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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 ] At present, the rate of axial precession corresponds to a period of 25,772 years, [ 3 ] so sidereal year is longer than tropical year by 1,224.5 seconds (20 min 24.5 s, ~365.24219*86400/25772).
A year has about 365.24 solar days but 366.24 sidereal days. Therefore, there is one fewer solar day per year than there are sidereal days, similar to an observation of the coin rotation paradox. [5] This makes a sidereal day approximately 365.24 / 366.24 times the length of the 24-hour solar day.
It differs from the sidereal period because the object's semi-major axis typically advances slowly. Also, the tropical period of Earth (a tropical year) is the interval between two alignments of its rotational axis with the Sun, also viewed as two passages of the object at a right ascension of 0 hr.
This ‘sidereal’ year is slightly longer than the calendar year, and that extra 5 hours 48 minutes and 56 seconds needs to be accounted for somehow.” according to the Smithsonian Institute.
"Some simple math will show that over four years the difference between the calendar years and the sidereal year is not exactly 24 hours. Instead, it’s 23.262222 hours," the Smithsonian explains ...
The Gaussian year is the sidereal year for a planet of negligible mass (relative to the Sun) and unperturbed by other planets that is governed by the Gaussian gravitational constant. Such a planet would be slightly closer to the Sun than Earth's mean distance. Its length is: 365.256 8983 days (365 d 6 h 9 min 56 s).
Erasmus Reinhold used Copernicus' theory to compute the Prutenic Tables in 1551, and gave a tropical year length of 365 solar days, 5 hours, 55 minutes, 58 seconds (365.24720 days), based on the length of a sidereal year and the presumed rate of precession. This was actually less accurate than the earlier value of the Alfonsine Tables.
Precession causes the stars to change their longitude slightly each year, so the sidereal year is longer than the tropical year. Using observations of the equinoxes and solstices, Hipparchus found that the length of the tropical year was 365+1/4−1/300 days, or 365.24667 days (Evans 1998, p. 209).