Tithi
Lunar day in the Hindu calendar
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Duration and variability
A tithi is defined as the time taken for the longitudinal angle between the Sun and the Moon to increase by 12°. While the average duration is approximately 23 hours 37 minutes, actual tithi lengths vary from about 19 hours, 59 minutes to 26 hours, 47 minutes depending on the Moon’s elliptical orbit and variable speed in the ecliptic.This variation is a result of the Moon’s non-uniform motion as described in Indian astronomical treatises such as the Surya Siddhānta and confirmed through modern astronomical observations.
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Calculation methods: traditional vs modern
Traditional Panchāngas often compute tithi boundaries using mean motions of the Sun and Moon as given in the Sūrya Siddhānta and later siddhāntic texts. These methods produce approximate times for tithi transitions. In contrast, modern almanacs generated by astronomical institutions use true longitudes derived from high-precision ephemerides (e.g., NASA JPL DE series).These differences in calculation can result in discrepancies of several minutes, and in rare cases, up to an hour, between traditional and modern Panchāngas.
Panchanga
A Hindu muhurta (forty-eight minute duration) can be represented in five attributes of Hindu astronomy namely, vara the weekday, tithi, nakshatra the Moon's asterism, yoga the angular relationship between the Sun and Moon and karana half of tithi.
Tithi plays an important role along with nakshatra in Hindus' daily as well as special activities in selecting the muhurta. There are auspicious tithis as well as inauspicious tithis, each considered more propitious for some purposes than for other.
In amānta lunar calendars, tithis are counted beginning at śukla pratipada, while in the pūrṇimānta lunar calendars, tithis are counted from kr̥ṣṇa pratipada. The śukla tithis are when the moon waxes, and the kr̥ṣṇa tithis are when the moon wanes. The average tithi lasts 23 hours 37.5 minutes, and can range from 19 hours 59 minutes to 26 hours 47 minutes. The calculation of tithi timings may also differ on whether one uses the traditional methods for calculating the Sun and Moon's movement as promulgated in the Sūrya Siddhānta or modern methods which correctly calculate the true motions of the Sun and Moon. The tithi in place at sunrise is considered the "tithi of the day", although the tithi may end before the next sunrise in which case the next tithi begins. Because the length of a tithi is also variable a case can arise where a tithi begins after sunrise and ends prior to the next sunrise, which is called a kṣaya tithi. The opposite phenomenon can occur where a tithi in place during a sunrise is still present in the following sunrise which is called an adhika or ahorātra tithi.
There are 30 tithis in each lunar month, named as: