Astronomical nutation in the context of "Retrograde and prograde motion"

The north and south celestial poles are the two points in the sky where Earth's axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently directly overhead to observers at Earth's North Pole and South Pole, respectively. As Earth spins on its axis, the two celestial poles remain fixed in the sky, and all other celestial points appear to rotate around them, completing one circuit per day (strictly, per sidereal day).

The celestial poles are also the poles of the celestial equatorial coordinate system, meaning they have declinations of +90 degrees and −90 degrees (for the north and south celestial poles, respectively). Despite their apparently fixed positions, the celestial poles in the long term do not actually remain permanently fixed against the background of the stars. Because of a phenomenon known as the precession of the equinoxes, the poles trace out circles on the celestial sphere, with a period of about 25,700 years. The Earth's axis is also subject to other complex motions which cause the celestial poles to shift slightly over cycles of varying lengths (see nutation, polar motion and axial tilt). Finally, over very long periods the positions of the stars themselves change, because of the stars' proper motions. To take into account such movement, celestial pole definitions come with an epoch to specify the date of the rotation axis; J2000.0 is the current standard.

In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In the absence of precession, the astronomical body's orbit would show axial parallelism. In particular, axial precession can refer to the gradual shift in the orientation of Earth's axis of rotation in a cycle of approximately 26,000 years. This is similar to the precession of a spinning top, with the axis tracing out a pair of cones joined at their apices. The term "precession" typically refers only to this largest part of the motion; other changes in the alignment of Earth's axis—nutation and polar motion—are much smaller in magnitude.

Earth's precession was historically called the precession of the equinoxes, because the equinoxes moved westward along the ecliptic relative to the fixed stars, opposite to the yearly motion of the Sun along the ecliptic. Historically, the discovery of the precession of the equinoxes is usually attributed in the West to the 2nd-century-BC astronomer Hipparchus. With improvements in the ability to calculate the gravitational force between planets during the first half of the nineteenth century, it was recognized that the ecliptic itself moved slightly, which was named planetary precession, as early as 1863, while the dominant component was named lunisolar precession. Their combination was named general precession, instead of precession of the equinoxes.

The Antarctic Circle is the most southerly of the five major circles of latitude that mark maps of Earth. The region south of this circle is known as the Antarctic, and the zone immediately to the north is called the Southern Temperate Zone. South of the Antarctic Circle, the Sun is above the horizon for 24 continuous hours at least once per year (and therefore visible at solar midnight) and the centre of the Sun (ignoring refraction) is below the horizon for 24 continuous hours at least once per year (and therefore not visible at solar noon); this is also true within the Arctic Circle, the Antarctic Circle’s counterpart in the Northern Hemisphere.

The position of the Antarctic Circle is not fixed and, not taking account of the nutation, currently runs 66°33′50.7″ south of the Equator. This figure may be slightly inaccurate because it does not allow for the effects of astronomical nutation, which can be up to 10″. Its latitude depends on the Earth's axial tilt, which fluctuates within a margin of more than 2° over a 41,000-year period, due to tidal forces resulting from the orbit of the Moon. Consequently, the Antarctic Circle is currently drifting southwards at a speed of about 14.5 m (48 ft) per year.

A polar circle is a geographic term for a conditional circular line (arc) referring either to the Arctic Circle or the Antarctic Circle. These are two of the keynote circles of latitude (parallels). On Earth, the Arctic Circle is currently drifting northwards at a speed of about 14.5 m per year and is now at a mean latitude (i.e. without taking into account the astronomical nutation) of 66°33′50.7″ N; the Antarctic Circle is currently drifting southwards at a speed of about 14.5 m per year and is now at a mean latitude of 66°33′50.7″ S. Polar circles are often equated with polar regions of Earth. Due to their inherent climate environment, the bulk of the Arctic Circle, much of which is sea, is sparsely settled whereas this applies to all of Antarctica which is mainly land and sheltered ice shelves.

If Earth had no atmosphere, then both polar circles (arcs) would see at least a day a year when the center of the Sun is continuously above the horizon and at least a day a year when it is always below the horizon – a polar day and a polar night as is the case for longer, within the circles. Up to and including the associated poles (North and South), known geographically as the frigid zones, such duration extends up to half of the year, namely, close to the poles. Instead, atmospheric refraction and the Sun's light reaching the planet as an extended object rather than a point source means that just within each circle the Earth's surface does not experience any proper polar night, 24 hours where the sun does not rise. By these same two factors, just outward of each circle still experiences a polar day (a day in which the sun does not fully set).

The Chandler wobble or Chandler variation of latitude is a small deviation in the Earth's axis of rotation relative to the solid earth, which was discovered by and named after American astronomer Seth Carlo Chandler in 1891. It amounts to change of about 9 metres (30 ft) in the point at which the axis intersects the Earth's surface and has a period of 433 days. This wobble, which is an astronomical nutation, combines with another wobble with a period of six years, so that the total polar motion varies with a period of about 7 years.

The Chandler wobble is an example of the kind of motion that can occur for a freely rotating object that is not a sphere; this is called a free nutation. Somewhat confusingly, the direction of the Earth's rotation axis relative to the stars also varies with different periods, and these motions—caused by the tidal forces of the Moon and Sun—are also called nutations, except for the slowest, which are precessions of the equinoxes.