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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) .
A tropical year is approximately 365.2422 days long and a synodic month is approximately 29.5306 days long, [4] so a tropical year is approximately 365.2422 / 29.5306 ≈ 12.36826 months long. Because 0.36826 is between 1 ⁄ 3 and 1 ⁄ 2, a typical year of 12 months needs to be supplemented with one intercalary or leap month every 2 to 3 years
Sidereal time vs solar time. Above left: a distant star (the small orange star) and the Sun are at culmination, on the local meridian m. Centre: only the distant star is at culmination (a mean sidereal day). Right: a few minutes later the Sun is on the local meridian again. A solar day is complete.
Because the number of days in the tropical year is not a whole number, a solar calendar must have a different number of days in different years. This may be handled, for example, by adding an extra day in leap years. The same applies to months in a lunar calendar and also the number of months in a year in a lunisolar calendar.
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