic is called the 'Parama Shara'.

Step 2: Key Formula or Approach:
In modern astronomy, the inclination of the Moon's orbit is approximately 5.14 degrees. Ancient Indian astronomers measured this in degrees and minutes.
1. The standard value given in texts like the Surya Siddhanta is 4.5 degrees or $4^\circ 30'$.
2. To convert this to minutes (Kalas):
\[ \text{Value in minutes} = (4 \times 60) + 30 \]
\[ \text{Value in minutes} = 240 + 30 = 270' \]

Step 3: Detailed Explanation:
The Moon's latitude (Shara) is a sine function of its distance from the nodes.
\[ \text{Shara} = \text{Parama Shara} \times \sin(\text{Distance from Node}) \]
When the Moon is 90 degrees away from Rahu or Ketu, its latitude reaches the maximum value of 270 minutes (or 4.5 degrees).
- This value is critical for predicting eclipses. An eclipse can only occur if the Moon is close enough to a node that its 'Shara' is less than the combined radii of the Sun and Moon.
- Other Options: 90' and 120' are too small. 10' is negligible. 270' is the standard Siddhantic constant for the lunar orbital tilt.

Step 4: Final Answer:
The maximum latitude (Parama-shara) of the Moon is 270 minutes.