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technically it's 365 1/4 days..
The motion of the Earth in its orbit (and therefore the apparent motion of the Sun among the stars) is not completely regular. This is due to gravitational perturbations by the Moon and planets. Therefore the time between successive passages of a specific point on the ecliptic will vary. Moreover, the speed of the Earth in its orbit varies (because the orbit is elliptical rather than circular). Furthermore, the position of the equinox on the orbit changes due to precession. As a consequence (explained below) the length of a tropical year depends on the specific point that you select on the ecliptic (as measured from, and moving together with, the equinox) that the Sun should return to.Therefore astronomers defined a mean tropical year, that is an average over all points on the ecliptic; it has a length of about 365.24219 SI days. Besides this, tropical years have been defined for specific points on the ecliptic: in particular the vernal equinox year, that start and ends when the Sun is at the vernal equinox. Its length is about 365.2424 days.An additional complication: We can measure time either in "days of fixed length": SI days of 86,400 SI seconds, defined by atomic clocks or dynamical days defined by the motion of the Moon and planets; or in mean solar days, defined by the rotation of the Earth with respect to the Sun. The duration of the mean solar day, as measured by clocks, is steadily getting longer (or conversely, clock days are steadily getting shorter, as measured by a sundial). One must use the mean solar day because the length of each solar day varies regularly during the year, as the equation of time shows.As explained at Error in Statement of Tropical Year, using the value of the "mean tropical year" to refer to the vernal equinox year defined above is, strictly speaking, an error. The words "tropical year" in astronomical jargon refer only to the mean tropical year, Newcomb-style, of 365.24219 SI days. The vernal equinox year of 365.2424 mean solar days is also important, because it is the basis of most solar calendars, but it is not the "tropical year" of modern astronomers.The number of mean solar days in a vernal equinox year has been oscillating between 365.2424 and 365.2423 for several millennia and will likely remain near 365.2424 for a few more. This long-term stability is pure chance, because in our era the slowdown of the rotation, the acceleration of the mean orbital motion, and the effect at the vernal equinox of rotation and shape changes in the Earth's orbit, happen to almost cancel out.In contrast, the mean tropical year, measured in SI days, is getting shorter. It was 365.2423 SI days at about AD 200, and is currently near 365.2422 SI days.
The sidereal year is the time taken for the Sun to return to the same position with respect to the stars of the celestial sphere. It is the orbital period of Earth, equal to 365.25636042 mean solar days (that is 366.25636042 earth rotations or sidereal days). (A true cycle will always compare two objects that differ mathematically by exactly 1). The sidereal year is 20 minutes and 24 seconds longer than the tropical year.The Sun and the stars cannot be seen at the same time; if one looks every dawn at the eastern sky, the last stars seen appearing are not always the same. In a week or two an upward shift can be noted. As an example, in July in the Northern Hemisphere, Orion cannot be seen in the dawn sky, but in August it becomes visible. In a year, all the constellations rotate through the entire sky.If one looks regularly at the sky before dawn, this motion is much more noticeable and easier to measure than the north/south shift of the sunrise point in the horizon, which defines the tropical year on which the Gregorian calendar is based. This is the reason many cultures started their year on the first day a particular special star, (Sirius, for instance), could be seen in the East at dawn. In Hesiod's Works and Days, the times of the year for sowing, harvest, and so on are given by reference to the first visibility of stars.Up to the time of Hipparchus, the years measured by the stars were thought to be exactly as long as the tropical years. In fact, sidereal years are very slightly longer than tropical years. The difference is caused by the precession of the equinoxes. One sidereal year is roughly equal to 1 + 1/26000 or 1.000039 tropical years.
*whoosh* Hear that? That's that post going right over my head.