The Five Astronomical Canons

In a similar way, stanza 6 lists the moon’s equations of the center The "equation of the center" is the correction needed to account for a planet's elliptical orbit rather than a perfect circle for every 15 degrees of anomaly. These equations do not match very closely with the equivalent figures provided by Ptolemy Claudius Ptolemy, the 2nd-century Greco-Egyptian astronomer, who calculated the maximum equation as 5° 1'.—The length of the revolution of the moon’s node The points where the moon's path crosses the ecliptic is recorded in Chapter VIII, stanza 8, as 6,796 days and 7 hours. This is quite close to Ptolemy’s calculation of the same value, which was 6,796 days and 14 hours, etc.—Regarding the maximum latitude of the moon, we find two contradictory statements in VIII. 11 and VIII. 14, assuming the interpretation provided in this translation is correct. According to the first, it would be 240' 4 degrees; according to the second, it would be 270' 4.5 degrees, which is the value typically found in Indian astronomical works. Concerning the explanation of stanza 14, I should note that my collaborator attempted to link the rule to the standard estimate of the moon’s maximum latitude. However, the fraction 21/9, if the denominator is treated as the reduced Radius, would actually result in a maximum latitude of 280'. While it might seem unlikely that a single book would give different values for the same measurement, it is entirely possible that the older Siddhântas Siddhântas are traditional Indian astronomical treatises included practical rules gathered from various sources without fully understanding the underlying logic.

Stanza 13 provides 30' and 34' as the average measurements for the diameters of the sun and moon, respectively. Stanza 15 provides the standard Indian rule for determining the actual diameters based on these average diameters and the relationship between their actual and average speeds.

The maximum parallax The apparent shift in position of a celestial body when viewed from different locations is, as is common in Indian astronomy, assumed to be equal to the average movement during four nâḍikâs A nâḍikâ is a unit of time equal to 24 minutes; four nâḍikâs equal 96 minutes. This explains the rule in stanza 9 for calculating the parallax in longitude, where the result represents the difference between the solar and lunar parallaxes.

The parallax in latitude is calculated using the same principle (stanzas 10—14). However, the result does not provide the difference between the sun and moon's parallax, but only the moon's, as the solar parallax is ignored. The translation notes an error in the initial calculation of the zenith distance of the nonagesimal The highest point of the ecliptic above the horizon.—The rule for calculating the length of an eclipse once the true latitude is known (stanza 16) follows the standard method.

The parts of the Romaka Siddhânta The "Roman Treatise," an Indian astronomical work influenced by Western/Greek methods that remain unexplained are primarily the various kshepa-quantities Additive constants or "interpolations" used to adjust calculations for a specific epoch found in the rules for determining the ahargaṇa The number of elapsed days from a fixed epoch (Chapter I) and the average positions of the sun, moon, etc. (Chapter VIII). They,