Krishna Chaturthi

Krishna Chaturthi is the nineteenth tithi overall, the fourth day of the dark fortnight, and like its bright-fortnight counterpart it is sacred to Ganesha. Sankashti Chaturthi, kept on this waning-side fourth tithi each month, is a fast dedicated to Ganesha as the remover of obstacles and difficulties, the name means the fourth that removes distress, and is broken after the moonrise sighting. In the fivefold grouping the fourth tithi is Rikta, generally unfavourable for ordinary beginnings, but the Ganesha observance overrides that for its devotees. The waning Moon rises late in the night by this tithi. These are the conventions of the calendar and festival tradition, in which the fourth day of both fortnights belongs to Ganesha.

Sankashti Chaturthi is calculated by a rule distinct from most other festival tithis: it is fixed not to sunrise or midday but to whichever date the fourth tithi is prevailing at moonrise, since the fast is broken only upon sighting the risen Moon, so almanacs must compute the specific hour the Moon crosses the horizon on the relevant evening, a calculation that varies by latitude and longitude and is one of the more technically demanding routine determinations panchanga makers perform each month. Among the twelve monthly Sankashti Chaturthis, the one falling in the month of Magha, called Sakat Chauth in North Indian practice, is regarded as the most important of the year.

Behind the observance sits a piece of arithmetic. A tithi is the time the Moon takes to open a further twelve degrees of separation from the Sun. Krishna Chaturthi occupies the arc from 216 to 228 degrees of that separation. Because the Moon travels an elliptical orbit its angular speed is not constant, so that twelve degree arc is crossed in anywhere from roughly nineteen to roughly twenty six hours. The convention that resolves this is simple and consequential: the civil day takes the name of the tithi that is running at sunrise. A tithi shorter than the interval between two sunrises can therefore be skipped entirely, which the tradition calls a kshaya tithi, and one longer than that interval can carry its name over two civil days, an adhika or vriddhi tithi. Both occur in the ordinary course of a year, and both are why an observance can appear on two dates in the same almanac.

Each tithi is halved again, and each half carries a karana, so the first half of Krishna Chaturthi carries Bava, first of the seven movable karanas, and the second Balava, the second movable karana. Seven of the eleven karanas repeat, cycling eight times through the month, while four are fixed to particular half tithis at the month's opening and close.

The Moon is waning through this arc, rising later each night and showing about 87 per cent of the disc lit. The phase follows from the elongation and not the other way round, so the tithi and the shape of the disc are two readings of one measurement.