Discernment of the Truth of Astronomical Principles

The Axis and the Four Cities

Mount Meru the sacred mountain at the center of the world in Hindu cosmology passes through the middle of the Earth-sphere Bhūgola|The physical, spherical planet Earth and emerges on both sides. At the top of this axis, located at the center, dwell the ancient Great Sages and the Gods 13.

In the same way, at the bottom, the Asuras original: asurāḥ; often translated as demons or titans, they are the inhabitants of the lower realms reside, occupying the opposite side. Within the circle of the Earth's equator Nirukta-deśa|The equatorial region where the day and night are of equal length, there are four primary cities:

• Lanka is situated in the middle of the Earth.

• To the East is Yamakoti.
  t. vi. 5 A reference likely pointing to a specific verse or chapter in a commentary

• To the West is the city called Romaka.

• Directly opposite Lanka, "below," is Siddhapura.

In the North is Meru, and in the South is the other pole. Thus, there are always six primary locations situated around the Earth's core 16. One should imagine themselves at any one of these locations. All beings, whether gods or humans, are situated "upright" relative to their own position, even if they appear "upside down" original: adhasthāt; meaning below or underneath to those on the opposite side of the sphere 17.

Calculating the Sphere

For those who understand the Sphere of the World Loka-gola|The cosmic or terrestrial sphere, the prime meridian original: rekhā; literally 'line', referring here to the line of zero longitude passing through Lanka and Meru is the reference for one's own country 18. By understanding the division of countries, one calculates the Gnomon Śaṅku|A vertical rod used in ancient astronomy to measure shadows and determine latitude.

To everyone, Meru always appears to be in the North. Similarly, for those at the other pole, Meru appears to be in the South 19.

When the sun rises in Lanka, it is midday in Yamakoti, sunset in Siddhapura, and midnight in Romaka 1-2. This is the constant rule for the equatorial regions. A true "Knower of the Sphere" Gola-vid|An expert in spherical astronomy understands that "East" is simply the direction in which the sun is first seen at any given location 3-4.

The Mathematics of the Circle

Just as we determine the circumference of the Earth's sphere from its diameter, the knowledge of the diameter leads to the result of the circumference 5. According to the tradition of the Sūrya Siddhānta Sūrya Siddhānta|A foundational Sanskrit treatise on Indian astronomy, dated to the 4th-5th century CE, the calculation is made precise.

Without knowing the proportion of the diameter to the circumference, the true size of the Earth cannot be known 7. The ancient sages followed a specific rule for this. The compassionate Sun God referring to the divine source of the Sūrya Siddhānta provided the rule:

The square of the diameter multiplied by ten gives the square of the circumference.

This describes the ancient Indian approximation of Pi (π) as the square root of 10, or approximately 3.1622

Therefore, the diameter is the square root of the circumference's square divided by ten 9. By utilizing the Sines Kramajyā|The trigonometric Sine function and their inverse equivalents, one can determine the exact measurements of the planetary orbits and the Earth's dimensions 10. These calculations are refined by the division of the circle into degrees and minutes to avoid errors in time and position 11-12.