Principles of the religious calendar

Religious holidays are determined by a lunisolar calendar that is based on calculations of the actual postions of the Sun and Moon. Most holidays occur on specified lunar dates (tithis), as is explained later; a few occur on specified solar dates. The calendrical methods presented here are those recommended by the Calendar Reform Committee (1957). They serve as the basis for the calendar published in The Indian Astronomical Ephemeris. However, many local calendar makers continue to use traditional astronomical concepts and formulas, some of which date back 1500 years.

The Calendar Reform Committee attempted to reconcile traditional calendrical practices with modern astronomical concepts. According to their proposals, precession is accounted for and calculations of solar and lunar position are based on accurate modern methods. All astronomical calculations are performed with respect to a Central Station at longitude 82°30' East, latitude 23°11' North. For religious purposes solar days are reckoned from sunrise to sunrise.

A solar month is defined as the interval required for the Sun's apparent longitude to increase by 30o, corresponding to the passage of the Sun through a zodiacal sign (rasi). The initial month of the year, Vaisakha, begins when the true longitude of the Sun is 23° 15' (see Table below). Because the Earth's orbit is elliptical, the lengths of the months vary from 29.2 to 31.2 days. The short months all occur in the second half of the year around the time of the Earth's perihelion passage.

Lunar months are measures from one New Moon to the next (although some groups reckon from the Full Moon). Each lunar month is given the name of the solar month in which the lunar month begins. Because most lunations are shorter than a solar month, there is occasionally a solar month in which two New Moons occur. In this case, both lunar months bear the same name, but the first month is described with the prefix adhika, or intercalary. Such a year has thirteen lunar months. Adhika months occur every two or three years following patterns described by the Metonic cycle or more complex lunar phase cycles.

More rarely, a year will occur in which a short solar month will pass without having a New Moon. In that case, the name of the solar month does not occur in the calendar for that year. Such a decayed (ksaya) month can occur only in the months near the Earth's perihelion passage. In compensation, a month in the first half of the year will have had two New Moons, so the year will still have twelve lunar months. Ksaya months are separated by as few as nineteen years and as many as 141 years.

Lunations are divided into 30 tithis, or lunar days. Each tithi is defined by the time required for the longitude of the Moon to increase by 12o over the longitude of the Sun. Thus the length of a tithi may vary from about 20 hours to nearly 27 hours. During the waxing phases, tithis are counted from 1 to 15 with the designation Sukla. Tithis for the waning phases are designated Krsna and are again counted from 1 to 15. Each day is assigned the number of the tithi in effect at sunrise. Occasionally a short tithi will begin after sunrise and be completed before the next sunrise. Similarly a long tithi may span two sunrises. In the former case, a number is omitted from the day count. In the latter, a day number is carried over to a second day.

History of the Indian calendar

The history of calendars in India is a remarkably complex subject owing to the continuity of Indian civilization and to the diversity of cultural influences. In the mid-1950s, when the Calendar Reform Committee made its survey, there were about 30 calendars in use for setting religious festivals for Hindus, Buddhists, and Jainists. Some of these were also used for civil dating. These calendars were based on common principles, though they had local characteristics determined by long-established customs and the astronomical practices of local calendar makers. In addition, Muslims in India used the Islamic calendar, and the Indian government used the Gregorian calendar for administrative purposes.

Early allusions to a lunisolar calendar with intercalated months are found in the hymns from the Rig Veda, dating from the second millennium B.C.E. Literature from 1300 B.C.E. to C.E. 300, provides information of a more specific nature. A five-year lunisolar calendar coordinated solar years with synodic and sidereal lunar months.

Indian astronomy underwent a general reform in the first few centuries C.E., as advances in Babylonian and Greek astronomy became known. New astronomical constants and models for the motion of the Moon and Sun were adapted to traditional calendric practices. This was conveyed in astronomical treatises of this period known as Siddhantas, many of which have not survived. The Surya Siddhanta, which originated in the fourth century but was updated over the following centuries, influenced Indian calendrics up to and even after the calendar reform of C.E. 1957.

The author Pingree provides a survey of the development of mathematical astronomy in India. Although he does not deal explicitly with calendrics, this material is necessary for a full understanding of the history of India's calendars.