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How Panchangam is caluculated
The panchangam calculation requires two important heavenly bodies – the sun and the moon, and will be as accurate as how these heavenly bodies are calculated. In ancient times, there were many methods of calculating them. The most ancient one is Vakyam and the later one is the Driga Ganita (Thirukanitham). The Vakyam is an ancient system where planetary motions are described in simple sentences (hence the Vakyam).
The difference between Thiruganitam, Vakyam
The Vakyam has not been updated in 1500 years. The eclipse calculations in the Vakya panchangam and others are copied from the Druka ganita calculations. This has created great confusion. Which one is accurate? The Druka Ganitam / Thiruganitam relies on modern calculations using spherical trigonometry or NASA’s JPL. The inaccuracies in the Vakyam calculations can have errors.
'Thirukanitham' more accurately represents the actual position of the celestial bodies.
'Vakyam' is a more approximate method that computes the positions of planets based on the mean motions of planets.