The Hindu calendar is based on a geocentric model of the Solar System. 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 ( IAST:):
Of these, only the last four are in active use and are explained here.
The chandra mÃÂna () of the Hindu calendar is defined based on the movement of the Moon around the Earth. The new moon () and full moon () are important markers in this calendar.
The chandra mÃÂna of the Hindu calendar defines the following synodic calendar elements:
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 180ð with respect to the Earth-Sun axis.
A chÃÂndramÃÂsa () is the time taken by the moon to move from a new moon to the next new moon (as per the amÃÂnta [<nowiki/>] tradition) or a full moon to the next full moon (as per the pà «rá¹ÂimÃÂnta [<nowiki/>] tradition). In other words a chÃÂndramÃÂsa is the synodic period of the Moon, or two paká¹£as. During a chÃÂndramÃÂsa, the Moon advances 360ð with respect to the Earth-Sun axis.
A chandra mÃÂna vará¹£a or lunar year is made up of 12 consecutive chandramÃÂsa. These twelve candramÃÂsa are designated by unique names chaitra, vaià ÂÃÂkha, etc.
In some instances an additional chandramÃÂsa, known as an adhikamÃÂsa, is added to synchronise the chandra mÃÂna vará¹£a with the solar year or saura mÃÂna vará¹£a.
A tithi () is the time taken by the Moon to advance 12ð with respect to the Earth-Sun axis. In other words a tithi is the time taken for the Moon's elongation (on the ecliptic plane) to increase by 12ð. A tithi is one fifteenth of a paká¹£a and one thirtieth of a cÃÂndramÃÂsa. A tithi corresponds to the concept of a lunar day.
Tithi have Sanskrit numbers according by their position in the paká¹£a, i.e. prathama (first), dvitëya (second) etc. The fifteenth, that is, the last tithi of a ká¹Âá¹£á¹Âa paká¹£a is called amÃÂvÃÂsya (new moon) and the fifteenth tithi of a à Âukla paká¹£a is called pà «rá¹Âimà(full moon).
The saura mÃÂna () of the Hindu calendar is defined by the movement of the Earth around the Sun. It contains sidereal () and tropical () elements.
A saura mÃÂna vará¹£a 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 to Spica ()..
A rÃÂà Âi (') is a 30ð arc of the orbit of the Sun around the Earth (i.e an arc of the ecliptic). Starting in the vicinity of Zeta Piscium (IAST: revatë), the twelve (i.e. 360ð divided by 30ð) rÃÂà Âi are designated meá¹£a (), vá¹Âá¹£abha () etc. A sauramÃÂsa () is the time taken by the Sun to traverse a rÃÂà Âi. SauramÃÂsa get their names from the corresponding rÃÂà Âi. sauramÃÂsa corresponds to the concept of a month. The moment in time when the Sun enters a rÃÂà Âi is known as a saá¹ kramaá¹Âa (') or saá¹ krÃÂnti (').
These time periods are defined based on the solstices () and equinoxes ().
The time taken by the Sun to move from the winter solstice to the summer solstice is known as northward movement () and time taken by the Sun to move from the summer solstice to the winter solstice is called southward movement (). Due to the axial tilt of the Earth, the Sun appears to move towards the north from the Tropic of Capricorn to the Tropic of Cancer during uttarÃÂyaá¹Âa, and towards the south from the tropic of Cancer to the tropic of Capricorn during daká¹£iá¹ÂÃÂyana.
The time taken by the Sun to move from the spring equinox (ecliptic longitude 0ð) to the autumnal equinox (ecliptic longitude 180ð) is known as devayÃÂna (). The time taken by the Sun to move from the autumnal equinox to the spring equinox is designated as pitá¹ÂyÃÂá¹Âa (). Due to the axial tilt of the Earth, the Sun appears to be in the north celestial sphere during devayÃÂna and the south celestial sphere during pitá¹ÂyÃÂá¹Âa. In Hindu tradition, the north celestial sphere is consecrated to the gods (deva) and the south celestial sphere is consecrated to the ancestors (pitá¹Â). DevayÃÂna and pitá¹ÂyÃÂá¹Âa are not in active calendric use any longer but do form the basis for pitá¹Âpaká¹£a.
A á¹Âtu () is the time taken by the Sun to move sixty degrees on its orbit around the Earth. á¹Âtu corresponds to the concept of a season.
The six á¹Âtu of the year are known as
NÃÂká¹£hatra mÃÂna () 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. 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. A dina is ~4 minutes short of 24 hours.
A ghaá¹Âikà() or nÃÂá¸Âë () is one sixtieth of a naká¹£atra dina, or just under 24 minutes.
A vighaá¹Âikà() or vinÃÂá¸Âë () is one sixtieth of a ghaá¹ÂikÃÂ, or just under 24 seconds.
A prÃÂá¹Âa () or asu () is one sixth of a vighaá¹ÂikÃÂ, or just under four seconds.
SÃÂvana mÃÂna () of the Hindu calendar defines civil time.
A dina () is the time between two succeeding sunrises. dina corresponds to the concept of a solar day. The length of a dina varies with daytime length.
Apart from the four mÃÂna explained above, the concept of naká¹£atra is an important characteristic of the Hindu calendar. This term has multiple meanings:
The four mÃÂna explained above are used in combination in the Hindu calendar.
<big>adhikamÃÂsa</big>
As seen above, both the cÃÂndra mÃÂna and saura mÃÂna of the calendar define a vará¹£a comprising twelve mÃÂsa, but the duration of the vará¹£a differ; the cÃÂndra mÃÂna vará¹£a is shorter than the saura mÃÂna vará¹£a by about eleven sÃÂvana dina. As a result, unless explicitly synchronised, these two parts of the calendar will diverge over time, as the cÃÂndra mÃÂna vará¹£a will keep "falling behind" the saura mÃÂna vará¹£a.
In order to synchronise these two parts of the calendar, an additional cÃÂndramÃÂsa is introduced into some cÃÂndra mÃÂna vará¹£a. Such a cÃÂndramÃÂsa is referred to as adhikamÃÂsa ('). A adhikamÃÂsa takes its name from the name of the cÃÂndramÃÂsa which follows, viz. adhika ÃÂà Âvina precedes ÃÂà Âvina.
Most times every cÃÂndramÃÂsa witnesses a saá¹ kramaá¹Âa. If a cÃÂndramÃÂsa does not witness a saá¹ kramaá¹Âa, that cÃÂndramÃÂsa is designated as a adhikamÃÂsa thus resulting in the cÃÂndra mÃÂna vará¹£a "catching up" with the saura mÃÂna vará¹£a. This happens approximately once every two and a half (solar) years.
<big>dina and tithi</big>
As seen above, both the cÃÂndra mÃÂna and sÃÂvana mÃÂna 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.
Human life is regulated by the rising of the Sun and not by the movement of the Moon through a 12ð 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 sÃÂvana dina.
To illustrate: consider the Gregorian date 18th Sep 2021. Instead of referring to it as "2nd dina of kanyàmasa" Hindus will refer to it as " bhÃÂdrapada mÃÂsa, à Âukla paká¹£a, dvitiyàtithi", which is the tithi prevailing at sunrise on that sÃÂvana dina. Even though the Moon moves into the trayodaà Âë arc soon after sunrise (at 6:54AM), that entire sÃÂvana dina is considered to be dvÃÂdaà Âë tithi.
<big>adhika tithi and ká¹£aya tithi</big>
It is possible that two consecutive sunrises may have the same tithi, i.e. the Moon continues to remain within the same 12ð arc across two consecutive sunrises. In such a case, two consecutive sÃÂvana dina will be associated with the same tithi. The tithi associated with the second sÃÂvana 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 12ð 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 sÃÂvana 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 ká¹£aya (') (lost) tithi.
<big>Subdivisions of a sÃÂvana dina</big>
Above that a naká¹£atra dina is divided into ghaá¹Âikà(of 24 modern minutes each) and vighaá¹Âikà(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 ghaá¹ÂikÃÂ, the next 24 minutes the second ghaá¹Âikàand so on.
<big>pitá¹Âpaká¹£a</big>
pitá¹Âpaká¹£a (') is a paká¹£a during which the Sun crosses the equator and transitions overhead the southern hemisphere, i.e. the autumnal equinox occurs within pitá¹Âpaká¹£a.
bhÃÂdrapada mÃÂsa ká¹Âá¹£á¹Âa paká¹£a is identified with pitá¹Âpaká¹£a. This identification is not always correct. For instance, in the Gregorian year 2020, bhÃÂdrapada mÃÂsa ká¹Âá¹£á¹Âa paká¹£a ended with the new moon on 17 September while autumnal equinox occurred five days later, on 22 September.