The Sentience

The Sentience

Monday, July 11, 2011

The Hindu Calendar

Hindu Calendars are by far the nearest approaches to the actual machinery of astronomical phenomena governing life on our planet. (Hashim Amir Ali)

The are more than 30 variations of the calendars used in India, the best known of which is the classical Hindu Calendar Surya Siddhanta which is said to have been revealed to Asura Maya the Assyrian at the end of the last Golden Age (2,163,154 BCE). The Hindu lunisolar calendar is similar to the Chinese calendar, but varies in terms of application of fixed ancient methods to approximate true sun and true moon, based on sidereal year. Hindu longitudes are sidereal, having their origin near Piscium, the 6th brightest star in Pisces. However, having sidereal longitudes doesn't really affect the calculations. The calendar is lunisolar in the sense that it uses lunar months to approximate the sidereal year. The epoch used for Hindu calendars dates to January 23, -3101 in the Gregorian Calendar. The era in the Indian calendar is called the Vikram Era, or the Vikram Samvat, which began in 57 BCE.

There are two types of Hindu Lunisolar Calendars:
  • Amanta - one which is based on new moon ending of the lunar month
  • Parimanta - the other is based on full moon ending of the lunar month
I would be designing the Amanta Lunisolar Calendar for KCalendarSystem.

The Month
The amanta month runs from new moon to the next new moon. Each amanta month and hence the lunar year are expressed in integral number of civil days. The lunar month is either 29 or 30 civil days long but always comprises of 30 lunar days. In general, the month is named after the solar month in which the moment of its defining initial new moon falls. The month is divided into two halves, the sudi and the vadi. The sudi half is also known as the sukla paksha or the bright half-month, covering the time period from new moon to the next full moon. The vadi half, also known as the krishna paksha or the dark half-month, covers the period from the full moon to the next new moon.

There are twelve months in Hindu lunar Calendar:

  1. Chaitra (चैत्र, चैत)
  2. Vaishakh (वैशाख, बैसाख)
  3. Jyeshtha(ज्येष्ठ, जेठ)
  4. Ashadha (आषाढ, आषाढ़)
  5. Shravana (श्रावण, सावन)
  6. Bhadrapada (भाद्रपद, भादो)
  7. Ashwin (आश्विन)
  8. Kartik (कार्तिक)
  9. Margashirsha (मार्गशीर्ष, अगहन)
  10. Paush (पौष)
  11. Magh (माघ)
  12. Phalgun (फाल्गुन)
Leap Months
The lunar calendar year is shorter than the solar sidereal year and hence leap months are occasionally added at intervals to keep the lunar calendar and the solar calendar in sync. When a solar month completely covers a lunar month, that is when there are two new moons (one falling at the beginning and the other falling at the end of the solar month), the lunar month that begins at the first new moon is treated as a leap month and is prefixed with the title adhika. An adhika month generally occurs at average intervals of 2 years 8.4 months.

Missing Months
Very rarely, the lunar month can completely cover a solar month, i.e, there is no new moon falling in that solar month and hence no lunar month naming after it. This missing month is called the kshaya or decayed month. When a kshaya month occurs in a lunar year, there will always be two adhika months (one before and on after the kshaya month).

In the Hindu calendar, the day starts with local sunrise. It is allotted five properties, called angas. They are:
  • the tithi (one of 30 divisions of a synodic month) active at sunrise
  • the vaasara, vaar (ravi-vaar, som-vaar, etc.) or weekday
  • the nakshatra (one of 27 divisions of the celestial ecliptic) in which the moon resides at sunrise
  • the yoga (one of 27 divisions based on theecliptic longitude of the sun and moon) active at sunrise
  • the karana (divisions based on tithis) active at sunrise.
Together these are called the panchangas.

Vaar refers to the days of the week and bear striking similarities with the names of the week in many western cultures:


Sanskrit name of
the weekday
Celestial object

Ravi vaar रविवार Sun

Soma vaar सोमवार Moon

Mangala vaar मंगलवार Mars

Budha vaar बुधवार Mercury

Guru vaar गुरुवार
Bruhaspati vaar बृहस्पतिवार

Shukra vaar शुक्रवार Venus

Shani vāsara शनिवार Saturn

Day numbers are determined by the tithi, the time required by the longitude of the moon to increase by 12 degrees over the longitude of the Sun. Sometimes we call it a lunar day. There are 29 or 30 days in a lunar month. Each day is assigned the number of the tithi in effect at sunrise,. However, days are not always counted serially from 1 to 29 or 30. To understand why, it is important to note the fact that the value of a tithi varies from 19.48 hours to 26.78 hours. A short tithi, may begin after sunrise and end before the next sunrise. In this case, a number is omitted from the day count and hence we have skipped a kshaya day. Similarly, a longer tithi may span two sunrises, i.e., there is no tithi ending in that day. Then a day number is carried over to the second day and is treated as a leap day, suffixed by the term adhika.

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