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The synodic day is distinguished from the sidereal day, which is one complete rotation in relation to distant stars [1] and is the basis of sidereal time. In the case of a tidally locked planet, the same side always faces its parent star, and its synodic day is infinite. Its sidereal day, however, is equal to its orbital period.
The period of the Moon's orbit as defined with respect to the celestial sphere of apparently fixed stars (the International Celestial Reference Frame; ICRF) is known as a sidereal month because it is the time it takes the Moon to return to a similar position among the stars (Latin: sidera): 27.321 661 days (27 d 7 h 43 min 11.6 s).
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 astronomy, the rotation period or spin period [1] of a celestial object (e.g., star, planet, moon, asteroid) has two definitions. The first one corresponds to the sidereal rotation period (or sidereal day), i.e., the time that the object takes to complete a full rotation around its axis relative to the background stars (inertial space).
Due to tidal locking, this equals the time that the Moon takes to complete one synodic orbit around Earth, a synodic lunar month, returning to the same lunar phase. The synodic period is about 29 + 1 ⁄ 2 Earth days, which is about 2.2 days longer than its sidereal period.
The fundamental unit of solar time is the day, based on the synodic rotation period. Traditionally, there are three types of time reckoning based on astronomical observations: apparent solar time and mean solar time (discussed in this article), and sidereal time, which is based on the apparent motions of stars other than the Sun. [1]
Viewed from the same location, a star seen at one position in the sky will be seen at the same position on another night at the same time of day (or night), if the day is defined as a sidereal day (also known as the sidereal rotation period). This is similar to how the time kept by a sundial can be used to find the location of the Sun
The mean calendar year of such a calendar approximates the sidereal year. Leaping from one lunation to another, but one Sidereal year is the period between two occurrences of the sun, as measured by the stars' solar calendar, which is derived from the Earth's orbit around the sun every 28 years. [3]