In astronomy, the rotation period of a celestial object is the time that it takes to complete one revolution around its axis of rotation relative to the background stars. It differs from the planet's solar day, which includes an extra fractional rotation needed to accommodate the portion of the planet's orbital period during one day.
For solid objects, such as rocky planets and asteroids, the rotation period is a single value. For gaseous/fluid bodies, such as stars and gas giants, the period of rotation varies from the equator to the poles due to a phenomenon called differential rotation. Typically, the stated rotation period for a gas giant (Jupiter, Saturn, Uranus, Neptune) is its internal rotation period, as determined from the rotation of the planet's magnetic field. For objects that are not spherically symmetrical, the rotation period is, in general, not fixed, even in the absence of gravitational or tidal forces. This is because, although the rotation axis is fixed in space (by the conservation of angular momentum), it is not necessarily fixed in the body of the object itself. As a result of this, the moment of inertia of the object around the rotation axis can vary, and hence the rate of rotation can vary (because the product of the moment of inertia and the rate of rotation is equal to the angular momentum, which is fixed). Hyperion, a satellite of Saturn, exhibits this behaviour, and its rotation period is described as chaotic.
Earth's rotation period relative to the Sun (its mean solar day) consists of 86,400 seconds of mean solar time, by definition. Each of these seconds is slightly longer than an SI second because Earth's solar day is now slightly longer than it was during the 19th century, due to tidal deceleration. The mean solar second between 1750 and 1892 was chosen in 1895 by Simon Newcomb as the independent unit of time in his Tables of the Sun. These tables were used to calculate the world's ephemerides between 1900 and 1983, so this second became known as the ephemeris second. The SI second was made equal to the ephemeris second in 1967.
Earth's rotation period relative to the fixed stars, called its stellar day by the International Earth Rotation and Reference Systems Service (IERS), is 86164.098 903 691 seconds of mean solar time (UT1) (23h 56m 4.098 903 691s). Earth's rotation period relative to the precessing or moving mean vernal equinox, its sidereal day, is 86164.090 530 832 88 seconds of mean solar time (UT1) (23h 56m 4.090 530 832 88s). Thus the sidereal day is shorter than the stellar day by about 8.4 ms. The length of the mean solar day in SI seconds is available from the IERS for the periods 1623–2005 and 1962–2005. Recently (1999–2005) the average annual length of the mean solar day in excess of 86400 SI seconds has varied between 0.3 ms and 1 ms, which must be added to both the stellar and sidereal days given in mean solar time above to obtain their lengths in SI seconds.