Question

In the context of Indian Mathematical Astronomy (Siddhanta Jyotish), what is the specific numerical value of 'Paramakrānti' (the maximum declination or the obliquity of the ecliptic) in degrees?

• A. 10
• B. 24
• C. 12
• D. 27

Hint:

Remember: Modern science = \(23.5^{\circ}\), Ancient Indian science = \(24^{\circ}\). In Jyotish exams, always stick to the classical value of 24 unless modern astronomy is specifically mentioned.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The term 'Paramakrānti' refers to the maximum angular distance that the Sun can reach either North or South of the Celestial Equator. In modern Western astronomy, this is known as the 'Obliquity of the Ecliptic', which is approximately \(23.44^{\circ}\). However, in the classical Indian astronomical treatises such as the Sūrya Siddhānta, Siddhānta Śirōmaṇi, and the works of Āryabhaṭa, this value was traditionally standardized as \(24^{\circ}\). This constant is fundamental for calculating the Sun's position, the length of the day, and the ascensional difference (Cara).

Step 2: Detailed Explanation:
The path of the Sun in the sky is called the 'Krānti-vr̥tta' (Ecliptic), while the projection of the Earth's equator into the celestial sphere is the 'Nāḍī-vr̥tta' (Celestial Equator). These two circles are not in the same plane; they intersect at an angle. The maximum separation between these two circles occurs at the Summer and Winter Solstices (Ayanānta).

The value of \(24^{\circ}\) was used by ancient Indian astronomers because it simplified trigonometric calculations. In the Indian sine system (Jyā), the radius of the circle was often taken as 3438 minutes of arc. With a Paramakrānti of \(24^{\circ}\), the sine of this angle (\(24^{\circ}\)) is approximately 1397. This specific value appears repeatedly in mathematical formulas to determine the 'Krānti' (declination) of the Sun at any given point in the zodiac using the formula:
\[ \sin(\text{Krānti}) = \sin(\text{Longitude}) \times \sin(\text{Paramakrānti}) \]
While modern measurements show that this angle is gradually decreasing over thousands of years due to the Earth's axial tilt variations, the traditional Jyotish texts maintain \(24^{\circ}\) as the working constant for calculating the 'Pañcāṅga'. This value is also crucial in determining the boundaries of the tropical zones and the exact timing of the 'Saṃkrāntis' (entry of the Sun into a new zodiac sign).

Furthermore, the Paramakrānti is the basis for constructing the 'Krānti-pātī' or the tables of declination. It allows astronomers to calculate the 'Lagnāntara' (difference in rising times of signs) and helps in the correct orientation of a 'Śaṅku' (gnomon) shadow. Even today, for traditional ritualistic timings, the value of 24 is often preferred in the 'Saurapakṣa' and 'Brāhmapakṣa' traditions of Siddhanta.

Step 3: Final Answer:
The value of Paramakrānti is \(24^{\circ}\).