The Correctly Established Doctrine of Brahma, Volume 2

Everywhere, the results of observation are found to be identical; therefore, it is proven that the Earth has a spherical shape. One should not argue that this is merely a circular proof—that we are only proving what we have already assumed. By assuming sphericity, we find that in a triangle formed with a vertical pillar, the properties of an isosceles triangle are maintained This likely refers to the consistency of shadow lengths and angles at equal distances from a central point. Furthermore, the uniformity of results everywhere is based entirely on empirical testing; thus, all doubt is dismissed. In reality, the Earth has a slightly elongated body original: "bhū-dīrgha-piṇḍa"; a reference to the Earth's non-spherical irregularities or perhaps an early intuition of its oblate nature. However, because the difference between the minor diameter and the major diameter is extremely small, all the great teachers have treated them as equal.

Here, it is explained how the Celestial Equator and the Time-Circle are defined.

Even though the celestial sphere is rotated by the Pravaha wind The "provector wind" believed in ancient Indian astronomy to drive the daily rotation of the stars, over many years, no change is observed in the distance of the stars from the fixed Pole Star (the sine of the diurnal arc). From this, it is understood that the planes of the Celestial Equator and the diurnal circles—which originate from the fixed center of the actual celestial sphere—remain stable. It is appropriate to calculate time based on these two circles rotated by the uniform Pravaha wind, because time is beginningless, endless, and as unchanging as the Supreme Being (Achyuta). This same logic is used to understand time through ancient and modern water-clocks and other instruments.

The diurnal arc of the star called Kadamba The Pole of the Ecliptic is fixed, but the stars within the Kadamba region are seen to move. From this, it is inferred that the zodiac has a motion other than that caused by the Pravaha wind. It is clear from the logic of the sphere that this motion occurs along a path that is a great circle originating from the Kadamba. It is inferred that the cause of this oscillating motion referring to the theory of Trepidation or the precession of the equinoxes is a specific "hand-strike" or impulse given to the zodiac at the moment it was released by the Pravaha wind. The amount of shifting of the zodiac from the Celestial Equator (the primary path of the Pravaha) along this great circle is defined by the teachers as the Ayanāṃśa The precession of the equinoxes; the longitudinal difference between the tropical and sidereal zodiacs.

The calculation of this can be done by observing the disk of a star or a planet which has a constant position relative to the aforementioned great circle. Therefore, the knowledge of the zodiac's shift is determined specifically by observing the disk of the Sun. To determine the path of this great circle, one must understand how to find the "fixed" celestial declination from the "observed" celestial declination by knowing the difference between the planes of the observational equator and the fixed celestial equator; this is explained in this very book under the section on the "Rationalization of the Moon's Revolutions."

On the second day, in a period of sixty ghatikas 24 hours, the point where the Sun is situated returns to the meridian. The time it takes for the Sun to return to the meridian, multiplied by six, gives the difference in degrees of the equator (Right Ascension), because the meridian of one's own location acts as the horizon for the equator. The declination is known by the method mentioned. By doing this over many days, placing a sphere in front of oneself, marking the great circle called the Celestial Equator, and marking the daily declinations on the meridian circles corresponding to the successive differences in Right Ascension, it is observed that a great circle connecting these points of declination is formed. By this, it is proven that the Sun's path of travel is a Great Circle. Because it passes through the points of declination (Krānti), the name "Circle of Declination" (Krāntivṛtta - the Ecliptic) is most appropriate.