Question

In the context of spherical astronomy and gnomonics, what is the definition of 'Shanku' (Sine of Altitude)?

• A. Natamshajya
• B. Charajya
• C. Unnatamshajya
• D. Lagnajya

Hint:

'Unnata' = Elevated/High. 'Amsha' = Degrees. 'Jya' = Sine. Therefore, the Sine of the Elevation (Altitude) is the Shanku. Remember: Shanku = Sine(Altitude).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The 'Shanku' is one of the most fundamental parameters in the Indian system of coordinates (Tri-Prashna). Physically, it refers to a vertical gnomon (a stick) of 12 units. Mathematically, in the celestial sphere, it represents the Sine of the Altitude of a celestial body. It describes how high a planet or the Sun is above the horizon.

Step 2: Key Formula or Approach:
In a right-angled triangle formed by the observer, the planet, and the horizon:
1. Unnatamsha: Altitude (the angle above the horizon).
2. Natamsha: Zenith Distance (the angle from the point directly overhead).
\[ \text{Natamsha} = 90^\circ - \text{Unnatamsha} \]
3. Shanku = \( R \sin(\text{Unnatamsha}) \) (where R is the radius of the circle).

Step 3: Detailed Explanation of Options:
- Unnatamshajya: This is the Sine (Jya) of the Altitude (Unnatamsha). By definition, this is the Shanku.
- Natamshajya: This is the Sine of the Zenith Distance. In the context of the shadow triangle, this is known as the 'Drigjya'.
- Charajya: This is the Sine of the ascensional difference (Chara), used to calculate the length of the day.
- Lagnajya: The Sine of the longitude of the rising sign (Lagna), which is not related to vertical altitude.

Step 4: Final Answer:
The mathematical definition of Shanku is Unnatamshajya.