Saptami

Saptami is the seventh tithi of the bright fortnight, a Bhadra or wholesome tithi in the fivefold grouping. Its presiding deity is Surya, the Sun, and the seventh tithi carries solar observances: Ratha Saptami, in the bright fortnight of Magha, marks the Sun's turn toward the northern hemisphere and is kept as a kind of solar new year and day of purification. By this tithi the waxing Moon stands near its first quarter, half-lit in the evening sky. The panchanga reads Saptami as generally auspicious. These are the conventions of the calendar tradition, and the solar association of the seventh day sits alongside the lunar reckoning that defines the tithi itself, a reminder that the Hindu luni-solar calendar tracks both lights at once.

Ratha Saptami takes its name from the image of Surya's chariot, drawn by seven horses representing the colours of visible light and driven by the charioteer Aruna, and the observance of bathing before dawn on this tithi is explained in some sources as a ritual re-enactment of that chariot's turn toward the northern hemisphere. The pairing of a solar festival with a fundamentally lunar unit of time, the tithi, is a reminder that the Hindu calendar is properly luni-solar rather than purely lunar: months and tithis are reckoned from the Moon, but the year as a whole is kept aligned to the solar seasons through the insertion of an extra intercalary month, Adhika Masa, roughly once every three years, without which the lunar months would drift steadily out of step with the seasons over time.

The panchanga measures a tithi as an angle rather than a duration: one thirtieth of the circle the Moon travels away from the Sun and back again. Saptami occupies the arc from 72 to 84 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 Saptami carries Gara, the fifth, and the second Vanija, the merchant's 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 waxing through this arc, setting later each evening and carrying about 40 per cent of the disc lit. 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.