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The above formulae give the length of the tropical year in ephemeris days (equal to 86,400 SI seconds), not solar days. It is the number of solar days in a tropical year that is important for keeping the calendar in synch with the seasons (see below).
The oldest solar calendars include the Julian calendar and the Coptic calendar. They both have a year of 365 days, which is extended to 366 once every four years, without exception, so have a mean year of 365.25 days. As solar calendars became more accurate, they evolved into two types.
The dates the Sun passes through the 12 astronomical constellations of the ecliptic are listed below, accurate to the year 2011. The dates will progress by an increment of one day every 70.5 years. The corresponding tropical and sidereal dates are given as well.
The sidereal year differs from the solar year, "the period of time required for the ecliptic longitude of the Sun to increase 360 degrees", [2] due to the precession of the equinoxes. The sidereal year is 20 min 24.5 s longer than the mean tropical year at J2000.0 (365.242 190 402 ephemeris days). [1]
In this frame of reference, Earth's rotation is close to constant, but the stars appear to rotate slowly with a period of about 25,800 years. It is also in this frame of reference that the tropical year (or solar year), the year related to Earth's seasons, represents one orbit of Earth around the Sun. The precise definition of a sidereal day is ...
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The traditional lunar year of 12 synodic months is about 354 days, approximately eleven days short of the solar year. Thus, every 2 to 3 years there is a discrepancy of 22 to 33 days, or a full synodic month. For example, if the winter solstice and the new moon coincide, it takes 19 tropical years for the coincidence to recur.
The Chinese, Coligny and Hebrew [a] lunisolar calendars track more or less the tropical year whereas the Buddhist and Hindu lunisolar calendars track the sidereal year. Therefore, the first three give an idea of the seasons whereas the last two give an idea of the position among the constellations of the full moon.
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