Calendar

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.
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.

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
[http://aa.usno.navy.mil/data/docs/JulianDate.php]

Months

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).

Weekday (Graha)

Diameter in kmRadius of rotation in kmRevolution in daysRevolution in yearsArc angle in degrees
Sun1,391,0000.5328
Mercury4,87857,895,20087.970.2410.003
Venus12,104108,160,800224.700.6150.0167
Earth12,756149,600,000365.260
Moon3,476384,4000.5182
Mars6,794227,990,400686.981.8810.005
Jupiter142,984778,368,8004,332.5911.8620.013
Saturn120,5361,426,735,20010,759.2229.4570.0054

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