Astronomical basis of the Hindu calendar
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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 (
- brāhma māna
- divya māna
- pitraya māna
- prājāpatya māna
- guror māna
- saura māna
- sāvana māna
- candra māna
- nākṣatra māna
Of these, only the last four are in active use[3] and are explained here.
Candra māna
The candra māna (
The candra māna of the Hindu calendar defines the following
Pakṣa
A pakṣa (
Candramāsa
A cāndramāsa (
of the Moon, or two pakṣas. During a cāndramāsa, the Moon advances 360° with respect to the Earth-Sun axis.Candra māna varṣa
A candra māna varṣa or
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.
Tithi
A tithi (
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]
Saura māna
The saura māna (
Sidereal elements
A saura māna varṣa or
A rāśi (
Tropical elements
These time periods are defined based on the
The time taken by the Sun to move from the
The time taken by the Sun to move from the
A ṛtu (
The six ṛtu of the year are known as
- Śiśira ṛtu (winter)
- Vasanta ṛtu (spring)
- Grīṣma ṛtu (summer)
- Varṣā ṛtu the monsoon season, beginning at summer solstice
- Śarada ṛtu (autumn)
- Hemanta ṛtu (pre-winter)
Nākṣatra māna
Nākṣatra māna (
A dina (
A ghaṭikā (
A vighaṭikā (
A prāṇa (
Sāvana māna
Sāvana māna (
A dina (
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:[20]
- A nakṣatra (Sanskrit: नक्षत्र) is a star.
- A nakṣatra is an IAST:yogatārā). 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.[6] 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.[note 8] 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).[citation needed] 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.
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 (
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 (
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 (
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.
See also
Notes
- ^ All examples in this article assume the amānta tradition.
- ^ These names are derived from the nakṣatra in which the Moon is positioned at the time of full moon.
- ^ Not everyone is in agreement with this definition. Mercier argues that Ketkar has interpreted a Sanskrit source in a way that is different from other authorities. Yet, this definition is widely used to create Hindu almanacs or pañcāṅga).[10]
- ^ The Surya Siddhantha defines uttarāyaṇa and dakṣiṇāyana using rāśi instead of the equinoxes and solstices.[14] That definition assumed a coincidence of the winter solstice and makara saṅkramaṇa. As a result of the precesstion of the equinoxes, that coincidence no longer exists thus making that definition incorrect. To illustrate, as per the Surya Siddhantha definition, the period from winter solstice (Dec 21) to makara saṅkramaṇa (Jan 14) is considered part of dakṣiṇāyana but the Sun is moving towards the north during this period.
- ^ The Surya Siddhanta defines ṛtu in terms of various rāśi[15] assuming that makara saṅkramaṇa coincides with the winter solstice.[16] Due to the precession of the equinoxes, that assumption is no longer true and hence those definitions of ṛtu are no longer accurate.
- ^ 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.
- ^ 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.
- ^ abhijit is an asterism for which there is no corresponding arc segment.
- ^ This is a common calendric technique and is known as intercalation
- ^ As a result, almost all Hindu festivals 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).
- IAST:pitṛ), Hindus perform special religious rites in honour of their ancestors during pitṛpakṣa.
References
- ^ Burgess 1935, p. 285 (XII. 32)
- ^ Burgess 1935, p. 310 (XIV. 1)
- ^ Burgess 1935, p. 310 (XIV. 2)
- ^ a b c Burgess 1935, p. 8
- ^ Burgess 1935, p. 7 (I. 13)
- ^ a b Burgess 1935, p. 104 (II. 64)
- ^ Burgess 1935, p. 106
- ^ "Satapatha-brahmana Verse 8.7.3.10 [Sanskrit text]". www.wisdomlib.org. 18 September 2021. Retrieved 8 December 2022.
- ^ Ketkar 1923. pp. 34–35
- ^ Mercier (2018). pp. 74–75
- ^ Burgess 1935, p. 230
- ^ Burgess 1935, p. 16 (I. 28)
- ^ Tilak 1955, pp. 20–31
- ^ Burgess 1935, p. 313 (XIV. 9)
- ^ Burgess 1935, p. 313 (XIV. 10)
- ^ Burgess 1935, p. 207
- ^ Burgess 1935, p. 314 (XIV. 15)
- ^ Burgess 1935, p. 5 (I. 11)
- ^ Burgess 1935, p. 319 (XIV. 18)
- ^ Burgess 1935, pp. 202–250
Bibliography
- Burgess, Ebenezer (1935). Gangooly, Phanidarlal (ed.). Translation of the Surya Siddhanta – a text-book of Hindu astronomy (PDF). University of Calcutta.
- Ketkar, Venkatesh Bapuji (1923). "Indian and Foreign Chronology". Journal of the Asiatic Society of Bombay. Issue 75, Part 1 of Journal: Extra number. British Indian Press.
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has extra text (help) - Mercier, Raymond (2018). Astronomical Computations for the History of Indian Astronomy. New Delhi: Munshiram Manoharlal Publishers Pvt. Ltd. ISBN 978-81-215-1177-3.
- Tilak, Bal Gangadhar (1955). The Orion or Researches into the Antiquity of the Vedas (PDF). Tilak Bros.
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.