Question

While the Sun appears to move along the 'Krānti-vr̥tta' (Ecliptic), along which specific circle do the other planets (Grahas) move, considering their celestial latitude (Śara)?

• A. Krānti-vr̥ttē (Ecliptic)
• B. Ahōrātra-vr̥ttē (Diurnal Circle)
• C. Vimandala-vr̥ttē (Planetary Orbit Circle)
• D. Kadamba-vr̥ttē (Polar Circle)

Hint:

Mnemonic: 'Vi' in Vimandala stands for 'Vikshepa' (Latitude). If a planet has latitude, it is in its Vimandala. Only the Sun has 0 latitude and stays in the Krantivritta.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In the geocentric model of Indian astronomy, the Sun is the only body that always moves strictly along the Ecliptic (Krānti-vr̥tta). The other planets (Moon, Mars, Mercury, Jupiter, Venus, and Saturn) have orbits that are slightly inclined relative to the Ecliptic. The angular distance of a planet from the Ecliptic is called 'Śara' (Celestial Latitude). Therefore, planets move on their own individual orbital planes.

Step 2: Detailed Explanation:
The circle representing the actual orbital path of a planet is called the 'Vimandala' (sometimes also called the 'Vikṣēpa-vr̥tta'). While the Krānti-vr̥tta is the reference plane, the Vimandala represents the plane in which the planet is physically located as it revolves around the Sun (or as seen from Earth).

1. Nodes (Pāta): The points where the Vimandala intersects the Krānti-vr̥tta are called 'Pātas' (Nodes). For the Moon, these are Rāhu and Kētu. When a planet is at its Pāta, its Śara (latitude) is zero, and it is momentarily on the Krānti-vr̥tta.
2. Latitude (Śara): As the planet moves along the Vimandala, it goes North or South of the Ecliptic. The maximum separation occurs \(90^{\circ}\) away from the nodes.
3. Contrast with other circles:
- Ahōrātra-vr̥tta: This is the daily path of a star or planet due to the Earth's rotation (parallel to the Equator). It is used for finding rising and setting times.
- Kadamba-vr̥tta: This refers to circles related to the poles of the ecliptic.
The Vimandala is essential for calculating 'Dr̥k-karma' (visibility corrections). Because planets are not exactly on the ecliptic, their rising and setting times differ from the points of the ecliptic they inhabit. Indian astronomers use the Vimandala to calculate the 'Vikṣēpa' (deflection) and then apply corrections to the longitude to find the 'Spaṣṭa' (true) visibility.

The Vimandala essentially describes the 3D reality of planetary motion. Every planet has its own unique Vimandala with a specific inclination (Kṣēpa). For example, the Moon's Vimandala is inclined at about \(5^{\circ}\) to the Krānti-vr̥tta, while the other planets have much smaller inclinations. Understanding the Vimandala is key to predicting eclipses (Grahaṇa) and planetary conjunctions (Yuddha).

Step 3: Final Answer:
The planets move along the Vimandala-vr̥ttē.