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The World Calendar is broadly three types:
(1) solar calendar (saura maana) based on:
(a) seasonal (equinox) and
(b) Sun transit along zodiac (in elliptic)
(2) lunar calendar (chaandra maana) based on:
(a) phases (waxing, waning, tithi or thyathi) and
(b) Moon transit along zodiac (in elliptic) with reference to 27 or 28 constellations or stars. Nakshatra or star-clusters or constellations, which lie along the ecliptic, or path of the sun/moon. An individual's nakshatra, or birth star, is the constellation the moon was aligned with at the time of birth.
(3) Mixing both, in different combination, one gets lunisolar calendar. In India, there are many combinations developed over time.

Precession of the equinoxes

The north and south celestial poles are the two imaginary points in the sky where the Earth's axis of rotation, indefinitely extended, intersects the imaginary rotating sphere of stars called the celestial sphere. The north and south celestial poles appear directly overhead to an observer at the Earth's North Pole and South Pole respectively. The celestial poles do not remain permanently fixed against the background of the stars.
Because of a phenomenon known as the precession of the equinoxes, the poles trace out circles on the celestial sphere, with a period of about 25,700 years. The north celestial pole currently is within a degree. (25,800 year cycle, Spica in 285 CE, around the date of the Surya Siddhanta). of the bright star Polaris (pole star). It will remain a good approximation for about 1,000 years, by which time the pole will have moved to be closer to Alrai (Gamma Cephei). In about 5,500 years, the pole will have moved near the position of the star Alderamin (Alpha Cephei). Polaris has numerous traditional names: Alruccabah, Cynosura, Dhruv, Phoenice, Tramontana, Angel Stern, Navigatoria, Star of Arcady, Yilduz, Mismar, Gwiazda Polarna, Polyarnaya.
The form of the Hari which is present in heaven, consisting of the constellations, is that of a porpoise, with Dhruva situated in the tail. As Dhruva revolves, it causes the moon, sun, and stars to turn round also; looks as if all are bound to the polar-star by aerial cords. The porpoise-like figure of the celestial sphere is supposed to be upheld by Narayana, and Dhruva, shines in the tail of the stellar porpoise. Center of milky way beyond pole star (a black hole) is Vaikunda or dark Krishna. Sun during Maargazhi (மார்கழி), is in star mula (मूल) means first star, which corresponds to Vaikunda ekadasi.
Sigma Octantis is identified as the south pole star, over a degree away from the pole, but with a magnitude of 5.5 it is barely visible on a clear night. The south celestial pole can be located from the Southern Cross (Crux) and its two "pointer" stars α Centauri and β Centauri.

Tropical calendar

A tropical year is the time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice. Because of the precession of the equinoxes, the seasonal cycle does not remain exactly synchronized with the position of the Earth in its orbit around the Sun. As a consequence, the tropical year is about 20 minutes shorter than the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed stars (the sidereal year).

Ancient Indian Systems (six/sexadecimal)

Many calendars were in use by different tribes in ancient India. But tropical and sexadecimal systems look popular.
A day into 60 equal parts called ghatikas. (means little jar or water clocks ) A ghatika is further divided into 60 vinadikas.
1 rithu or season = 60 days
1 year = 6 rithus or seasons

Ancient Indians had a six‐day week and 60 weeks per year. There is no particular day name. (some tribes develop their identification based on local traditions like names of colors, grains, gem stones, jewelery)

  1. black - inertia ignorance
  2. blue - bravery, manliness, determination, the ability to deal with difficult situations, stable mind
  3. green - new beginning, harvest, life and happiness
  4. red (or saffron) - purity, sensuality, dynamic and incites fear
  5. yellow - knowledge and learning, happiness, peace, meditation, competence and mental development.
  6. white - peace, purity, cleanliness, knowledge
60 is convenient for division by 2,3,4,5 and 6. That way one can express fraction of a season by number of days.
Much later 60 years cycle of Jupiter and Saturn alignment has been developed.

Gregorian Hijri calendars

Julius Caesar introduced the Julian calendar in 45BC to approximate the tropical year (starting with March). It has a regular year of 365 days divided into 12 months, and a leap day is added to February every four years. Hence the Julian year is on average 365.25 days. Later New year starts with December solstice (day for Sun which became birthday for God's son). Gregorian calendar is based on Gregory, who dropped 10 days from October 1582 so that October 15 should follow immediately after October 4 of that year. Every 400th year is not a leap year.
The Hijri calendar beginning in AD 622 is a lunar calendar with 354 or 355 days and hence a year is about 11 days shorter than the solar year. Actual observation of the crescent marks the end of the previous lunar cycle and hence the previous month.

Julian dates

Julian dates (abbreviated JD) are simply a continuous count of days and fractions since noon Universal Time on January 1, 4713 BC (on the Julian calendar). Julian dates are widely used as time variables within astronomical software. This solves the problem of working with various calendar systems in use at different times and places around the world. It is assumed that 7-day weeks have formed an uninterrupted sequence since ancient times. Thus, the day of the week can be obtained from the remainder of the division of the Julian date by 7.
1st Jan 2000AD 00:00 is 2,451,544.5 JD


Sunrise/Sunset directions

Position of Sunrise/Sunset varies as the Earth orbits the Sun. Because the Earth is inclined at an angle of 23.5 degrees to the plane of its orbit, and because the direction of the inclination (with respect to the stars) does not change as the Earth moves around the Sun, sometimes the Earth is tilted towards the Sun and sometimes it is tilted away from it. This cause the Sun to take different paths across the sky across the year and gives us seasons. In the Northern hemisphere the pattern of the position of Sunrise/Sunset is as follows (in the Southern hemisphere exchange North for South and vice versa): Only on the equinoxes (Sept/Mar 21st) does the Sunrise/set at due East/West. At the solstices (Dec/June 21st) the position is its furthest South/North of East/West. How far to the North or South that is depends on your lattitude. The position of Moonrise and Moonset, like that of Sunrise and Sunset varies as the Earth goes around the Sun, but also with the phases of the Moon. Position of Sunrise/Sunset
Season Northern hemisphereSouthern hemisphere
Winter Southeast/SouthwestNortheast/Northwest
Spring East/WestEast/West
Summer Northeast/NorthwestSoutheast/Southwest
Autumn East/WestEast/West

Only on the equinoxes (Sept/Mar 21st) does the Sunrise/set at due East/West. At the solstices (Dec/June 21st) the position is its furthest South/North of East/West. How far to the North or South that is depends on your lattitude. Now lets get to the Moon. The time of day that the Moon rises or sets depends on its phase. This should be obvious when you remember that the phase of the Moon depends on the relative positions of the Sun, Moon and Earth. For example when the Moon is Full it is opposite the Earth from the Sun, so when the Sun sets, the Moon must rise and vice versa. Here is a table summarizing that by local noon and local midnight means the points when the Sun crosses the meridian, and exactly 12 hours later. This can be different from the time on watch because we define time zones which all use the local time at the centre of the zone. So when the Moon is new, it rises and sets with the Sun, and the position of Moonrise/set varies just like that of Sunrise/set. When the Moon is full however the pattern is inverted.

Moon phase Moonrise Moonset
New Sunrise Sunset
1st quarter Local noon Local midnight
Full Sunset Sunrise
3rd quarter Local midnight Local noon


Panchanga (five anga): DayIn the Hindu calendar, the day starts with local sunrise. It is allotted five "properties", called angas. They are:

  1. the vaasara or weekday (in honour of seven grahas or seven visible moving celestial objects)
  2. the tithi (one of 30 divisions of a synodic month) active at sunrise or noon (for srardha purposes as srardha has to be performed at noon)
  3. the nakshatra (one of 27 divisions of the celestial ecliptic) in which the moon resides at sunrise (27 or 28 stars)
  4. the yoga (one of 27 divisions based on the ecliptic longitude of the sun and moon) active at sunrise
  5. .the karana (divisions based on tithis) active at sunrise.
Note: Together these are called the panchāngas (Sanskrit: pancha = five). Month name corresponding to Solar month, is based on position of the sun in Zodiac. This was added later and tithi or nakshatra is used to count days instead of sequential dates for each month (unlike western one May 20th).

Key data on earth and 7 Grahas

Diameter in kmRadius of rotation in kmRevolution in daysRevolution in yearsArc angle in degrees

Weekday (Graha)

The seven day week appears to have been introduced by chaldean astrologers, adopted by the Persian, Greek, Guptas and Tang. It was associated with the seven gods or heavenly bodies; the Sun, Moon, Mars, Mercury, Jupiter, Venus and Saturn. The ordering of the weekday names is not by distance/apparent size or speed of heavenly bodies.

Chaldeans ordered gods: sun; venus; mercury; moon; saturn; jupiter; and mars.
They had 24 hours day and each God takes care of an hour by turns. Starting with G1 on first day, G4 will start on second day. This is repeated for all 7 days, forming a heptagram within the circle.

Weekday (Tamil)Vaasara (Sanskrit)Lord or PlanetChaldean meaningPlanets Spend in each Sign
(1)Sundayஞாயிற்றுக்கிழமைRavi-vaasaraSun -Aditya -Son of Aditi (the unchangeable)Sun-Shamash-God of Law and Justice1 month
(2)Mondayதிங்கட்கிழமைSoma-vaasaraMoon -Soma -Peace, GentlenessMoon-Sin-God of Agriculture2.25 days
(3)Tuesdayசெவ்வாய்க்கிழமைMangala-vaasaraMars -Ankgaraka -Burning coalMars-Nergal-God of War45 days
(4)Wednesdayஅறிவன் கிழமைBudha-vaasaraMercury-Budha -IntellectMercury-Nabu-God of Writing1 month
(5)Thursdayவியாழக்கிழமைGuru VaasaraJupiter-Brihaspati-Great (brihat) protector (pati)Jupiter-Marduk-King of the Gods1 year
(6)Fridayவெள்ளிக்கிழமைSukra-vaasaraVenus -Shukra -Refined, SensualVenus-Ishtar-God of Fertility1 month
(7)Saturdayகாரிக்கிழமைShani-vaasaraSaturn -Shani -SlowSaturn-Ninib-God of Pestilence and Misery2.5 year
.Moon's North Node-Rahu-Dragon's Head1.5 year
Moon's South Node-Ketu -Dragon's Tail1.5 year

9 day week?

Around the time of Gautama Buddha, seven visible planet system was converted in to 9 graha system by including Rahu and Ketu.
Each nakshatra has a ruler as shown below:
  1. Ketu - Ashwini, Maghaa, Moola
  2. Venus - Bharani, Pubba, Poorvashada
  3. Sun - Krittika, Uttara, UttaraShada
  4. Moon - Rohini, Hastaa, Shravana
  5. Mars - Mrigashira, Chitra, Dhanishta
  6. Rahu - Aardhra, Swati, Shatabhisha
  7. Jupiter - Punarvasu, Vishaka, Poorva Bhadra
  8. Saturn - Pushya, Anooradha, Uttara Bhadra
  9. Mercury - Aashlesha, Jyeshta, Revathi
Whatever constellation or nakshatra, the Moon was in at sunrise, the entire day was named after it. The nine rulers of the nakshatras are repeated three times in sequence for 27 days sidereal month. This is something like a nine-day week.

Month names and Rashi (Zodiac)

Sun and Moon move towards 12 constellations in Zodiac in one year and month respectively. Solar month is based on position of the sun in Zodiac.
Lunar month is based on sun position on full moon day
Season for NZTamil month nameSanskirit namePeriodWesternPeriod
Sharath (autumn)Chitirai (சித்திரை) Mesham 14 Apr -14 May AriesMar 21 - Apr 19
Sharath (autumn)Vaikasi (வைகாசி) Vrishabam15 May -15 June TaurusApr 20 - May 20
Hemanta (early winter)Aani (ஆனி) Mithunam16 June -16 July GeminiMay 21 - Jun 21
Hemanta (early winter)Aadi (ஆடி) Karkata17 July -17 Aug CancerJun 22 - Jul 22
Sishira (late winter)Aavani (ஆவணி) Simham18 Aug -17 Sep LeoJul 23 - Aug 22
Sishira (late winter)Purratasi (புரட்டாசி) Kanya18 Sep -17 Oct VirgoAug 23 - Sep 22
Vasanta (spring)Aiypasi (ஐப்பசி) Tula18 Oct -16 Nov LibraSep 23 - Oct 22
Vasanta (spring)Kaarthigai (கார்த்திகை) Vrischikam17 Nov -16 Dec ScorpioOct 23 - Nov 21
Grishma (summer)Maargazhi (மார்கழி) Dhanur17 Dec -14 Jan SagittariusNov 22 - Dec 21
Grishma (summer)Thai (தை) Makaram15 Jan -13 Febr CapriconDec 22 - Jan 19
Varsha (rainy)Maasi (மாசி) Kumbham14 Febr -14 Mar AquariusJan 20 - Feb 18
Varsha (rainy)Panguni (பங்குனி)Meenam15 Mar -13 Apr PiscesFeb 19 - Mar 20


Daksha, (may be chaldean astronomer), identified and named 28 stars and all stars are considered as his daughter. The North and South celestial poles do not remain permanently fixed against the background of the stars. Due to precession of the equinoxes, the poles trace out circles on the celestial sphere, with a period of about 25,700 years. North pole identified by polar-star, is part of porpoise-like constellation (stars of Cassiopeia make its tail, Andromeda and Triangulum form its body, and Aries makes its head)
Below 28 stars with tamil and astronomical names are listed. Angle with reference to Aswin are given in degrees. Currently, Aswin rises at 31 Deg on March Equinox. For simplification, all stars are assumed to be equally distributed at 13.33 deg from one another, starting with Mesha rasi at 0 deg. So, simplified value used in panchangam are given in brackets
1) Aswinee - Asvini - Beta Arietis (3) - 0 deg [0]
2) Apabarani - Barani - 35 Arietis (3) - 11 deg [13.33]
3) Krittikaa - Karthikai - Eta Tauri in Pleiades cluster (6) - 26 deg [26.67]
4) Rohinee - Rohini - Aldebaran (5) - 38 deg [40]
5) Mrigaseeroo - Mirugasirsham - Lambda Orionis (3) - 51 deg [53.33]
6) Ardra - Thiruvadirai - Alpha Orionis (1) - 67 deg [66.67]
7) Punarvasu - Punarpoosam - Beta Geminorium (2 to 4) - 84 deg [80]
8) Pushya - Poosam - Delta Cancri (3) - 93 deg [93.33]
9) Aslesha - Aayilyam - Alpha Hydroe (1) - 104 deg [106.67]
10) Makha - Magam - Regulus (5) - 121 deg [120]
11) Poorvaphalguni - Pooram - Delta Leonis (2) - 137 deg [133.33]
12) Uthraphalguni - Uttaram - Beta Leonis (2) - 146 deg [146.67]
13) Hastha - Hastham - Delta Corvi (3) - 159 deg [160]
14) Chitraa - Chitirai - Spica Virginis - Vegus (1) - 172 deg [173.33]
15) Swathi - Swati - Arcturus (1) - 183 deg [186.67]
16) Vishakha - Visakam - Alpha Libroe (2) - 193 deg [200]
17) Anuradha - Anusham - Delta Scorpio (4) - 209 deg [213.33]
18) Jyeshta - Kettai - Antares (3) - 217 deg [226.67]
19) Moola - Moolam - Lambda Scorpio (11) - 229 deg [240]
20) Poorvashada - Pooradam - Delta Sagittari (2) - 251 deg [253.33]
21) Uthrashada - Uttaradam - Sigma sagittari (3) - 272 deg [266.67]
21a) Abhijit - Vega, in constellation of Lyra - 285 deg [-]
22) Sravana - Thiruvonam - Alpha Aquiloe (3) - 294 deg [280]
23) Dhanishta - Avittam - Beta Delphinum (4) - 304 deg [293.33]
24) Sathabhisha - Sadayam - Lambda Aquarius (100) - 312 deg [306.67]
25) Poorvabhadrapada - Purattadhi - Alpha Pegasi (2) - 329 deg [320]
26) Utharabhadrapada - Uttarattadhi - Gama Pegasi (2) - 341.5 deg [333.33]
27) Rewati - Revathi - Zeta Piscum (32) - 351.5 deg [346.67]

Daksha named 28 stars and they are called his daughters. Head or first star refers to Abhijit, which was later removed by Badra. This gave to mythological story, Daksha's human head was cut and replaced with mesha head. So, new star system starts with Krittika in mesha rasi. Now first star is Ashvini.

Lunar day or Tithi

Tithi or thithi is a lunar day, or the time it takes for the longitudinal angle between the Moon and the Sun to increase by 12°. Varies in duration approximately a day. They are: (1) Pratipada (2) Dwitiya (3) Tritiya (4) Chaturthi (5) Panchami (6) Shashthi (7) Saptami (8) Ashtami (Half Moon) (9) Navami (10) Dashami (11) Ekadasi (12) Dwadashi (13) Trayodashi (14) Chaturdashi (15) Ammavasya (New Moon) if krishna பக்ஷெ or Purnima (Full Moon) if sukla பக்ஷெ

Metonic cycle

Metonic cycle is 19 years or 235 lunar months or approx 6940 days, nearly a common multiple of the solar year and the synodic (lunar) month. With in 19 years, every 8 and 11 are close match.

Callippic cycle, a 76-year cycle with a more accurate approximation = 27759 days.
Tamil Solar New year will be on new moon in 2010 and on full moon in 2014.
yearfull sideral monthsfull synodic monthsideral Lag -Leadsynodic Lag -Lead
0{ 19-38-57-76}0000
1{ 20-39-58-77}131210.1 - 17.210.9 - 18.6
2{ 21-40-59-78}262420.1 - 7.221.8 - 7.8
3{ 22-41-60-79}40372.9 - 24.43.1 - 26.4
4{ 23-42-61-80}534913.0 - 14.314.0 - 15.5
5{ 24-43-62-81}666123.1 - 4.324.9 - 4.6
6{ 25-44-63-82}80745.8 - 21.56.3 - 23.3
7{ 26-45-64-83}938615.9 - 11.417.2 - 12.4
8{ 27-46-65-84}1069826.0 - 1.428.1 - 1.5
9{ 28-47-66-85}1201118.7 - 18.69.4 - 20.1
10{ 29-48-67-86}13312318.8 - 8.520.3 - 9.2
11{ 30-49-68-87}1471361.5 - 25.81.7 - 27.9
12{ 31-50-69-88}16014811.6 - 15.712.5 - 17.0
13{ 32-51-70-89}17316021.7 - 5.623.4 - 6.1
14{ 33-52-71-90}1871734.4 - 22.94.8 - 24.7
15{ 34-53-72-91}20018514.5 - 12.815.7 - 13.8
16{ 35-54-73-92}21319724.6 - 2.726.6 - 3.0
17{ 36-55-74-93}2272107.3 - 20.07.9 - 21.6
18{ 37-56-75-94}24022217.4 - 9.918.8 - 10.7
19{ 38-57-76-95}2542350.2 - 27.20.2 - 29.4
385084700.3 - 27.00.4 - 29.2
577627050.5 - 26.80.5 - 29.0
7610169400.6 - 26.70.7 - 28.8
95127011750.8 - 26.50.9 - 28.7

Year for selected cultures

Egyptians, Phoenicians, Persians, Greeks, Roman, and many cultures began their new year with the fall equinox. Around 1800 years back the day Sun enters Makara Rashi (Capricorn) was coinciding with the day of Uttarayana or Winter Solstice or Surya beginning Northern journey (Northern hemisphere). This happens to be harvest season. It is also Thiruvalluvar new year or early Tamil New Year. start a year with winter or December solstice (Dec 23). Because of Leap year calculation errors, Gregorian new year shifted by 7 or 8 days. Because of earth's precession, Tamil new year shifted by 21 or 22 days.

Mesopotamians and early vedics celebrated around the time of the vernal equinox, March 23 (Current Hindu Saka calendar). Saka era or Shalivahana Sakabda is the vernal equinox of the year AD 78. Later many Indian systems shifted new year from solstice to March Equinox, during the time of Bhadra, Indian astronomer.

Ancient Hindu system is Saka era or Shalivahana Sakabda (year AD 78) starting with vernal (March) equinox. This is Indian Government new year, which is not popular.

Early Tamil New Year starts with winter or December solstice (Dec 23) or harvest season. The ancient Tamil calendar was made up of twelve months and every two months constituted a season, starting with vadavazhi vizhavu, the festival of welcoming the Lord Surya back to home on Winter Solstice (December). (Thirukkural or Silappathikaram period or ancient Tamil system).

Hindu calendar is a collective name for most of the luni-sidereal calendars and Shalivahana calendar in the Deccan States of Karnataka, Telangana, Maharashtra and Andhra Pradesh

Buddhist Era starts on 543 or 544 BC, replaced by Vikrama Samvat calendar which began in 56 BC. Astronomical calculations are based on Kaliyuga start alignment on 3102 BC (by Aryabhatta). There are other eras such as: Vedanga Jyotisa; Gaurabda Gaudiya; and Kolla Varsham.

Kalacakra calendar - 60 Year names:

Surya Siddhantic list starts with Vijaya.
Kalacakra calendar with 60 year cycle starting with Prabhava and Mesha sankaranthi, popularized by Pandita Somanatha of Tibet/Himalayas, in 1027. This is followed by kalingas, Cholas, Pallavas, Thais, Khmer etc..
Pandita Somanatha further developed sexa decimal system. The earth's axis wobble that causes the precession of the equinoxes is approximately 25,920 years or 432 sixty year cycles. Many ancient sites reflect the number 432 in their alignment to stars and planets and the earths path through space.

1987 Prabava: 1988 Vibava: 1989 Sukla: 1990 Pramodoota: 1991 Prajothpatthi: 1992 Angirisa: 1993 Srimuka: 1994 Bava: 1995 Yuva: 1996 Thathu: 1997 Eswara: 1998 Veguthanya: 1999 Pramathi: 2000 Vikrama: 2001 Vishu: 2002 Chitrabanu: 2003 Subanu: 2004 Tharana: 2005 Parthiba: 2006 Viya: 2007 Sarvajithu: 2008 Sarvathari: 2009 Virothi: 2010 Vikruthi: 2011 Kara: 2012 Nandana: 2013 Vijaya: 2014 Jaya: 2015 Manmata: 2016 Thurmugi: 2017 Avilambi: 2018 Vilambi: 2019 Vihari: 2020 Sarvari: 2021 Pilava: 2022 Subakiruthu: 2023 Sobakirathu: 2024 Kurothi: 2025 Visuvavasu: 2026 Parabava: 2027 Bilavanga: 2028 Keelaka: 2029 Sowmya: 2030 Sadarana: 2031 Virothikiruthu: 2032 Parithabi: 2033 Pramadhicha: 2034 Ananda: 2035 Rakshasa: 2036 Nala: 2037 Pingala: 2038 Kalayukthi: 2039 Siddharthi: 2040 Rauthiri: 2041 Thunmathi: 2042 Thunthubi: 2043 Ruthrothkari: 2044 Rakthakshi: 2045 Kurothana: 2046 Akshaya


Gregorian year 2000 CE corresponds, respectively with:
1.Year 5101 in Kaliyuga calendar;
2.Year 2544 in Buddha Nirvana calendar;
3.Year 2543 in Buddhist Era (BE) of the Thai solar calendar
4.Year 2057 in Bikram Samvat calendar;
5.Year 1922 in Saka era or Shalivahana Sakabda (began in 78AD)
6.Year 1921 of the Vedanga Jyotisa calendar;
7.Year 1407 in Bengali calendar;
8.Year 514 in Gaurabda Gaudiya calendar;
9.Year 1176 in Malayalam calendar or Kolla Varsham calendar.
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