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length of solar day = length of sidereal day / 1 − length of sidereal day / orbital period . When calculating the formula for a retrograde rotation, the operator of the denominator will be a plus sign (put another way, in the original formula the length of the sidereal day must be treated as negative).
The formal lunar day is therefore the time of a full lunar day-night cycle. 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 29.53 Earth days, which is about 2.2 days longer than its sidereal period.
27.321661 days [7] (equal to sidereal orbital period due to spin-orbit locking, a sidereal lunar month) 27 d 7 h 43 m 11.5 s: 29.530588 days [7] (equal to synodic orbital period, due to spin-orbit locking, a synodic lunar month) none (due to spin-orbit locking) Mars: 1.02595675 days [3] 1 d 0 h 37 m 22.663 s: 1.02749125 [8] days: Ceres: 0.37809 ...
W1 is the ecliptic longitude of the Moon w.r.t. the fixed ICRS equinox: its period is the sidereal month. If we add the rate of precession to the sidereal angular velocity, we get the angular velocity w.r.t. the Equinox of the Date: its period is the tropical month (which is rarely used). l is the mean anomaly: its period is the anomalistic month.
A synodic day (or synodic rotation period or solar day) is the period for a celestial object to rotate once in relation to the star it is orbiting, and is the basis of solar time. 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.
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).
The exact length has been variously defined as either that of a solar day or of a sidereal day. [ 1 ] [ 2 ] [ 3 ] Astronomical days were historically used by astronomers (in contrast most commonly to solar days), but since the Industrial Revolution this usage has generally fallen out of favor, in order to avoid confusion with more conventional ...
Such an observer will see the star transit at the zenith, once every day (strictly speaking sidereal day). At the time of the March equinox , Earth's orbit carries the observer in a southwards direction, and the star's apparent declination is therefore displaced to the south by an angle of κ {\displaystyle \kappa } .