Question

According to the Surya Siddhanta, what is the measure of the Earth's circumference (Bhuparidhi) in the unit of Yojanas?

• A. 5060 yojanas
• B. 1581 yojanas
• C. 4967 yojanas
• D. 5120 yojanas

Hint:

Memorize the "1600-5060" pair for the Surya Siddhanta. 1600 is the Diameter, and 5060 is the Circumference. Most questions in this exam cycle use these specific constants.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In Indian mathematical astronomy, the Earth is considered a sphere, and measuring its dimensions is the first step toward understanding planetary distances and parallax. The 'Bhuparidhi' refers to the equatorial circumference of the Earth. The unit used is the 'Yojana', which is a traditional measure of distance. Different Siddhantas give slightly different values for this circumference based on their specific terrestrial observations and mathematical constants.

Step 2: Key Formula or Approach:
The Surya Siddhanta (Bhugola-adhyaya) provides the following measures for the Earth:
1. Diameter (Vyasa): 1600 Yojanas.
2. Circumference (Paridhi): Defined by the ratio of the diameter to the circumference using a specific value of \(\pi\).
In the text, the verse states: "Yojanani shatani tri-shashtih..." implying a circumference of approximately 5059 and 2/3 yojanas.

Step 3: Detailed Explanation:
The value of 1600 yojanas for the diameter is a round figure used for ease of calculation. If we use the ancient Indian approximation for \(\pi\) (often \(\sqrt{10}\) or 22/7 in different contexts), the circumference is derived. The Surya Siddhanta explicitly defines the equatorial circumference as 5059.64 yojanas, which is conventionally rounded to 5060 yojanas in many practical manuals and exam contexts.
- Significance of Bhuparidhi: This value is essential for calculating the 'Deshantara' (longitudinal correction). Since 360 degrees of the Earth's surface correspond to 5060 yojanas, an astronomer can calculate how many yojanas correspond to one minute of time or one degree of arc.
- Sphuta Paridhi: It is important to note that 5060 is the circumference at the Equator. For any other location, the circumference (Sphuta Paridhi) decreases as we move toward the poles, calculated as \( \text{Equatorial Circumference} \times \cos(\text{Latitude}) \).
- Modern Comparison: While the exact length of a 'Yojana' is debated (ranging from 5 to 9 miles), if we take 1 yojana \(\approx\) 5 miles, 5060 yojanas \(\approx\) 25,300 miles, which is remarkably close to the modern equatorial circumference of approximately 24,901 miles.

Step 4: Final Answer:
The Surya Siddhanta specifies the Earth's circumference as 5060 yojanas.