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The Hindu calendar is based on a geocentric model of the Solar System. [1] 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 (Sanskrit : मान IAST:māna): [2]
Of these, only the last four are in active use [3] and are explained here.
The candra māna (Sanskrit : चन्द्र मान) of the Hindu calendar is defined based on the movement of the Moon around the Earth. The new moon (Sanskrit : अमावास्य, romanized: amāvāsya) and full moon (Sanskrit : पूर्णिमा, romanized: pūrṇimā) are important markers in this calendar.
The candra māna of the Hindu calendar defines the following synodic calendar elements:
A pakṣa (Sanskrit : पक्ष) 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 (Sanskrit : शुक्ल पक्ष, romanized: śukla pakṣa) and the waning phase is known as the dark side (Sanskrit : कृष्ण पक्ष, romanized: kṛṣṇa pakṣa). During a pakṣa, the Moon advances 180° with respect to the Earth-Sun axis.
A cāndramāsa (Sanskrit : चन्द्रमास) is the time taken by the moon to move from a new moon to the next new moon (as per the amānta [ Sanskrit : अमान्त] tradition) or a full moon to the next full moon (as per the pūrṇimānta [ Sanskrit : पूर्णिमान्त] tradition). [4] [note 1] In other words a cāndramāsa is the synodic period of the Moon, or two pakṣas. During a cāndramāsa, the Moon advances 360° with respect to the Earth-Sun axis.
A candra māna varṣa or lunar year is made up of 12 consecutive candramāsa. [5] These twelve candramāsa are designated by unique names caitra, vaiśākha, etc. [note 2]
In some instances an additional candramāsa, known as an adhikamāsa, is added to synchronise the candra māna varṣa with the solar year or saura māna varṣa.
A tithi (Sanskrit : तिथि) is the time taken by the Moon to advance 12° with respect to the Earth-Sun axis. [6] 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 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 amāvāsya (new moon) and the fifteenth tithi of a śukla pakṣa is called pūrṇimā (full moon). [7]
The saura māna (Sanskrit : सौर मान) of the Hindu calendar is defined by the movement of the Earth around the Sun. [8] It contains sidereal (Sanskrit : निरयन; nirayana) and tropical (Sanskrit : सायन; sāyana) 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 to Spica (Sanskrit : चित्रा, romanized: citrā). [9] [note 3] . [11]
A rāśi ( Sanskrit : राशि) is a 30° arc of the orbit of the Sun around the Earth [12] (i.e an arc of the ecliptic). Starting in the vicinity of Zeta Piscium (IAST: revatī), the twelve (i.e. 360° divided by 30°) rāśi are designated meṣa (Sanskrit : मेष), vṛṣabha (Sanskrit : वृषभ) etc. A sauramāsa (Sanskrit : सौरमास) is the time taken by the Sun to traverse a rāśi. [4] 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 ( Sanskrit : सङ्क्रमण) or saṅkrānti ( Sanskrit : सङ्क्रान्ति).
These time periods are defined based on the solstices (Sanskrit : अयन; IAST: ayana) and equinoxes (Sanskrit : विषुवत्; IAST: viṣuvat). [13]
The time taken by the Sun to move from the winter solstice to the summer solstice is known as northward movement (Sanskrit : उत्तरायण, romanized: uttarāyaṇa) and time taken by the Sun to move from the summer solstice to the winter solstice is called southward movement Sanskrit : दक्षिणायन, romanized: dakṣiṇāyana. 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 uttarāyaṇa, and towards the south from the tropic of Cancer to the tropic of Capricorn during dakṣiṇāyana. [note 4]
The time taken by the Sun to move from the spring equinox (ecliptic longitude 0°) to the autumnal equinox (ecliptic longitude 180°) is known as devayāna (Sanskrit : देवयान). The time taken by the Sun to move from the autumnal equinox to the spring equinox is designated as pitṛyāṇa (Sanskrit : पितृयाण). 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 (Sanskrit : ऋतु) [note 5] is the time taken by the Sun to move sixty degrees on its orbit around the Earth. [note 6] Ṛtu corresponds to the concept of a season.
The six ṛtu of the year are known as
Nākṣatra māna (Sanskrit : नाक्षत्र मान) is defined with respect to the fixed stars, so all elements are sidereal in nature.
A dina (Sanskrit : दिन) is the time taken by the celestial sphere to complete one sidereal rotation around the Earth. [17] [note 7] 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 (Sanskrit : घटिका) or nāḍī (Sanskrit : नाडी) is one sixtieth of a nakṣatra dina, or just under 24 minutes.
A vighaṭikā (Sanskrit : विघटिका) or vināḍī (Sanskrit : विनाडी) is one sixtieth of a ghaṭikā, or just under 24 seconds.
A prāṇa (Sanskrit : प्राण) or asu (Sanskrit : असु) is one sixth of a vighaṭikā, or just under four seconds. [18]
Sāvana māna (Sanskrit : सावन मान) of the Hindu calendar defines civil time.
A dina (Sanskrit : दिन) is the time between two succeeding sunrises. [19] dina corresponds to the concept of a solar day. The length of a dina varies with daytime length.
Apart from the four māna explained above, the concept of nakṣatra is an important characteristic of the Hindu calendar. This term has multiple meanings: [20]
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. [note 9] Such a cāndramāsa is referred to as adhikamāsa ( Sanskrit : अधिकमास). 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. [4] [note 10]
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 date 18th Sep 2021. Instead of referring to it as "2nd dina of kanyā masa" Hindus will refer to it as " bhādrapada māsa, śukla pakṣa, dvitiyā 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 ( Sanskrit : अधिक) (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 ( Sanskrit : क्षय) (lost) tithi.
Subdivisions of a sāvana dina
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 ( Sanskrit : पितृपक्ष) is a pakṣa during which the Sun crosses the equator and transitions overhead the southern hemisphere, i.e. the autumnal equinox occurs within pitṛpakṣa. [note 11]
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.
A solstice is the time when the Sun reaches its most northerly or southerly excursion relative to the celestial equator on the celestial sphere. Two solstices occur annually, around 20-22 June and 20-22 December. In many countries, the seasons of the year are defined by reference to the solstices and the equinoxes.
Hindu astrology, also called Indian astrology, Jyotisha and, more recently, Vedic astrology, is the traditional Hindu system of astrology. It is one of the six auxiliary disciplines in Hinduism that is connected with the study of the Vedas.
The Hindu calendar, also called Panchanga, 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 similar underlying concept for timekeeping based on sidereal year for solar cycle and adjustment of lunar cycles in every three years, but differ in their relative emphasis to moon cycle or the sun cycle and the names of months and when they consider the New Year to start. Of the various regional calendars, the most studied and known Hindu calendars are the Shalivahana Shaka found in the Deccan region of Southern India and the Vikram Samvat (Bikrami) found in Nepal and the North and Central regions of India – both of which emphasize the lunar cycle. Their new year starts in spring. In regions such as Tamil Nadu and Kerala, the solar cycle is emphasized and this is called the Tamil calendar and Malayalam calendar and these have origins in the second half of the 1st millennium CE. A Hindu calendar is sometimes referred to as Panchangam (पञ्चाङ्गम्), which is also known as Panjika in Eastern India.
A panchāngam is a Hindu calendar and almanac, which follows traditional units of Hindu timekeeping, and presents important dates and their calculations in a tabulated form. It is sometimes spelled Panchāngamu, Pancanga, Panchanga, Panchaanga, or Panchānga, and is often pronounced Panchāng. Panchangas are used in Jyotisha.
Sankranti refers to the transmigration of the sun from one zodiac to another in Indian astronomy. In Saurmanavarsha, there are twelve Sankrantis corresponding with twelve months of a year. The Sankrantis can be broadly classified into four main categories: Ayan (Solstice), Vishuva (Equinox), Vishnupadi and Shadshitimukhi sankrantis.
Nakshatra is the term for Lunar mansion in Hindu astrology and Buddhist astrology. A nakshatra is one of 27 sectors along the ecliptic. Their names are related to a prominent star or asterisms in or near the respective sectors. In essence, a nakshatra simply is a constellation. Every nakshatra is divided into four padas related to the Char Dham, a set of four pilgrimage sites in India.
Vikram Samvat, also known as the Vikrami calendar is a national Hindu calendar historically used in the Indian subcontinent and still also used in several Indian states and Nepal. It is a solar calendar, using twelve to thirteen lunar months each solar sidereal years. The year count of the Vikram Samvat calendar is usually 57 years ahead of the Gregorian calendar, except during January to April, when it is ahead by 56 years.
The September equinox is the moment when the Sun appears to cross the celestial equator, heading southward. Because of differences between the calendar year and the tropical year, the September equinox may occur from September 21 to 24.
The March equinox or northward equinox is the equinox on the Earth when the subsolar point appears to leave the Southern Hemisphere and cross the celestial equator, heading northward as seen from Earth. The March equinox is known as the vernal equinox in the Northern Hemisphere and as the autumnal equinox in the Southern Hemisphere.
The term Uttarāyaṇa is derived from two different Sanskrit words – "uttaram" (North) and "ayanam" (movement) – thus indicating the northward movement of the Sun. In the Gregorian calendar, this pertains to the "actual movement of the sun with respect to the earth." Also known as the six month period that occurs between the winter solstice and summer solstice. According to the Indian solar calendar, it refers to the movement of the Sun through the zodiac. This difference is because the solstices continually precess at a rate of 50 arcseconds per year due to the precession of the equinoxes, i.e. this difference is the difference between the sidereal and tropical zodiacs. The Surya Siddhanta bridges this difference by juxtaposing the four solstitial and equinoctial points with four of the twelve boundaries of the rashis.
Amāvásyā is the lunar phase of the new moon in Sanskrit. Indian calendars use 30 lunar phases, called tithi in India. The dark moon tithi is when the Moon is within 12 degrees of the angular distance between the Sun and Moon before conjunction (syzygy). The New Moon tithi is the 12 angular degrees after syzygy. Amāvásyā is often translated as new moon since there is no standard term for the Moon before conjunction in English.
The Surya Siddhanta is a Sanskrit treatise in Indian astronomy dated to 4th to 5th century, in fourteen chapters. The Surya Siddhanta describes rules to calculate the motions of various planets and the moon relative to various constellations, diameters of various planets, and calculates the orbits of various astronomical bodies. The text is known from a 15th-century CE palm-leaf manuscript, and several newer manuscripts. It was composed or revised probably c. 800 CE from an earlier text also called the Surya Siddhanta. The Surya Siddhanta text is composed of verses made up of two lines, each broken into two halves, or pãds, of eight syllables each.
Ekadashi is the eleventh lunar day (tithi) of the waxing and waning lunar cycles in a Vedic calendar month. Ekadashi is popularly observed within Vaishnavism one of the major paths within Sanatan Dharma. Followers offer their worship to the god Vishnu by fasting or just symbolically; the idea was always to receive self-discipline and the benefits of fasting and it was connected to the way of life via Sanatam Dharma practices.
Vedanga Jyotisha, or Jyotishavedanga, is one of earliest known Indian texts on astrology (Jyotisha). The extant text is dated to the final centuries BCE, but it may be based on a tradition reaching back to about 700-600 BCE.
Gaurabda is the name of the moon calendar used by Gaudiya Vaishnavism as part of the liturgy.
In lunar calendars, a lunar month is the time between two successive syzygies of the same type: new moons or full moons. The precise definition varies, especially for the beginning of the month.
Gargiya-jyotisha, also known as Garga-samhita, is a 1st-century Indian Sanskrit-language astrological treatise attributed to Garga. The oldest extant text of the Indian astrology (jyotiḥśāstra), it is written in form of a dialogue between Garga and Kraushtuki.
The nirayana system is a traditional Indian system of calendrical computations in which the phenomenon of precession of equinoxes is not taken into consideration. In Indian astronomy, the precession of equinoxes is called ayana-calana which literally means shifting of the solstices and so nirayana is nir- + ayana meaning without ayana. Ayanacalana refers to the continuous backward movement of the point of intersection of the ecliptic and the celestial equator. In contrast, the Indian systems of calendrical computations which take into consideration the effects of precession of equinoxes are called sayana systems.
In Indian astronomy, yoga (also called nityayoga) is a period of time, of varying lengths, during which the sum of the nirayana longitudes of the Sun and the Moon increases by an amount of 13 degrees 20 minutes (or, equivalently, 800 minutes). While considering the sum, when the sum is 360 degrees or more, then the angle 360 degrees is subtracted from the sum to make the sum an angle between 0 degree and 360 minutes. Consider a moment T1 when the sum of the longitudes of the Sun and the Moon is 0 degree and let T2 be the next immediate moment when the sum of the longitudes of the Sun and the Moon is 13 degree 20 minutes. The duration of time between the moments T1 and T2 is the first yoga. Similarly, let the next immediate moment when the sum of the longitudes of the Sun and Moon is 26 degrees 40 minutes. The duration of time between the moments T2 and T3 is the second yoga. The third, fourth and higher yoga-s are defined in a similar way. Since 27 X 13 degrees 20 minutes = 360 degrees, at the end-moment of the 27th yoga, the sum of the nirayana longitudes of the Sun and Moon would be 0 degree. The numbering of the yoga-s then starts afresh from that point. It appears that the astronomical yoga-s are in no way related to any astronomical phenomena. S. B. Dikshit in his Bhāratīya Jyotiṣ Śāstra observes: "It is not known what planetary position in the sky is indicated by yoga, and it is useful only in astrology."
In Indian astronomy, a karaṇa is a half of a tithi. It is the duration of time in which the difference of the longitudes of the Sun and the Moon is increased by 6 degrees. A lunar month has 30 tithi-s and so the number of karaṇa-s in a lunar month is 60. These sixty karaṇa-s are not individually named. Instead, the originators of the concept have chosen 11 names to be associated with the karaṇa-s which means several karaṇa-s will be associated with the same name. Of these 11 names, four are fixed or immovables in the sense that they are associated with four unique karaṇa-s in a lunar month. These constant names are Śakuni, Catuṣpāda, Nāga and Kimstughna. The remaining seven names are variable or movable in the sense that there are several karaṇa-s associated with each of them. These names are Bava, Bālava, Kaulava, Taitila, Gara, Vaṇij and Vṛṣṭi.