Astronomical Bases of Calendars

This section describes astronomical bases of calendars. There are three principal astronomical cycles: Day, Month, and Year. There are three types of calendar systems: Solar calendar, Lunar calendar, and Lunisolar calendar.

There are three principal astronomical cycles that can be used by a calendar:

The year, also called the tropical year, is defined as the mean interval between vernal equinoxes; corresponding to the cycle of the seasons. The following expression, based on the orbital elements of Laskar (1986), is used for calculating the length of the tropical year: 365.2421896698 - 0.00000615359 T - 7.29E-10 T^2 + 2.64E-10 T^3 [days], where T = (JD - 2451545.0)/36525 and JD is the Julian day number. However, the interval from a particular vernal equinox to the next may vary from this mean by several minutes.

The month, also called the synodic month, is defined as the mean interval between conjunctions of the moon and sun, corresponding to the cycle of lunar phases. The following expression for the synodic month is based on the lunar theory of Chapront-Touze' and Chapront (1988): 29.5305888531 + 0.00000021621 T - 3.64E-10 T^2 [days], where T = (JD - 2451545.0)/36525 and JD is the Julian day number. Any particular phase cycle may vary from the mean by up to seven hours.

In the preceding formulas, T is measured in Julian centuries of Terrestrial Dynamical Time (TDT), which is independent of the variable rotation of the Earth. Thus, the lengths of the tropical year and synodic month are here defined in days of 86400 seconds of International Atomic Time (TAI).

Julian day number seems to be defined as 4713. But, I am not sure if this is correct.

Depending which cycles are used, calendars are divided into three groups:

Table of Contents

 About This Book

Chinese Calendar Background Information

Astronomical Bases of Calendars

 The Gregorian Calendar

 The Chinese Calendar

 Chinese Calendar Algorithm and Program

 Chinese Calendars: Year 1901 to 1910

 Chinese Calendars: Year 1911 to 1920

 Chinese Calendars: Year 1921 to 1930

 Chinese Calendars: Year 1931 to 1940

 Chinese Calendars: Year 1941 to 1950

 Chinese Calendars: Year 1951 to 1960

 Chinese Calendars: Year 1961 to 1970

 Chinese Calendars: Year 1971 to 1980

 Chinese Calendars: Year 1981 to 1990

 Chinese Calendars: Year 1991 to 2000

 Chinese Calendars: Year 2001 to 2010

 Chinese Calendars: Year 2011 to 2020

 Chinese Calendars: Year 2021 to 2030

 Chinese Calendars: Year 2031 to 2040

 Chinese Calendars: Year 2041 to 2050

 Chinese Calendars: Year 2051 to 2060

 Chinese Calendars: Year 2061 to 2070

 Chinese Calendars: Year 2071 to 2080

 Chinese Calendars: Year 2081 to 2090

 Chinese Calendars: Year 2091 to 2100

 References

 PDF Printing Version