Multiply the sine of the anomaly (Kendra-jya) by the epicycle and divide by 360; the arc of the result is the Manda-correction (Equation of the Center).
Modern Technical Commentary:
The fundamental formula for the Equation of the Center. It transforms the mean eccentricity into a longitudinal correction (Phala) using a sine-wave model. This represents the Sun's non-uniform motion as seen from Earth.
Multiply the sine of the anomaly (Kendra-jya) by the epicycle and divide by 360; the arc of the result is the Manda-correction (Equation of the Center).
Modern Technical Commentary:
The fundamental formula for the Equation of the Center. It transforms the mean eccentricity into a longitudinal correction (Phala) using a sine-wave model. This represents the Sun's non-uniform motion as seen from Earth.
Core Algorithm:
1. Calculate the Sine of the Anomaly (Kendra-jya).
2. Resulting Phala (Equation of Center) = (Kendra-jya * Epicycle) / 360.
3. Apply the correction to the Mean Sun based on the Kendra half-orbit.
Parameters
ahargana: number
Current day count
Returns number
True solar longitude (Ravisphuta) in degrees [0, 360)
Calculate the True Longitude (Spashta-Surya) of the Sun.
[Ch. II, v.39, 45]
Siddhantic Proof: Spashta (True Longitudes) v.39
Sanskrit (Devanagari):
तद्गुणे भुजकोटिज्ये भगणांशविभाजिते। तद्भुजज्याफलधनुर्मान्दं लिप्तादिकं फलम्॥
Translation (Burgess):
Multiply the sine of the anomaly (Kendra-jya) by the epicycle and divide by 360; the arc of the result is the Manda-correction (Equation of the Center).
Modern Technical Commentary:
The fundamental formula for the Equation of the Center. It transforms the mean eccentricity into a longitudinal correction (Phala) using a sine-wave model. This represents the Sun's non-uniform motion as seen from Earth.
Siddhantic Proof: Spashta (True Longitudes) v.39
Sanskrit (Devanagari):
तद्गुणे भुजकोटिज्ये भगणांशविभाजिते। तद्भुजज्याफलधनुर्मान्दं लिप्तादिकं फलम्॥
Translation (Burgess):
Multiply the sine of the anomaly (Kendra-jya) by the epicycle and divide by 360; the arc of the result is the Manda-correction (Equation of the Center).
Modern Technical Commentary:
The fundamental formula for the Equation of the Center. It transforms the mean eccentricity into a longitudinal correction (Phala) using a sine-wave model. This represents the Sun's non-uniform motion as seen from Earth.