Pratipada

Pratipada is the first tithi, the opening lunar day of the fortnight. A tithi in the Hindu calendar is not a solar day but the time the Moon takes to gain twelve degrees of longitude on the Sun, so the thirty tithis divide one synodic month into two fortnights (paksha) of fifteen each. This Pratipada falls in the Shukla or bright fortnight, the waxing half that begins just after the new moon. In the traditional fivefold grouping of tithis it is a Nanda tithi, one of the joyful days, and its presiding deity is commonly given as Agni or Brahma. Being the start of the waxing Moon, it is read in the panchanga as favourable for beginnings and fresh undertakings. These are the calendar tradition's conventions; the astronomical basis is simply the widening angle between Moon and Sun after conjunction.

A tithi's real-world duration is never fixed: because the Moon's angular speed varies between roughly eleven and fifteen degrees a day over its elliptical orbit while the Sun's varies far less, the twelve-degree gain that defines a tithi can take as little as about nineteen hours or as long as about twenty-six, so Pratipada on one date is not the same length of clock time as Pratipada a few months later. This variability produces two calendrical phenomena the panchanga must account for: tithi kshaya, when a tithi begins and ends between one sunrise and the next and so never governs a civil day at all and is skipped in the naming of dates, and tithi vriddhi, when a tithi is long enough to span two consecutive sunrises and so the same tithi name is given to two days running. Both are ordinary arithmetic consequences of the Moon's uneven motion, not irregularities in the count itself.

A tithi is not a day. It is an arc, the interval in which the Moon gains twelve degrees of longitude on the Sun, and the civil day merely borrows its name. Pratipada occupies the arc from 0 to 12 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 Pratipada carries Kimstughna, the fixed karana that opens the lunar month and belongs to no repeating cycle, and the second Bava, first of the seven movable karanas. 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 waxing through this arc, setting later each evening and carrying under one per cent of the disc lit, which is to say effectively none. That figure is a consequence of the definition rather than an observation added to it: elongation fixes the phase, so naming the tithi already names how much of the disc is lit.