The

Hindu calendar The Hindu calendar, Panchanga () or Panjika is one of various lunisolar calendars that are traditionally used in the Indian subcontinent and Southeast Asia, with further regional variations for social and Hindu religious purposes. They adopt a ...

is based on a geocentric model of the solar system.Burgess 1935, p. 285 (XII. 32) A geocentric model describes the solar system as seen by an observer on the surface of the earth. The Hindu calendar defines nine measures of time ():Burgess 1935, p. 310 (XIV. 1) # brāhma māna # divya māna # pitraya māna # prājāpatya māna # guror māna # saura māna # sāvana māna # cāndra māna # nākṣatra māna Of these, only the last four are in active use and are explained here.

Cāndra māna

The ''cāndra māna'' () of the Hindu calendar is defined based on the movement of the moon around the earth. The new moon () and

full moon The full moon is the lunar phase when the Moon appears fully illuminated from Earth's perspective. This occurs when Earth is located between the Sun and the Moon (when the ecliptic longitudes of the Sun and Moon differ by 180°). This means ...

() are important markers in this calendar. The ''cāndra māna'' of the Hindu calendar defines the following synodic calendar elements:

Pakṣa

A ''pakṣa'' () is the time taken by the moon to move from a new moon to a full moon and vice versa. The waxing phase of the moon is known as the bright side () and the waning phase is known as the dark side (). During a ''pakṣa'', the moon advances 180° with respect to the earth-sun axis.

Cāndramāsa

A ''cāndramāsa'' () is the time taken by the moon to move from a new moon to the next new moon (as per the amānta nowiki/>tradition'')'' or a full moon to the next full moon (as per the pūrṇimānta nowiki/>tradition).Burgess 1935, p. 8All examples in this article assume the amānta tradition. In other words a ''cāndramāsa'' is the

synodic period The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, ...

of the moon, or two ''pakṣas''. During a ''cāndramāsa'', the moon advances 360° with respect to the earth-sun axis.

Cāndra māna varṣa

A ''cāndra māna varṣa'' or

lunar year A lunar calendar is a calendar based on the monthly cycles of the Moon's phases ( synodic months, lunations), in contrast to solar calendars, whose annual cycles are based only directly on the solar year. The most commonly used calendar, the Gr ...

is made up of 12 consecutive ''cāndramāsa''.Burgess 1935, p. 7 (I. 13) These twelve cāndramāsa are designated by unique names ''caitra'', ''vaiśākha'', etc.These names are derived from the nakṣatra in which the moon is positioned at the time of full moon. In some instances an additional ''cāndramāsa'', known as an ''adhikamāsa'', is added to synchronise the ''cāndra māna varṣa'' with the solar year or ''saura māna varṣa''.

Tithi

A ''tithi'' () is the time taken by the moon to advance 12° with respect to the earth-sun axis.Burgess 1935, p. 104 (II. 64) In other words a ''tithi'' is the time taken for the moon's elongation (on the ecliptic plane) to increase by 12°. A ''tithi'' is one fifteenth of a ''pakṣa'' and one thirtieth of a ''cāndramāsa''. A ''tithi'' corresponds to the concept of a lunar day. ''Tithi'' have

Sanskrit Sanskrit (; attributively , ; nominally , , ) is a classical language belonging to the Indo-Aryan branch of the Indo-European languages. It arose in South Asia after its predecessor languages had diffused there from the northwest in the late ...

numbers according by their position in the ''pakṣa'', i.e. ''prathama'' (first), ''dvitīya'' (second) etc. The fifteenth, that is, the last ''tithi'' of a ''kṛṣṇa pakṣa'' is called ''amāvāsyā'' (new moon) and the fifteenth ''tihi'' of a śukla pakṣa is called ''pūrṇimā'' (full moon).

Saura māna

The ''saura māna'' () of the Hindu calendar is defined by the movement of the earth around the Sun. It contains sidereal () and

tropical The tropics are the regions of Earth surrounding the Equator. They are defined in latitude by the Tropic of Cancer in the Northern Hemisphere at N and the Tropic of Capricorn in the Southern Hemisphere at S. The tropics are also referred to ...

() elements.

Sidereal elements

A ''saura māna varṣa'' or sidereal year is the time taken by the sun to orbit the earth once and return to the starting point with respect to the fixed stars. The starting point is taken to be the position of the Sun when it is in

opposition Opposition may refer to: Arts and media * ''Opposition'' (Altars EP), 2011 EP by Christian metalcore band Altars * The Opposition (band), a London post-punk band * '' The Opposition with Jordan Klepper'', a late-night television series on Com ...

Spica Spica is the brightest object in the constellation of Virgo and one of the 20 brightest stars in the night sky. It has the Bayer designation α Virginis, which is Latinised to Alpha Virginis and abbreviated Alpha Vir or α Vir. Analys ...

().. A ''rāśi'' (') is a 30° arc of the orbit of the sun around the earth (i.e an arc of the

ecliptic The ecliptic or ecliptic plane is the orbital plane of the Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic agains ...

). Starting in the vicinity of Zeta Piscium ( IAST: revatī), the twelve (i.e. 360° divided by 30°) rāśi are designated meṣa (), vṛṣabha () etc. A ''sauramāsa'' () is the time taken by the sun to traverse a rāśi. Sauramāsa get their names from the corresponding rāśi. sauramāsa corresponds to the concept of a month. The moment in time when the sun enters a rāśi is known as a ''saṅkramaṇa (') or saṅkrānti (').''

Tropical elements

These time periods are defined based on the

solstice A solstice is an event that occurs when the Sun appears to reach its most northerly or southerly excursion relative to the celestial equator on the celestial sphere. Two solstices occur annually, around June 21 and December 21. In many countr ...

s () and

equinox A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" and se ...

es ().Tilak 1955, pp. 20–31 The time taken by the sun to move from the

winter solstice The winter solstice, also called the hibernal solstice, occurs when either of Earth's poles reaches its maximum tilt away from the Sun. This happens twice yearly, once in each hemisphere (Northern and Southern). For that hemisphere, the winter ...

to the summer solstice is known as northward movement () and time taken by the sun to move from the summer solstice to the

is called southward movement . Due to the

axial tilt In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orb ...

of the earth, the sun appears to move towards the north from the

Tropic of Capricorn The Tropic of Capricorn (or the Southern Tropic) is the circle of latitude that contains the subsolar point at the December (or southern) solstice. It is thus the southernmost latitude where the Sun can be seen directly overhead. It also reac ...

to the

Tropic of Cancer The Tropic of Cancer, which is also referred to as the Northern Tropic, is the most northerly circle of latitude on Earth at which the Sun can be directly overhead. This occurs on the June solstice, when the Northern Hemisphere is tilted tow ...

during ''uttarāyaṇa'', and towards the south from the tropic of Cancer to the tropic of Capricorn during ''dakṣiṇāyana''. The time taken by the sun to move from the spring equinox (

ecliptic longitude The ecliptic coordinate system is a celestial coordinate system commonly used for representing the apparent positions, orbits, and pole orientations of Solar System objects. Because most planets (except Mercury) and many small Solar System b ...

0°) to the autumnal equinox (ecliptic longitude 180°) is known as ''devayāna'' (). The time taken by the sun to move from the autumnal equinox to the spring equinox is designated as ''pitṛyāṇa'' (). Due to the axial tilt of the earth, the sun appears to be in the north celestial sphere during ''devayāna'' and the south celestial sphere during ''pitṛyāṇa''. In Hindu tradition, the north celestial sphere is consecrated to the gods (deva) and the south celestial sphere is consecrated to the ancestors (pitṛ). Devayāna and pitṛyāṇa are not in active calendric use any longer but do form the basis for pitṛpakṣa. A ''ṛtu'' () is the time taken by the sun to move sixty degrees on its orbit around the earth.Since a rāśi is a 30° arc of the ecliptic, a ṛtu can be considered as the time taken by the sun to transit through two rāśi. Ṛtu corresponds to the concept of a season. The six ṛtu of the year are known as *''śiśira ṛtu'', the cold season, begins at winter solstice *''vasanta ṛtu'' (spring) *''grīṣma ṛtu'' (summer) *''varṣā ṛtu'' the monsoon season, beginning at summer solstice *''śarad ṛtu'' (autumn) *''hemanta ṛtu'' (winter)

Nākṣatra māna

Nākṣatra māna () is defined with respect to the fixed stars, so all elements are sidereal in nature. A ''dina'' () is the time taken by the celestial sphere to complete one sidereal rotation around the earth.A sidereal rotation is defined with respect to the fixed stars, i.e. at the end of a sidereal rotation all the fixed stars are back in their starting position. In reality, this movement is caused by the diurnal rotation of the earth on its axis. This definition is not used in practice but is required for defining the following smaller units of time. Ā ''dina'' is ~4 minutes short of 24 hours. A ''ghaṭikā'' () or ''nāḍī () is one sixtieth of a nakṣatra dina, or just under 24 minutes. A ''vighaṭikā'' () or ''vināḍī'' () is one sixtieth of a ghaṭikā, or just under 24 seconds. A ''prāṇa'' () or ''asu'' () is one sixth of a vighaṭikā, or just under four seconds.Burgess 1935, p. 5 (I. 11)

Sāvana māna

''Sāvana māna'' () of the Hindu calendar defines

civil time In modern usage, civil time refers to statutory time as designated by civilian authorities. Modern civil time is generally national standard time in a time zone at a fixed offset from Coordinated Universal Time (UTC), possibly adjusted by dayligh ...

. A ''dina'' () is the time between two succeeding sunrises.Burgess 1935, p. 319 (XIV. 18) dina corresponds to the concept of a

solar day A synodic day (or synodic rotation period or solar day) is the period for a celestial object to rotate once in relation to the star it is orbiting, and is the basis of solar time. The synodic day is distinguished from the sidereal day, which is ...

. The length of a ''dina'' varies with daytime length.

nakṣatra

Apart from the four māna explained above, the concept of nakṣatra is an important characteristic of the Hindu calendar. This term has multiple meanings:Burgess 1935, pp. 202–250 # A ''nakṣatra (')'' is a star. # A ''nakṣatra'' is an asterism. One of the stars in the asterism is designated as its principal star (). There are twenty eight such nakṣatra and they are individually named. The name of a nakṣatra and its yogatārā are identical. For example, revatī is an asterism whose principal star is revatī (Zeta Piscium). # A ''nakṣatra'' is a 13° 20' arc of the ecliptic. There are twenty seven such nakṣatra (i.e. 360° divided by 13° 20'). Starting in the vicinity of revatī (Zeta Piscium), they are named aśvinī, bharaṇī etc.abhijit is an asterism for which there is no corresponding arc segment. These names are identical to the names of the asterisms that are located within the respective arc segments. For example, revatī refers to both an asterism and the arc segment within which the asterism is located. # In calendric terms, a ''nakṣatra'' is the time taken by the moon to traverse a ''nakṣatra'' (as defined in point 3). Hence, nakṣatra is a sidereal element (unlike the tithi which it is similar to) and corresponds to the concept of a day.

Combining the different measures of time

The four māna explained above are used in combination in the Hindu calendar. adhikamāsa As seen above, both the cāndra māna and saura māna of the calendar define a varṣa comprising twelve māsa, but the duration of the varṣa differ; the cāndra māna varṣa is shorter than the saura māna varṣa by about eleven sāvana dina. As a result, unless explicitly synchronised, these two parts of the calendar will diverge over time, as the cāndra māna varṣa will keep "falling behind" the saura māna varṣa. In order to synchronise these two parts of the calendar, an additional cāndramāsa is introduced into some cāndra māna varṣa.This is a common calendric technique and is known as intercalation Such a cāndramāsa is referred to as ''adhikamāsa (')''. A adhikamāsa takes its name from the name of the cāndramāsa which follows, viz. adhika āśvina precedes āśvina. Most times every cāndramāsa witnesses a saṅkramaṇa''.'' If a cāndramāsa does not witness a saṅkramaṇa, that cāndramāsa is designated as a adhikamāsa thus resulting in the cāndra māna varṣa "catching up" with the saura māna varṣa. This happens approximately once every two and a half (solar) years. dina and tithi As seen above, both the cāndra māna and sāvana māna of the calendar define the concept of a day as tithi and dina respectively. dina are not named and are not used for calendric purposes. The tithi takes precedence instead.As a result, almost all

Hindu festivals Across the globe, Hindus celebrate a diverse number of festivals and celebrations, typically marking events from ancient India and often coinciding with seasonal changes. These celebrations take place either on a fixed annual date on the solar ...

are defined in cāndra māna terms. Hence these annual festivals do not repeat on the same day on any solar calendar (neither saurana māna nor Gregorian). Human life is regulated by the rising of the sun and not by the movement of the moon through a 12° arc. Hence, the position of the moon at sunrise is used to determine the tithi prevailing at sunrise. This tithi is then associated with the entire sāvana dina. To illustrate: consider the Gregorian dat
18th Sep 2021
Instead of referring to it as "2nd dina of kanyā masa" Hindus will refer to it as " bhādrapada māsa, śukla pakṣa, dvādaśī tithi", which is the tithi prevailing at sunrise on that sāvana dina. Even though the moon moves into the trayodaśī arc soon after sunrise (at 6:54AM), that entire sāvana dina is considered to be dvādaśī tithi. adhika tithi and kṣaya tithi It is possible that two consecutive sunrises may have the same tithi, i.e. the moon continues to remain within the same 12° arc across two consecutive sunrises. In such a case, two consecutive sāvana dina will be associated with the same tithi. The tithi associated with the second sāvana dina is referred to as a ''adhika (') (additional) tithi''. It is also possible that an entire tithi elapses between two sunrises, i.e. the moon traverses a 12° arc in between two sunrises (it enters the arc after one sunrise and exits the arc before the next sunrise). In this such a case, neither sāvana dina will be associated with this tithi, i.e. this tithi will be skipped over in the calendar. Such a tithi is referred to as a ''kṣaya (') (waste) tithi''. Subdivisions of a sāvana dina We have seen above that a nakṣatra dina is divided into ghaṭikā (of 24 modern minutes each) and vighaṭikā (of 24 modern seconds each). These same units are used to subdivide a savana dina using sunrise as the starting point, i.e. the first 24 minutes after sunrise constitute the first ghaṭikā, the next 24 minutes the second ghaṭikā and so on. pitṛpakṣa ''pitṛpakṣa (')'' is a pakṣa during which the sun crosses the equator and transitions overhead the southern hemisphere, i.e. the autumnal equinox occurs within pitṛpakṣa.Since the south celestial sphere is consecrated to the ancestors ( IAST:pitṛ), Hindus perform special religious rites in honour of their ancestors during pitṛpakṣa. bhādrapada māsa kṛṣṇa pakṣa is identified with pitṛpakṣa. This identification is not always correct. For instance, in the Gregorian year 2020, bhādrapada māsa kṛṣṇa pakṣa ended with the new moon on 17 September while autumnal equinox occurred five days later, on 22 September.

Notes

References

Bibliography

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External links

Ahargana - The Astronomy of the Hindu Calendar
Explains the various calendric elements of the Hindu calendar by means of astronomical simulations created using Stellarium.
drikPanchang
an online Hindu almanac ( IAST: pañcāṅga).
Stellarium
the astronomy software that was used to create the animations featured in this article. {{calendars Hindu calendar Hindu astronomy Articles containing video clips