John Snow wrote:
question to satyarthi garu>
Then what is the difference between Chandra mana samvatsre (lunar) to soura mana samvatsre. Maharashtrians, Telugus, Kannadigas follow chandramana, where as tamil people follow sourmana (solar based)
Usually the computed difference comes out to be roughly 14 days ( the difference also in telugu new year and tamil new year).
Is adhika masam only related to chaandramana calendar?
A purely solar year, like the Tamil new year, starts exactly when sun transits into Mesha (Mesha sankranti). But the Indian luni-solar years either start at the new moon in the same solar month (amanta system), or on the previous full moon (purnimanta system). This means there will be difference between start of a solar year and a lunar year. Also start of amanta and purnimanta years are off by a fortnight.
Adhika masa is associated with luni-solar calendar, i.e. it arises due to a need to maintain the lunar year in tandem with the solar year. In a purely solar calendar, there is no need for adhika masa. More explanations below.
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1.
Sidereal or nirayana year : Measures year by the time taken by sun to reappear in the same background of stars. In Indian system initial point is taken as Mesha (or Aries) rashi. Sidereal year is 365.256363 days. So nirayana (sidereal) year is longer than the sayana (tropical) year by 0.014173 days.
2.
Tropical year or sayana year : Measures year by the time from vernal equinox to vernal equinox = 365.24219 days. This is called sayana year in Indian system, or tropical year in western system. The term "tropical" just means when you count time from equinoxes or solstices.
The difference between a tropical year and sidereal year is due to precession of earth's axis. This slow precession causes, the equinoxes and solstices to shift back slightly every year.
Since a tropical year effectively subtracts out the precessional difference and is tied to the equinoxes and solstices, this effect of precession is not noticed, and the equinoxes and solstices occur around the same date every year.
In a sidereal year this effect due to precession is noticeable over time. If sun used to cross into Makara at winter solstice in 285 AD, now it is ahead by about 24 days. So according to solar sidereal calendar, the solstice has shifted into the previous month by 24 days than that at 285 AD.
3.
Gregorian calendar:
(i) Is a solar calendar, that uses the tropical year, but the length of the year is given in an integral number of days, usually 365, but can be 366 in leap years.
(ii) To account for 0.24219 days deficit in a standard year of 365 days, every 4 years an extra day is added.
(iii) But since 0.24219 is not exactly 0.25, other corrections are introduced. A century year is not allowed to be a leap year unless divisible by 400. This means that in a period of 400 years there are 97 leap years. Which gives mean gregorian year as 365.2425 days, which is slightly longer than the tropical year. So even the Gregorian calendar would need some tuning after some time.
(iii) Months have 31, 30, 28 (or 29) days so that the sum works out to 365 (or 366) days.
4.
Indian solar (sauramAna) calendar:
(i) is a solar calendar that uses the nirayana (sidereal) year of 365.256363 days. Surya Sidhhanta gave sidereal year as 365.258756 days which is slightly longer than the current estimates. Year's beginning is typically when Sun transits into Mesha (Aries) rAshi.
(ii)Due to the fractional part of 0.256363 days (about 6 hours 9 minutes 10 seconds), Sun enters the Mesha rashi every year later in the day by about 6 hours. Depending upon how the beginning of the day is determined, there can be a difference of a day in deciding when the year has started. Since the beginning days of the months are similarly decided (when the sun enters a rashi corresponding to that month), beginning days of months can also have similar variation.
(iii) Entering of a rashi by the Sun is called sankranti. That is why the comment about Makara-sankranti in the Frontline article was stupid. Because on Makara sankranti day, sun actually crosses into Makara (or capricorn).
(iv) Due to the precession of earth's axis at a slow rate, of 50.3 arcseconds per year, the tropical year is shorter than the sidereal year. This also means that the start of the year in a sidereal system, as identified by sun moving into Mesha (Aries) rashi, moves with respect to the equinoxes (or solstices) by this much amount. Therefore over time, the start of the year appears in a different season. Since the seasons are dependent upon time interval from equinoxes and solstices.
(v) Tropical system arbitrarily redifines "Aries" to start from the vernal equinox. But due to the precession, vernal equinox is no more in Aries but is off by 24 days and closer to Pisces. This fact must be kept in mind. In Indian system Mesha is the actual, fixed constellation spanning 30 degrees in the background of stars. In Western tropical astronomy, so called "Aries" is a patch of sky 30 degrees wide, which moves around.
(vi) Note that vernal equinox point coincided with true Aries (Mesha sankranti) in year 285 AD. Since then it has moved by about 24.4 ( (2008-285)*0.014173) days.
4.
National calendar of 1957:
It is a solar tropical calendar. It was an attempt to make Indian calendar tropical instead of sidereal. The year starts on vernal equinox day and has months of 30 or 31 day lengths, with a leap year convention piggy backing on Gregorian calendar, It was an attempt to introduce Gregorian calendar with Indian sounding terminology, and hasn't found any real uses.
5.
Lunar or chandramAna calendar:
(i) It is not a true lunar calendar, but a luni-solar calendar. Where the year is still decided by the sun, but the months (mAsa) and dates (tithi) are decided by moon.
(ii) A lunar calendar's basic unit is a lunar month =(new moon to new moon). In some calendars full moon to full moon = 29.5306 days.
(iii) A sidereal solar month is transit of the sun from one rashi to next rashi and is = 365.256363/12 = 30.43803 days.
(iv) Solar months are named after the nakshatra visible opposite to the sun, so chaitra month is associated with sighting chitrA nakshatra opposite the sun, i.e. is the nakshatra rising when the sun is setting.
(v) A lunar month is named after the solar month in which the new moon falls.
(vi) Since the lunar month is smaller than the solar month more than one new moon can fall within the same solar month.
(vii)
Tithi: There are 30 thithis in a lunar month. 15 in the shukla paksha and 15 in the krishna paksha. Since a lunar month has 29.5306 solar days, a tithi works out to be slightly smaller than a solar day , i.e 1 mean Tithi = 29.5306/30 = 0.98435 solar days = 23.6244 hours. The significance of a tithi is that it marks a fixed amount of advancement in lunar phase. since lunar month is new moon to new moon, one tithi works out to = 360/30 = 12 degrees change in lunar phase.
(viii) Since a tithi is smaller than a solar day, even if a tithi's beginning matched with sunrise at a certain date, it will drift and in general a tithi can start at any time of a solar day.The days of a month are numbered according to the tithi during sunrise. The naming convention "chaitra shukla panchami" means in the lunar month of chaitra, in the bright half of the moon, the 5th tithi was going on at sunrise.
6.
Adhika or Mala months in luni-solar calendar:
(i) A lunar year of 12 lunar months is 29.5306 * 12 = 354.3672 days. While a nirayana (sidereal) solar year is 365.256363 days. Therefore a lunar year is shorter than a solar sidereal year by 10.89 days.
(ii) To keep the lunar year in tune with solar year, an extra lunar month needs to be added to a lunar year at certain intervals. Usually every 19 years 7 lunar months are added. With this correction 19 lunar years = (19*12+7)*29.5306 = 6939.69 days, which is pretty close to 19 sidereal years = 19 * 365.256363 = 6939.87 days. So to maintain a lunar year in tune with a solar year, 7 extra lunar months need to be added during a period of 19 years or on average one lunar month per 2.7 years.
(iii) Indian astronomers don't add these extra months at arbitrary intervals (such as Gregorian calendar does with leap years), but have an ingenious method. Since lunar month is smaller than a solar month, two new moons can occur within the same solar month. Then since by convention a lunar month is named by the prevailing solar month, you get two lunar months getting the name of the same solar month. This way an extra lunar month gets added with the same name as the previous one. The first month with the same name is called "adhika" or "mala". It turns out that this way of adding extra lunar months works out to have one lunar month added per 2.7 years.
(iv) This idea of "mala" masa and the so called "blue moon" have something in common.
7.
amanta and purnimanta luni-solar calendars:
(i) In Amanta system Month is from new moon to next new moon. The lunar year also starts at the new moon. The month is named by the solar month in which the new moon falls. The first lunar month of the year is chaitra.
(ii) Purnimanta system, month is from full moon to full moon, and starts one fortnight before the amanta month. But the year starts on a new moon!! This is the reason of the 14 day fortnight difference. So in a purnimanta calendar, the year starts in the middle of the lunar chaitra month. So, one half of chaitra gets counted in one year and other in the next!
(iii) Purnimanta is common in North India.
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