The nirayana system is a traditional Indian system of calendrical computations in which the phenomenon of precession of the equinoxes is not taken into consideration.[1] 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.[2] Ayanacalana refers to the continuous backward movement of the point of intersection of the ecliptic (which is a fixed circle) and the celestial equator (which keeps on moving backward). In contrast, the Indian systems of calendrical computations which take into consideration the effects of precession of equinoxes are called sayana systems.

Nirayana year

The nirayana year is the sidereal year and its duration is 365.256363 days (365 days 6 hours 9 minutes 10 seconds) approximately . It is the actual time required for the Earth to revolve once around the Sun with respect to a fixed point on the ecliptic. In the nirayana system in India, this fixed point is taken as that point on the ecliptic which is directly opposite to the star called Citrā (Alpha Virginis) which is remarkably conspicuous in the night sky by its high brightness. The longitude of the star Chitra from this point is 180°. The starting point of the nirayana year coincided with the March equinox in the year 285 CE. Since the stars are fixed with respect to the ecliptic, the starting point remains unchanged, hence the name nirayana.[3][4]

Nirayana months

In the calendars that follow the nirayana system, a month is an artificial unit of time. In the nirayana system, the ecliptic is divided into 12 parts of 30° and each part is called a rāśi. The first rāśi starts from the same point as that of the start the nirayana year. The beginning of a nirayana month is the moment at which the Sun enter into a rāśi. The length of a nirayana month is the duration of time taken by the Sun to travel completely in a rāśi, that is, to travel 30° of its elliptical orbit.[4] Since the speed at which the Sun is traversing its elliptical orbit around the sun is not constant, the durations of the sidereal months are also not constant. The mean length of a nirayana month is about 30.4369 days, but its actual length can vary from 29.45 days to 31.45 days.

The beginning of a nirayana month

Since the nirayana months are defined artificially, there are no astronomical phenomena associated with the beginning of a nirayana month. The exact moment at which a new nirayana month begins can occur at any time of day, early morning, evening or night. To felicitate dating of days, the first day of a month has to be properly defined. Unfortunately, there is no consensus on this among the traditional calendar makers across India. The tradition varies from region to region in India. A few of these traditions may be considered as illustrations.[4] In the following, saṃkrānti is the day on which the Sun enters a new rāśi.

  1. The Orissa rule: The month begins on the same day as the day on which the saṃkrānti falls.
  2. The Tamil rule: The month begins on the same day as the saṃkrānti if the saṃkrānti falls before the time of sunset on that day. Otherwise the month begins on the following day.
  3. The Kerala rule: The month begins on the same day as the saṃkrānti if the saṃkrānti occurs before the time of aparahna on that day. Otherwise the month starts on the following day. (Aparahna is the time at 3/5th duration of the period from sunrise to sunset. For example, if the times of sunrise and sunset are 6am and 6pm respectively. Then the time of the aparahna = [(3/5) x (18 – 6) + 6]am = 1.12pm.)
  4. The Bengal rule: When saṃkrānti takes place between the time of sunrise and midnight on that day, the month begins on the following day. If it occurs after midnight, the month begins on the next following day, that is, the third day. (In some special circumstances, there are some deviations from this rule.)

Duration of months

The table in the figure below gives the names and the duration of each of the 12 nirayana months. The tables gives the duration of months as per Ārya-Sinddhānta (Āryabhaṭīya) and as per Sūrya-Siddhānta. The abbreviations "gh." and "pa." stand for "ghaṭikā" (= 24 minutes) and "pala" (also called "vighatikā" = 24 seconds). The table is an extract from The Indian Calendar by Robert Sewell and Sankara Balakrishna Dikshit published in 1896.[5] The calendar makers of different regions of India follow different computational systems. Depending on the computational system, the duration of a nirayana month may vary from region to region.[6]

Duration of solar months as per Arya-Siddhanta and Surya-Sinddhanta (Internet Archive)

Major deficiency

The most important deficiency of the nirayana calendar is that the predictions of the dates of the onsets of the various seasons as per the nirayana system do not correspond to the actual dates on which they occur. This is because the seasons depend on the position of the sun on the ecliptic relative to the celestial equator. In particular, they depend on the positions of the equinoxes. Since, the positions of the equinoxes are slowly moving, the predictions of the seasons which ignore this movement of the equinoxes will be definitely erroneous.

To be more specific, the winter season begins on the winter solstice day which date is marked by sun's entry into Makara constellation. This event occurs on the 22nd December. But in the nirayana system, this happens not on the 22nd December but on the 14th January and the winter season is also supposed to begin on that date. Similar is the case with other seasons also. The result is that there is a clear difference of 23 days in the reckoning of seasons.[1]

Additional reading


  1. ^ a b Govt of India (1955). Report of the calendar reform committee. New Delhi: Council of Scientific and Industrial Reseaarch. p. 259. Retrieved 30 December 2023.
  2. ^ Article titled "Precession of the Equinoxes" and authored by K. V. Sarma in: Helaine Selin (2008). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer. pp. 1830–1831. ISBN 978-1-4020-4559-2.
  3. ^ S. K. Chatterjee (2004). "Uniform all-India nirayan solar calendar" (PDF). Indian Journal of History of Science. 39 (4): 519–514. Retrieved 31 December 2023.
  4. ^ a b c "Indian calendars" (PDF). Positional Astronomy Center. Retrieved 31 December 2023.
  5. ^ Robert Sewell (1896). The Indian Calendar. London: Swan Sonnenschein & Co. p. 10. Retrieved 1 January 2024.
  6. ^ S.K. Uma, Padmaja Venugopal, K. Rupa and S. Balachandra Rao (2018). "The solar ingress according to makarandasarini and other Indian astronomical texts" (PDF). Journal of Astronomical History and Heritage. 21 (2): 202–210. Retrieved 1 January 2024.((cite journal)): CS1 maint: multiple names: authors list (link)