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 (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
- Sidereal month 27.321661 days (27 d 7 h 43 min 11.5 s).
- Tropical month is customary to specify positions of celestial bodies with respect to the vernal equinox. 27.321582 days (27 d 7 h 43 min 4.7 s).
- Anomalistic month is the position of the extreme points (the line of the apsides: perigee and apogee), makes a full circle (lunar precession) in about nine years. 27.554551 days (27 d 13 h 18 min 33.2 s).
- Draconic month or 'draconitic' month or nodical monthis based on orbit of the moon lies in a plane that is tilted with respect to the plane of the ecliptic: it has an inclination of about five degrees. As a result, the time it takes the moon to return to the same node is shorter than a sidereal month. It lasts 27.212220 days (27 d 5 h 5 min 35.8 s). The plane of the moon's orbit precesses over a full circle in about 18.6 years.
- Synodic month is the average period of the Moon's revolution with respect to the Sun. The synodic month is a description of the Moon's phases, because the Moon's appearance depends on the position of the Moon with respect to the Sun as seen from the Earth. Because of perturbations in the orbits of the Earth and Moon, the actual time between lunations may range from about 29.27 to about 29.83 days. The long-term average duration is 29.530589 days (29 d 12 h 44 min 2.9 s). The synodic month is used in the Metonic cycle.
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 hemisphere||Southern hemisphere|
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:
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).
- the vaasara or weekday (in honour of seven grahas or seven visible moving celestial objects)
- 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)
- the nakshatra (one of 27 divisions of the celestial ecliptic) in which the moon resides at sunrise (27 or 28 stars)
- the yoga (one of 27 divisions based on the ecliptic longitude of the sun and moon) active at sunrise
- .the karana (divisions based on tithis) active at sunrise.
|Diameter in km||Radius of rotation in km||Revolution in days||Revolution in years||Arc angle in degrees|
|Weekday (Tamil)||Vaasara (Sanskrit)||Lord or Planet||Chaldean meaning||Planets Spend in each Sign|
|(1)Sunday||ஞாயிற்றுக்கிழமை||Ravi-vaasara||Sun -Aditya -Son of Aditi (the unchangeable)||Sun-Shamash-God of Law and Justice||1 month|
|(2)Monday||திங்கட்கிழமை||Soma-vaasara||Moon -Soma -Peace, Gentleness||Moon-Sin-God of Agriculture||2.25 days|
|(3)Tuesday||செவ்வாய்க்கிழமை||Mangala-vaasara||Mars -Ankgaraka -Burning coal||Mars-Nergal-God of War||45 days|
|(4)Wednesday||அறிவன் கிழமை||Budha-vaasara||Mercury-Budha -Intellect||Mercury-Nabu-God of Writing||1 month|
|(5)Thursday||வியாழக்கிழமை||Guru Vaasara||Jupiter-Brihaspati-Great (brihat) protector (pati)||Jupiter-Marduk-King of the Gods||1 year|
|(6)Friday||வெள்ளிக்கிழமை||Sukra-vaasara||Venus -Shukra -Refined, Sensual||Venus-Ishtar-God of Fertility||1 month|
|(7)Saturday||காரிக்கிழமை||Shani-vaasara||Saturn -Shani -Slow||Saturn-Ninib-God of Pestilence and Misery||2.5 year|
|.||Moon's North Node-Rahu-Dragon's Head||1.5 year|
|Moon's South Node-Ketu -Dragon's Tail||1.5 year|