by tonytran2015 (Melbourne, Australia).
#East Asia New Year, #lunar New Year, #lunar leap year, #lunar leap month, #lunisolar calendar, #Vietnamese New Year.
When traveling to or working with East Asia countries Westerners are sometimes puzzled by their Calendar and long New Year festivals which vary from year to year on the Western Calendar.
This blog gives simple explanation to Westerners the rules of East Asia Lunisolar calendar which is based on Celestial observations and has been designed to give season information to users.
To easily understand this article, readers are advised to first read the simple summary on stars in the sky  to know the declination, right ascension and the date of a star.
Simple calculations  shows that each lunar month is 29.530 days. Two lunar months has a length of 59.06 days. The lunisolar calendar used in China since ancient time has had Winter solstice falling on the 11th month of the year since more than 2000 years ago, since 113BC (Han Dynasty II p.38 ) .
The solstice point (the point from ecliptic most South of the celestial equator) is moving slowly in the sky and is currently opposite to 90 degree Right Ascension.
1. New Year time is just a convention.
A lunisolar year can be made to start at any of its seasonal point, the point can be in the Winter or in the Summer. It all comes to a matter of convention. For example, the Burmese lunisolar calendar has its New Years starting when the Sun enters the constellation Aries.
For East Asia lunisolar calendar making, there are two major alternatives for determining its New Years as in the following.
2. Simple rules.
Figure 1: Phase of the Moon. A new Moon is the Moon with a thin white crescent on its leading edge (top right corner of the picture) which is first visible right after sunset on the Western horizon.
If the calendar makers want their people to have simple and clear rule on the start of a New Year, they can define the New Year starting on the Second New Moon after Winter Solstice day.
This would be easy for ordinary people and people in remote areas to work out their two last (11th and 12th) lunar months of the year, and have enough time to prepare for the New Year festival.
3. Precision rules with uniform determination of months.
Figure: Inversion map of the Northern Celestial 3/4-sphere. The non-concentric circle is the ecliptic and winter solstice is its most distant point from the North pole (on the left of the North pole).
The Eastern Asia lunisolar Calendar requires each of its lunar month has a characteristic star in the sky to match with the seasons. There are 12 chosen characteristic stars. A lunar year has either 12 lunar months (normal year) or 13 lunar months (leap year). Any lunar month not containing any of those 12 chosen characteristic stars is called a leap month and is named after its preceding month.
If the Calendar Makers insist on astronomical precision with uniform determination of months then they can define each month having to contain a star at regular spacing of Right Ascension, that is 11th month having some star of 90 degree R.A. on the meridian line at midnight on one night of the month and so on , .
Therefore they would require that
11th month has a star of 90 degree R.A.,
12th month has a star of 120 degree R.A.,
1st month has a star of 150 degree R.A., (Regulus of Leo has 152.05° R.A., 12° decl.)
2nd month has a star of 180 degree R.A.,
3rd month has a star of 210 degree R.A.,
4th month has a star of 240 degree R.A., (Delta Scorpii has 240.22° R.A., –22.60° decl.)
5th month has a star of 270 degree R.A.,
6th month has a star of 300 degree R.A., (Altair of Aql has 297.7° R.A., 8.85° decl.)
7th month has a star of 330 degree R.A.,
8th month has a star of 0 degree R.A.,
9th month has a star of 30 degree R.A.,
10th month has a star of 60 degree R.A.,
any month that has no star in the above list is called a leap month bearing the same name as its preceding non-leap month. Therefore it is hard for ordinary people to know the beginning of the Year.
4. Most probable choice.
I would think that the ancient Calendar makers chose the first alternative rather than the more difficult second alternative.
The second alternative also has an additional complication that there is a precession of Equinox at a rate of 360 degree per(approximately) 25,920 years. In 2000 years the Winter Solstice has moved by 27.7 degrees (about one month). Chines Calendar Makers would have noticed it and saw the need for adjustment had they chosen the second alternative but I could not find any literature about that kind of adjustment.
It is most likely that Chinese Calendar Makers had chosen the first alternative. Their choice may have had influence on Calendar Makers of neighboring countries.
If East Asian Calendar Makers chose the easy rules of for determining New Year day then the 1st month of any East Asian New Year would contain a star that has a date of 18 February(= 21 December + 59.06 days), 59.06 days after Winter Solstice. That would come to a simple rule for star watchers (for the current configuration of Earth orbit):
The New Year starts on the second new moon after Winter Solstice day and the first lunar month of the lunisolar calendar should have a star of 18 February (= 21 December + 59.06 days) of Right Ascension of nearly 152 degrees (near to that of Regulus of Leo) on its meridian at midnight.
The second through to the tenth months of the lunisolar calendar have been anchored to seasons by requiring each to have a star chosen as specified in section 3. If bright stars of approximate Right Ascensions are chosen instead, there would only be more or less leap months repeating the name of the preceding months. The choice of bright stars of approximate Right Ascensions may also have been influenced by superstition and politics.
. tonytran2015, Finding North and time by stars ,survivaltricks.wordpress.com, https://survivaltricks.wordpress.com/2015/08/28/finding-north-and-time-by-stars/
. tonytran2015, Finding North direction and time accurately from the horn line of the Moon, survivaltricks.wordpress.com, https://survivaltricks.wordpress.com/2015/08/12/finding-north-direction-and-time-accurately-from-the-horn-line-of-the-moon/
. Sima Qian, Records of History by the grand historian (translated by Burton Watson), Qin Dynasty, Han Dynasty I (Rev. Ed.) and Han Dynasty II (Rev. Ed.), the Res. Cent. for Transl. The Chinese Univ. of Hon Kong and Colubia Univ. Press, Hong Kong and New York, 1961.
. Helmer Aslaksen, The Mathematics of the Chinese Calendar, http://www.math.nus.edu.sg/aslaksen/calendar/chinese.shtml, accessed 19 Jan 2017.
. Ho Ngoc Duc, Thuat toan am lich (in Vietnamese), https://www.informatik.uni-leipzig.de/~duc/amlich/calrules.html, accessed 19 Jan 2017.