TheInfoList

In
astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses mathematics, phys ...
, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its
orbit In celestial mechanics, an orbit is the curved trajectory of an physical body, object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an satellite, artificial satellite around an object or po ...

al axis, or, equivalently, the angle between its
equator The Equator is a circle of latitude, about in circumference, that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the N ...

ial plane and
orbital plane The orbital plane of a revolving body is the geometric plane in which its orbit In physics, an orbit is the gravitationally curved trajectory of an physical body, object, such as the trajectory of a planet around a star or a natural satel ...
. It differs from
orbital inclination Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a Plane of reference, reference plane and the orbital plane or Axis of rotation, axis of direction of the orbiting object. ...
. At an obliquity of 0 degrees, the two axes point in the same direction; i.e., the rotational axis is perpendicular to the orbital plane. Earth's obliquity oscillates between 22.1 and 24.5 degrees on a 41,000-year cycle. Based on a continuously updated formula (here Laskar, 1986, though since 2006 the IMCCE and the IAU recommend the P03 model), Earth's mean obliquity (without taking into account the nutation in obliquity) is currently about and decreasing; according to P03 astronomical model, its value (without taking into account the nutation in obliquity) was 23° 26' 11,570" (23.4365472133°) on January 1st 2021, 0 TT. Over the course of an
orbital period The orbital period is the time a given astronomical object takes to complete one orbit around another object, and applies in astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of th ...
, the obliquity usually does not change considerably, and the orientation of the axis remains the same relative to the of
stars A star is an astronomical object consisting of a luminous spheroid of plasma held together by its own gravity. The nearest star to Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. ...
. This causes one pole to be directed more toward the
Sun The Sun is the star A star is an astronomical object consisting of a luminous spheroid of plasma (physics), plasma held together by its own gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many othe ...

on one side of the
orbit In celestial mechanics, an orbit is the curved trajectory of an physical body, object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an satellite, artificial satellite around an object or po ...

, and the other pole on the other side—the cause of the
season A season is a division of the year based on changes in weather Weather is the state of the atmosphere An atmosphere (from the greek words ἀτμός ''(atmos)'', meaning 'vapour', and σφαῖρα ''(sphaira)'', meaning 'ball' or ...

s on
Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remaining 70.8% is Water distribution on Earth, covered wi ...

.

# Standards

There are two standard methods of specifying tilt. The
International Astronomical Union The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) is a Non-governmental organization, nongovernmental organisation with the objective of advancing astronomy in all aspects, including promoting ...
(IAU) defines the ''north pole'' of a planet as that which lies on Earth's north side of the
invariable plane The invariable plane of a planetary system, also called Laplace's invariable plane, is the plane passing through its barycenter (center of mass) perpendicular to its angular momentum In physics, angular momentum (rarely, moment of momentum or ...
of the
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...

; under this system,
Venus Venus is the second planet from the Sun. It is named after the Venus (mythology), Roman goddess of love and beauty. As List of brightest natural objects in the sky, the brightest natural object in Earth's night sky after the Moon, Venus can ...

is tilted 3° and rotates retrograde, opposite that of most of the other planets. The IAU also uses the
right-hand rule In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities an ...
to define a ''positive pole'' for the purpose of determining orientation. Using this convention, Venus is tilted 177° ("upside down").

# Earth

Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remaining 70.8% is Water distribution on Earth, covered wi ...

's
orbital plane The orbital plane of a revolving body is the geometric plane in which its orbit In physics, an orbit is the gravitationally curved trajectory of an physical body, object, such as the trajectory of a planet around a star or a natural satel ...

is known as the
ecliptic The ecliptic is the plane (geometry), plane of Earth's orbit around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the ...

plane, and Earth's tilt is known to astronomers as the ''obliquity of the ecliptic'', being the angle between the ecliptic and the
celestial equator The celestial equator is the great circle A great circle, also known as an orthodrome, of a sphere of a sphere A sphere (from Greek language, Greek —, "globe, ball") is a Geometry, geometrical object in solid geometry, three-dimensiona ...
on the
celestial sphere In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses ma ...

. It is denoted by the
Greek letter The Greek alphabet has been used to write the Greek language Greek (modern , romanized: ''Elliniká'', Ancient Greek, ancient , ''Hellēnikḗ'') is an independent branch of the Indo-European languages, Indo-European family of languages, nat ...
''''. Earth currently has an axial tilt of about 23.44°. This value remains about the same relative to a stationary orbital plane throughout the cycles of
axial precession In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In particular, it can refer to the gradual shift in the orientation of Earth's axis of rotation in ...
. But the ecliptic (''i.e''., Earth's orbit) moves due to planetary perturbations, and the obliquity of the ecliptic is not a fixed quantity. At present, it is decreasing at a rate of about 46.8″ per
century A century is a period of 100 years. Centuries are numbered names of numbers in English#Ordinal numbers, ordinally in English and many other languages. The word ''century'' comes from the Latin ''centum'', meaning ''one hundred''. ''Century'' is s ...

''(see details in
Short term Short may refer to: Places * Short (crater) Short is a Lunar craters, lunar impact crater that is located in the southern regions of the Moon, on the near side. It lies just to the south of the larger, prominent crater Moretus (crater), Moretu ...
below)''.

## History

Earth's obliquity may have been reasonably accurately measured as early as 1100 BC in India and China. The ancient Greeks had good measurements of the obliquity since about 350 BC, when
Pytheas Pytheas of Massalia (; Ancient Greek: Πυθέας ὁ Μασσαλιώτης ''Pythéas ho Massaliōtēs''; Latin: ''Pytheas Massiliensis''; born 350 BC, 320–306 BC) was a Greeks, Greek List of Graeco-Roman geographers, geographer, explore ...
of Marseilles measured the shadow of a
gnomon A gnomon (, from Greek , ''gnōmōn'', literally: "one that knows or examines") is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields. History A painted stick dating from 2 ...

Al-Mamun Abu al-Abbas Abdallah ibn Harun al-Rashid ( ar, أبو العباس عبد الله بن هارون الرشيد, Abū al-ʿAbbās ʿAbd Allāh ibn Hārūn ar-Rashīd; 14 September 786 – 9 August 833), better known by his regnal name al-Ma'mu ...
of Baghdad directed his astronomers to measure the obliquity, and the result was used in the Arab world for many years. In 1437,
Ulugh Beg Mīrzā Muhammad Tāraghay bin Shāhrukh ( chg, میرزا محمد طارق بن شاہ رخ, fa, میرزا محمد تراغای بن شاہ رخ), better known as Ulugh Beg () (22 March 1394 – 27 October 1449), was a Timurid sultan Su ...
determined the Earth's axial tilt as 23°30′17″ (23.5047°). It was widely believed, during the
Middle Ages In the history of Europe The history of Europe concerns itself with the discovery and collection, the study, organization and presentation and the interpretation of past events and affairs of the people of Europe since the beginning of ...
, that both precession and Earth's obliquity oscillated around a mean value, with a period of 672 years, an idea known as '' trepidation'' of the equinoxes. Perhaps the first to realize this was incorrect (during historic time) was
Ibn al-Shatir ʿAbu al-Ḥasan Alāʾ al‐Dīn ʿAlī ibn Ibrāhīm al-Ansari known as Ibn al-Shatir or Ibn ash-Shatir ( ar, ابن الشاطر; 1304–1375) was an Arab Astronomy, astronomer, mathematician and engineer. He worked as ''muwaqqit'' (موقت, r ...
in the fourteenth century and the first to realize that the obliquity is decreasing at a relatively constant rate was in 1538. The first accurate, modern, western observations of the obliquity were probably those of
Tycho Brahe Tycho Brahe ( ; born Tyge Ottesen Brahe; 14 December 154624 October 1601) was a Danish , known for his accurate and comprehensive astronomical observations. He was born in , which became part of Sweden in the next century. Tycho was well known ...

from
Denmark Denmark ( da, Danmark, ) is a Nordic country The Nordic countries, or the Nordics, are a geographical and cultural region In geography, regions are areas that are broadly divided by physical characteristics ( physical geography), hu ...

, about 1584, although observations by several others, including
al-Ma'mun Abu al-Abbas Abdallah ibn Harun al-Rashid ( ar, أبو العباس عبد الله بن هارون الرشيد, Abū al-ʿAbbās ʿAbd Allāh ibn Hārūn ar-Rashīd; 14 September 786 – 9 August 833), better known by his regnal name al-Ma'mu ...
, al-Tusi, Purbach,
Regiomontanus Johannes Müller von Königsberg (6 June 1436 – 6 July 1476), better known as Regiomontanus (), was a mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek, Greek: ) inc ...

, and Walther, could have provided similar information.

## Seasons

Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remaining 70.8% is Water distribution on Earth, covered wi ...

's axis remains tilted in the same direction with reference to the background stars throughout a year (regardless of where it is in its
orbit In celestial mechanics, an orbit is the curved trajectory of an physical body, object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an satellite, artificial satellite around an object or po ...

). This means that one pole (and the associated hemisphere of Earth) will be directed away from the Sun at one side of the orbit, and half an orbit later (half a year later) this pole will be directed towards the Sun. This is the cause of Earth's
season A season is a division of the year based on changes in weather Weather is the state of the atmosphere An atmosphere (from the greek words ἀτμός ''(atmos)'', meaning 'vapour', and σφαῖρα ''(sphaira)'', meaning 'ball' or ...

s.
Summer Summer is the hottest of the four temperate In geography Geography (from Greek: , ''geographia'', literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and phenom ...

occurs in the
Northern hemisphere The Northern Hemisphere is the half of Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remain ...

when the north pole is directed toward the Sun. Variations in Earth's axial tilt can influence the seasons and is likely a factor in long-term
climatic change ''Climatic Change'' is a biweekly Peer review, peer-reviewed scientific journal published by Springer Science+Business Media covering cross-disciplinary work on all aspects of climate change and variability. It was established in 1978 and the editor ...
''(also see
Milankovitch cycles Milankovitch cycles describe the collective effects of changes in the 's movements on its over thousands of years. The term is named for n and . In the 1920s, he hypothesized that variations in , , and resulted in cyclical variation in the r ...

)''.

## Oscillation

### Short term

The exact angular value of the obliquity is found by observation of the motions of Earth and
planets A planet is an astronomical body orbit In physics, an orbit is the gravitationally curved trajectory of an physical body, object, such as the trajectory of a planet around a star or a natural satellite around a planet. Normally, orbit r ...

over many years. Astronomers produce new fundamental ephemerides as the accuracy of
observation Observation is the active acquisition of information Information can be thought of as the resolution of uncertainty; it answers the question of "What an entity is" and thus defines both its essence and the nature of its characteristics. Th ...
improves and as the understanding of the
dynamics Dynamics (from Greek language, Greek δυναμικός ''dynamikos'' "powerful", from δύναμις ''dynamis'' "power (disambiguation), power") or dynamic may refer to: Physics and engineering * Dynamics (mechanics) ** Aerodynamics, the study o ...
increases, and from these ephemerides various astronomical values, including the obliquity, are derived. Annual
almanac An almanac (also spelled ''almanack'' and ''almanach'') is an annual publication Annual publications, more often simply called annuals, are periodical publications appearing regularly once per year."Annuals", in ''Encyclopedia of library and info ...
s are published listing the derived values and methods of use. Until 1983, the
Astronomical Almanac ''The Astronomical Almanac''The ''Astronomical Almanac'' for the Year 2015, (United States Naval Observatory/Nautical Almanac Office, 2014) . is an almanac An almanac (also spelled ''almanack'' and ''almanach'') is an listing a set of current, ...
's angular value of the mean obliquity for any date was calculated based on the work of Newcomb, who analyzed positions of the planets until about 1895: : where is the obliquity and is tropical centuries from B1900.0 to the date in question. From 1984, the Jet Propulsion Laboratory's DE series of computer-generated ephemerides took over as the
fundamental ephemerisA fundamental ephemeris of the Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual ...
of the
Astronomical Almanac ''The Astronomical Almanac''The ''Astronomical Almanac'' for the Year 2015, (United States Naval Observatory/Nautical Almanac Office, 2014) . is an almanac An almanac (also spelled ''almanack'' and ''almanach'') is an listing a set of current, ...
. Obliquity based on DE200, which analyzed observations from 1911 to 1979, was calculated: : where hereafter is Julian centuries from
J2000.0 In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses ma ...
. JPL's fundamental ephemerides have been continually updated. For instance, according to IAU resolution in 2006 in favor of the P03 astronomical model, the ''Astronomical Almanac'' for 2010 specifies:''Astronomical Almanac 2010'', p. B52 : These expressions for the obliquity are intended for high precision over a relatively short time span, perhaps several centuries. J. Laskar computed an expression to order good to 0.02″ over 1000 years and several
arcseconds A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol ', is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The n ...
over 10,000 years. : where here is multiples of 10,000 Julian years from
J2000.0 In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses ma ...
.See table 8 and eq. 35 in and erratum to article Units in article are arcseconds, which may be more convenient. These expressions are for the so-called ''mean'' obliquity, that is, the obliquity free from short-term variations. Periodic motions of the Moon and of Earth in its orbit cause much smaller (9.2
arcseconds A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol ', is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The n ...
) short-period (about 18.6 years) oscillations of the rotation axis of Earth, known as
nutation Nutation (from Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Roman ...
, which add a periodic component to Earth's obliquity. The ''true'' or instantaneous obliquity includes this nutation.

### Long term

Using
numerical methods (c. 1800–1600 BC) with annotations. The approximation of the square root of 2 is four sexagesimal Sexagesimal, also known as base 60 or sexagenary, is a numeral system with 60 (number), sixty as its radix, base. It originated with the ancient ...
to simulate
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...

behavior, long-term changes in Earth's
orbit In celestial mechanics, an orbit is the curved trajectory of an physical body, object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an satellite, artificial satellite around an object or po ...

, and hence its obliquity, have been investigated over a period of several million years. For the past 5 million years, Earth's obliquity has varied between and , with a mean period of 41,040 years. This cycle is a combination of precession and the largest term in the motion of the
ecliptic The ecliptic is the plane (geometry), plane of Earth's orbit around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the ...

. For the next 1 million years, the cycle will carry the obliquity between and . The
Moon The Moon is Earth's only natural satellite. At about one-quarter the diameter of Earth (comparable to the width of Australia (continent), Australia), it is the largest natural satellite in the Solar System relative to the size of its plane ...

has a stabilizing effect on Earth's obliquity. Frequency map analysis conducted in 1993 suggested that, in the absence of the Moon, the obliquity could change rapidly due to
orbital resonance . Conjunctions ''Conjunctions'' is a biannual American literature, American literary journal based at Bard College. It was founded in 1981 and is currently edited by Bradford Morrow. Morrow received the PEN/Nora Magid Award for Magazine Editing ...
s and chaotic behavior of the Solar System, reaching as high as 90° in as little as a few million years ''(also see
Orbit of the Moon The s in the direction and completes one relative to the and the in about 27.32 days (a and ) and one revolution relative to the in about 29.53 days (a ). Earth and the Moon orbit about their (common ), which lies about from Earth's ce ...
)''. However, more recent numerical simulations made in 2011 indicated that even in the absence of the Moon, Earth's obliquity might not be quite so unstable; varying only by about 20–25°. To resolve this contradiction, diffusion rate of obliquity has been calculated, and it was found that it takes more than billions of years for Earth's obliquity to reach near 90°. The Moon's stabilizing effect will continue for less than 2 billion years. As the Moon continues to recede from Earth due to
tidal acceleration and the Moon The Moon is Earth's only natural satellite. At about one-quarter the diameter of Earth (comparable to the width of Australia (continent), Australia), it is the largest natural satellite in the Solar System relative to the size ...
, resonances may occur which will cause large oscillations of the obliquity.

# Solar System bodies

All four of the innermost, rocky planets of the
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...

may have had large variations of their obliquity in the past. Since obliquity is the angle between the axis of rotation and the direction perpendicular to the orbital plane, it changes as the orbital plane changes due to the influence of other planets. But the axis of rotation can also move (
axial precession In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In particular, it can refer to the gradual shift in the orientation of Earth's axis of rotation in ...
), due to torque exerted by the sun on a planet's equatorial bulge. Like Earth, all of the rocky planets show axial precession. If the precession rate were very fast the obliquity would actually remain fairly constant even as the orbital plane changes. The rate varies due to tidal dissipation and
core Core or cores may refer to: Science and technology * Core (anatomy) In common parlance, the core of the body is broadly considered to be the torso. Functional movements are highly dependent on this part of the body, and lack of core muscular dev ...
-
mantle Mantle may refer to: *Mantle (geology) A mantle is a layer inside a planetary body A planet is an astronomical body Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a n ...
interaction, among other things. When a planet's precession rate approaches certain values,
orbital resonance . Conjunctions ''Conjunctions'' is a biannual American literature, American literary journal based at Bard College. It was founded in 1981 and is currently edited by Bradford Morrow. Morrow received the PEN/Nora Magid Award for Magazine Editing ...
s may cause large changes in obliquity. The amplitude of the contribution having one of the resonant rates is divided by the difference between the resonant rate and the precession rate, so it becomes large when the two are similar.
Mercury Mercury usually refers to: * Mercury (planet) Mercury is the smallest planet in the Solar System and the closest to the Sun. Its orbit around the Sun takes 87.97 Earth days, the shortest of all the Sun's planets. It is named after the Roman g ...

and
Venus Venus is the second planet from the Sun. It is named after the Venus (mythology), Roman goddess of love and beauty. As List of brightest natural objects in the sky, the brightest natural object in Earth's night sky after the Moon, Venus can ...

have most likely been stabilized by the tidal dissipation of the Sun. Earth was stabilized by the Moon, as mentioned above, but before its
formation Formation may refer to: Linguistics * Back-formation, the process of creating a new lexeme by removing or affixes * Word formation, the creation of a new word by adding affixes Mathematics and science * Cave formation or speleothem, a secondary m ...

, Earth, too, could have passed through times of instability.
Mars Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, being larger than only Mercury (planet), Mercury. In English, Mars carries the name of the Mars (mythology), Roman god of war and is often referred to ...

's obliquity is quite variable over millions of years and may be in a chaotic state; it varies as much as 0° to 60° over some millions of years, depending on perturbations of the planets. Some authors dispute that Mars's obliquity is chaotic, and show that tidal dissipation and viscous core-mantle coupling are adequate for it to have reached a fully damped state, similar to Mercury and Venus. The occasional shifts in the axial tilt of Mars have been suggested as an explanation for the appearance and disappearance of rivers and lakes over the course of the existence of Mars. A shift could cause a burst of methane into the atmosphere, causing warming, but then the methane would be destroyed and the climate would become arid again. The obliquities of the outer planets are considered relatively stable.

# Extrasolar planets

The stellar obliquity , i.e. the axial tilt of a star with respect to the orbital plane of one of its planets, has been determined for only a few systems. But for 49 stars as of today, the sky-projected spin-orbit misalignment has been observed, which serves as a lower limit to . Most of these measurements rely on the
Rossiter–McLaughlin effect Image:Rossiter-McLaughlin effect.svg, frame, center, The viewer is situated at the bottom. Light from the anticlockwise-rotating star is blue-shifted on the approaching side, and red-shifted on the receding side. As the planet passes in front of th ...
. So far, it has not been possible to constrain the obliquity of an extrasolar planet. But the rotational flattening of the planet and the entourage of moons and/or rings, which are traceable with high-precision photometry, e.g. by the space-based
Kepler space telescope The Kepler space telescope is a deactivated space telescope A space telescope or space observatory is a telescope located in outer space Outer space is the expanse that exists beyond Earth and between astronomical object, celestial b ...
, could provide access to in the near future. Astrophysicists have applied tidal theories to predict the obliquity of
extrasolar planets An exoplanet or extrasolar planet is a planet A planet is an astronomical body orbiting a star or Stellar evolution#Stellar remnants, stellar remnant that is massive enough to be Hydrostatic equilibrium, rounded by its own gravity, is not ma ...
. It has been shown that the obliquities of exoplanets in the
habitable zone In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses m ...

around low-mass stars tend to be eroded in less than 109 years, which means that they would not have seasons as Earth has.

*
Milankovitch cycles Milankovitch cycles describe the collective effects of changes in the 's movements on its over thousands of years. The term is named for n and . In the 1920s, he hypothesized that variations in , , and resulted in cyclical variation in the r ...

*
Polar motion Polar motion of the Earth is the motion of the Earth's rotational axis relative to its crust. This is measured with respect to a reference frame in which the solid Earth is fixed (a so-called ''Earth-centered, Earth-fixed'' or ECEF ECEF (ac ...

*
Rotation around a fixed axis Rotation around a fixed axis is a special case of al motion. The fixed- hypothesis excludes the possibility of an axis changing its orientation and cannot describe such phenomena as or . According to , simultaneous rotation along a number of s ...
*
True polar wander True polar wander is a solid-body rotation of a planet or moon with respect to its spin axis, causing the geographic locations of the north North is one of the four compass points or cardinal directions. It is the opposite of south and is pe ...