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How does the Tamil calendar system work?

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Can you please share, how does the Tamil calendar system work? How many day in each month? Is that day count vary like February in leap year?

According to the age old customs and beliefs of the astronomer acharyas of Tamil Land, a new month begins on the day if Sun moves from its old rASi to the new, before sunset of that day. (In Kerala, the rule is that Sun should have entered the new rASi at sunrise on that day.) The sun travels about 53 seconds of arc in one day, thus taking approximately 30 days to move through one rASi to the next. But these are all approximate figures and vary depending on several extraneous factors and so, the number of days in each month varies slightly.

There is no fixed rule like February or leap year in our Indian system of almanacs because we reckon the months basically on sun's entry into the 12 rASis.
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