Question

Match List I (Coordinate Relationships) with List II (Standard Terms):

List I		List II
A.	\(\text{Natamsha} - \text{Krantyansha}\)	I.	Krantyansha
B.	\(\text{Akshansha} + \text{Krantyansha}\)	II.	Lambansha
C.	\(\text{Natamsha} - \text{Akshansha}\)	III.	Natamsha
D.	\(90^\circ - \text{Akshansha}\)	IV.	Akshansha

• A. A-IV, B-III, C-I, D-II
• B. A-III, B-IV, C-II, D-I
• C. A-II, B-I, C-III, D-IV
• D. A-I, B-II, C-IV, D-III

Hint:

Remember the Midday Rule: Zenith Distance = Latitude $\pm$ Declination. If the Sun is on the Equator (Kranti = 0), then Zenith Distance = Latitude. This makes matching Aksha and Nata very easy.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In spherical astronomy, the relationships between the Latitude (Aksha), Declination (Kranti), Zenith Distance (Natamsha), and Altitude (Unnatamsha) are used to determine local time and position. These formulas are derived from the 'Meridian Triangle'.

Step 2: Detailed Matching of Components:
1. Akshansha (IV): The Latitude of a place. At midday, the Zenith Distance (Natamsha) of the Sun minus its Declination (Krantyansha) equals the Latitude.
\[ \phi = z - \delta \rightarrow \text{Akshansha} = \text{Natamsha} - \text{Krantyansha} \]
Therefore, A matches with IV.
2. Natamsha (III): The Zenith Distance. On the day when the Sun is at its peak declination, the total distance from the Zenith can be seen as the sum of local latitude and declination (if the Sun is South of the zenith).
\[ z = \phi + \delta \rightarrow \text{Natamsha} = \text{Akshansha} + \text{Krantyansha} \]
Therefore, B matches with III.
3. Krantyansha (I): Declination. From the same midday formula:
\[ \delta = z - \phi \rightarrow \text{Krantyansha} = \text{Natamsha} - \text{Akshansha} \]
Therefore, C matches with I.
4. Lambansha (II): This is the Co-latitude ($90 - \phi$). It is the angle between the Zenith and the celestial North Pole.
\[ \text{Lambansha} = 90 - \text{Akshansha} \]
Therefore, D matches with II.

Step 3: Verification:
Matching A-IV, B-III, C-I, D-II gives us Option (1).

Step 4: Final Answer:
The correct matches represent the fundamental equations of the Meridian Circle.