Sidereal day T1 is the period of axial rotation of the Earth relative to distant stars or, the same, the time interval between two successive upper culminations of the same star at some point on the Earth. Due to the orbital motion of the Earth, this period is slightly less than a solar day – one year contains one sidereal day more than solar days. The duration of a sidereal day is 23 hours 56 minutes 04 seconds or 0.99727 ordinary (solar) days.
Sidereal month T2 is the period of the Moon’s revolution around the Earth with respect to distant stars or the interval between two successive conjunctions of the Moon with a certain star. Similarly, due to the orbital motion of the Earth, the sidereal month is less than the period of changes in the lunar phases and is 27.3217 solar days.
Sidereal year T3 is the period of the Earth’s revolution around the Sun relative to distant stars or the interval between two successive conjunctions of the Sun with a star (without proper motion) near the ecliptic. This interval is somewhat different from the usual tropical year (the period between successive moments of the vernal equinox) due to the precession of the earth’s axis with a period of about 26,000 years. The vernal equinox is shifting relative to the stars in the same direction as the Sun, and the sidereal year is (1/26000) part longer than the tropical year. Its duration is 365.256 days. Based on this, we get the number of sidereal days (N1) and sidereal months (N2) in one sidereal year:
N = T3 / T1 = 366.26
N2 = T3 / T2 = 13.3687
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