KDE Core/Astronomical Calendars/Chinese

Introduction

The Chinese calendar is a lunisolar calendar, as it uses months to approximate the tropical year. By the modern definition, the tropical year has been defined as the time taken by the Sun's mean longitude to increase by 360 degrees. The Chinese lunar calendar is followed by many Asian countries like Japan, Vietnam and Korea. Similar to the Islamic Calendar, 12 synodic months fall short by 11 days to the tropical year. However, instead of using a leap year to compensate for this difference, the Chinese use 'leap months' in about every third year to maintain the synchronization with the tropical year. A more predictable method to get the insertion of leap months is to follow the Metonic Cycle according to which 235 synodic months are equal to 19 tropical years (with a difference of only two hours). To break this down in calendar arithmetics:

• 235 = 19x12 + 7

Therefore, 7 leap months are inserted in a period of 19 years. More details about the leap months have been mentioned in the forthcoming sections.

Despite the controversial debates going on between the Chinese calendar epoch, in our calculations we have been defined the Chinese epoch as March 8, 2637 BCE. There have been various controversies regarding the selection of the Chinese epoch. Scholars have claimed that the calendar was invented during the reign of Yellow Emperor Huangdi, which began in 2697 BCE. The debate is that some scholars claim that the year was invented in the first year of his reign (2697 BCE) while others claim that the year was invented in the 61st year of his reign (2637 BCE). There have been more than 50 calendar reforms in the Chinese calendar since its inception.

The Solar Terms

The Chinese astronomers use 24 solar nodes(solar terms) which correspond to significant events in the Chinese culture. Seasonal markers cut the ecliptic in 4 sections of 90degrees each. Solar terms cut the ecliptic in 24 sections of 15degrees each. The even terms are called the major solar terms or Zhongqi and the odd ones are called minor solar terms of Jieqi.

Ecliptic longitude	Chinese name	Approx Gregorian date	Translation
315°	lichun	February 4	start of spring
330°	yushui	February 19	rain water
345°	jingzhe	March 5	insects awaken
0°	chunfen	March 20	vernal equinox
15°	qingming	April 5	clear and bright
30°	guyu	April 20	grain rains
45°	lixia	May 6	start of summer
60°	xiaoman	May 21	grain full
75°	mangzhong	June 6	grain in ear
90°	xiazhi	June 21	summer solstice
105°	xiaoshu	July 7	minor heat
120°	dashu	July 23	major heat
135°	liqiu	August 7	start of autumn
150°	chushu	August 23	limit of heat
165°	bailu	September 8	white dew
180°	qiufen	September 23	autumnal equinox
195°	hanlu	October 8	cold dew
210°	shuangjiang	October 23	descent of frost
225°	lidong	November 7	start of winter
240°	xiaoxue	November 22	minor snow
255°	daxue	December 7	major snow
270°	dongzhi	December 22	winter solstice
285°	xiaohan	January 6	minor cold
300°	dahan	January 20	major cold

The Month

The Chinese system of 12 double hours starts at 11pm. This has a significant role to play in Chinese astrology. The new moon marks the beginning of the new Chinese month. Regarding the calculations based on locale, before 1929 the calculations of the Chinese astronomy were based on the meridian in Beijing(39.9167degrees, 116.4167degrees); but in 1928, China adopted the standard time zone of 120degrees longitude which is close to the republican capital Nanjing. There are a variety of series for naming months, such as flowers, numbers, etc.

#	Corresponding to Zodiac Sign	Solar Longitude	Corresponding to Flowers
1	正月 zhengyue	330°	正月Primens
2	二月 eryue	0°	杏月 Apricomens
3	三月 sanyue	30°	桃月 Peacimens
4	四月 siyue	60°	梅月 Plumens
5	五月 wuyue	90°	榴月 Guavamens
6	六月 liuyue	120°	荷月 Lotumens
7	七月 qiyue	150°	蘭月 Orchimens
8	八月 bayue	180°	桂月 Osmanthumens
9	九月 jiuyue	210°	菊月 Chrysanthemens
10	十月 shiyue	240°	良月 Benimens
11	十一月 shiyiyue	270°	冬月 Hiemens
12	十二月 shieryue	300°	臘月 Ultimens

The Year

Chinese Calendar = solar calendar + lunisolar calendar

The solar calendar starts at the December Solstice and follows the 24 solar terms. It is known as sui. The lunisolar calendar starts at the Chinese New Year and it consists of 12 or 13 months. It is called nian. The solar calendar follows the tropical year more closely than the lunisolar calendar,. The solar year has a fixed length whereas the length of the lunisolar year is variable. An important rule in implementing the Chinese calendar is the definition of the leap month. The rule followed is:

• December solstice falls in month 11. A sui is a leap sui if there are 12 complete months between the two 11th months at the beginning and the end of the sui.
• In a leap sui, the first month that does not contain a major solar term is the leap month.
• Leap months take the same number as the preceding month, and a prefix "Leap (閏)" before the number.

The Week

The modern Chinese calendar follows a 7-day week with Monday of the Gregorian Calendar being the first day of the week. The weekdays are named in pinyin as:

1. Xingqi Yi (Weekday One)
2. Xingqi Er (Weekday Two)
3. Xingqi San(Weekday Three)
4. Xingqi Si (Weekday Four)
5. Xingqi Wu (Weekday Five)
6. Xingqi Liu (Weekday Six)
7. Xingqi Tian (Sun Day)

Research Sources

The research has been documented from the following sources, namely:

1. Calendrical Calculations: Third Edition - Nachum Dershowitz and Edward M. Reingold
2. Notes and Errata on Calendrical Calculations: Third Edition - 25th May 2011
3. Astronomical Algorithms: First Edition - Jean Meeus
4. Practical Astronomy with your Calculator: Third Edition - Peter Duffet-Smith
5. How to compute planetary positions - Paul Schlyter
6. Mathematics of Chinese Calendar - Helmer Aslaksen

The amount of calculations required for the complete implementation of the calendar are highly extensive, and require very high precision. Without the astronomical calculations, the Islamic Calendar lacks accuracy by 1-2 days and therefore it becomes difficult to predict future dates in the Islamic Calendar. The astronomical calculations are so precisely timed that such an ambiguity in the prediction of dates of the Islamic Calendar is reduced to 1 day in 2500 years.

Astro Library

Most of the astronomical functions have already been described in the implementation of Islamic Calendar. A few functions were appended to the previously described Astro Library, namely:

astro.h

int roundOff(double value)

Rounds off the double value to the integer value

astrolunar.h

double newMoonBefore(double time)

Returns the moment of a New Moon occurrence before the given time

double newMoonAtOrAfter(double time)

Returns the moment of a New Moon occurrence at or after the given time

astrosolar.h

double estimatePriorSolarLongitude(double longitude, double time)

This function has an important role to play in implementing astronomical solar calendars, as it determines a particular solar longitude on or before the given date. The solar longitude can correspondingly help to find the day of the New Year as per the astronomical calendar.