Axial tilt

In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, or, equivalently, the angle between its equatorial plane and orbital plane.[1] It differs from orbital inclination.

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[2] on a 41,000-year cycle; Earth's mean obliquity is currently 23°26′12.5″ (or 23.4368°) and decreasing.

Over the course of an orbital period, the obliquity usually does not change considerably, and the orientation of the axis remains the same relative to the background of stars. This causes one pole to be directed more toward the Sun on one side of the orbit, and the other pole on the other side—the cause of the seasons on Earth.


The axial tilt of Earth, Uranus, and Venus

The positive pole of a planet is defined by the right-hand rule: if the fingers of the right hand are curled in the direction of the rotation then the thumb points to the positive pole. The axial tilt is defined as the angle between the direction of the positive pole and the normal to the orbital plane. The angles for Earth, Uranus and Venus are approximately 23°, 97°, and 177° respectively.

There are two standard methods of specifying tilt. The International Astronomical Union (IAU) defines the north pole of a planet as that which lies on Earth's north side of the invariable plane of the Solar System;[3] under this system, Venus is tilted 3° and spins retrograde, opposite that of most of the other planets.[4][5]

The IAU also uses the right-hand rule to define a positive pole[6] for the purpose of determining orientation. Using this convention, Venus is tilted 177° ("upside down").


Earth's axial tilt (obliquity) is currently about 23.4°.

Earth's orbital plane is known as the ecliptic 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 on the celestial sphere.[7] It is denoted by the Greek letter ε.

Earth currently has an axial tilt of about 23.4°.[8] This value remains about the same relative to a stationary orbital plane throughout the cycles of axial precession.[9] 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 47″ per century (see details in Short term below).


Earth's obliquity may have been reasonably accurately measured as early as 1100 BC in India and China.[10] The ancient Greeks had good measurements of the obliquity since about 350 BC, when Pytheas of Marseilles measured the shadow of a gnomon at the summer solstice.[11] About 830 AD, the Caliph Al-Mamun of Baghdad directed his astronomers to measure the obliquity, and the result was used in the Arab world for many years.[12] In 1437, Ulugh Beg determined the Earth's axial tilt as 23°30′17″ (23.5047°).[13]

It was widely believed, during the Middle Ages, 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 in the fourteenth century[14] and the first to realize that the obliquity is decreasing at a relatively constant rate was Fracastoro in 1538.[15] The first accurate, modern, western observations of the obliquity were probably those of Tycho Brahe from Denmark, about 1584,[16] although observations by several others, including al-Ma'mun, al-Tusi,[17] Purbach, Regiomontanus, and Walther, could have provided similar information.


Earth'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). 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 seasons. Summer occurs in the Northern hemisphere 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 climate change (also see Milankovitch cycles).

Axial tilt vs tropical and polar circles
Relationship between Earth's axial tilt (ε) to the tropical and polar circles


Short term

Obliquity of the ecliptic laskar
Obliquity of the ecliptic for 20,000 years, from Laskar (1986). The red point represents the year 2000.

The exact angular value of the obliquity is found by observation of the motions of Earth and planets over many years. Astronomers produce new fundamental ephemerides as the accuracy of observation improves and as the understanding of the dynamics increases, and from these ephemerides various astronomical values, including the obliquity, are derived.

Annual almanacs are published listing the derived values and methods of use. Until 1983, the Astronomical Almanac'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:

ε = 23° 27′ 8.26″ − 46.845″ T − 0.0059″ T2 + 0.00181T3

where ε is the obliquity and T is tropical centuries from B1900.0 to the date in question.[18]

From 1984, the Jet Propulsion Laboratory's DE series of computer-generated ephemerides took over as the fundamental ephemeris of the Astronomical Almanac. Obliquity based on DE200, which analyzed observations from 1911 to 1979, was calculated:

ε = 23° 26′ 21.448″ − 46.8150″ T − 0.00059″ T2 + 0.001813T3

where hereafter T is Julian centuries from J2000.0.[19]

JPL's fundamental ephemerides have been continually updated. For instance, the Astronomical Almanac for 2010 specifies:[8]

ε = 23° 26′ 21.406″ − 46.836769T0.0001831T2 + 0.00200340T3 − 5.76″ × 10−7 T4 − 4.34″ × 10−8 T5

These expressions for the obliquity are intended for high precision over a relatively short time span, perhaps ± several centuries.[20] J. Laskar computed an expression to order T10 good to 0.02″ over 1000 years and several arcseconds over 10,000 years.

ε = 23° 26′ 21.448″ − 4680.93″ t − 1.55″ t2 + 1999.25″ t3 − 51.38″ t4 − 249.67″ t5 − 39.05″ t6 + 7.12″ t7 + 27.87″ t8 + 5.79″ t9 + 2.45″ t10

where here t is multiples of 10,000 Julian years from J2000.0.[21]

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) short-period (about 18.6 years) oscillations of the rotation axis of Earth, known as nutation, which add a periodic component to Earth's obliquity.[22][23] The true or instantaneous obliquity includes this nutation.[24]

Long term

Using numerical methods to simulate Solar System behavior, long-term changes in Earth's orbit, 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 22° 2′ 33″ and 24° 30′ 16″, 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. For the next 1 million years, the cycle will carry the obliquity between 22° 13′ 44″ and 24° 20′ 50″.[25]

The Moon has a stabilizing effect on Earth's obliquity. Frequency map analysis conducted in 1993 suggested that, in the absence of the Moon, the obliquity can change rapidly due to orbital resonances 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).[26][27] However, more recent numerical simulations[28] 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°.[29] 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, resonances may occur which will cause large oscillations of the obliquity.[30]

Long-term obliquity of the ecliptic. Left: for the past 5 million years; note that the obliquity varies only from about 22.0° to 24.5°. Right: for the next 1 million years; note the approx. 41,000-year period of variation. In both graphs, the red point represents the year 1850. (Source: Berger, 1976).

Obliquity berger -5000000 to 0
Obliquity berger 0 to 1000000

Solar System bodies

All four of the innermost, rocky planets of the Solar System 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), 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.[31] The rate varies due to tidal dissipation and core-mantle interaction, among other things. When a planet's precession rate approaches certain values, orbital resonances 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.[31] Mercury and Venus have most likely been stabilized by the tidal dissipation of the Sun. Earth was stabilized by the Moon, as mentioned above, but before its capture, Earth, too, could have passed through times of instability. Mars'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.[26][32] 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.[4][33] 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.[34][35]

The obliquities of the outer planets are considered relatively stable.

Axis and rotation of selected Solar System bodies
Body NASA, J2000.0[36] IAU, 0 January 2010, 0h TT[37]
Axial tilt
North Pole Rotation
Axial tilt
North Pole Rotation
R.A. (degrees) Dec. (degrees) R.A. (degrees) Dec. (degrees)
Sun 7.25 286.13 63.87 609.12B 7.25A 286.15 63.89 14.18
Mercury 0.03 281.01 61.42 1407.6 0.01 281.01 61.45 6.14
Venus 2.64 272.76 67.16 –5832.6 2.64 272.76 67.16 −1.48
Earth 23.44 0.00 90.00 23.93 23.44 undef. 90.00 360.99
Moon 6.68 655.73 1.54C 270.00 66.54 13.18
Mars 25.19 317.68 52.89 24.62 25.19 317.67 52.88 350.89
Jupiter 3.13 268.05 64.49 9.93D 3.12 268.06 64.50 870.54D
Saturn 26.73 40.60 83.54 10.66D 26.73 40.59 83.54 810.79D
Uranus 82.23 257.43 –15.10 –17.24D 82.23 257.31 −15.18 −501.16D
Neptune 28.32 299.36 43.46 16.11D 28.33 299.40 42.95 536.31D
PlutoE 57.47 (312.99) (6.16) –153.29 60.41 312.99 6.16 −56.36
A with respect to the ecliptic of 1850
B at 16° latitude; the Sun's rotation varies with latitude
C with respect to the ecliptic; the Moon's orbit is inclined 5.16° to the ecliptic
D from the origin of the radio emissions; the visible clouds generally rotate at different rate
E NASA lists the coordinates of Pluto's positive pole; values in (parentheses) have been reinterpreted to correspond to the north/negative pole.

Extrasolar planets

The stellar obliquity ψs, 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 λ has been observed,[38] which serves as a lower limit to ψs. Most of these measurements rely on the Rossiter–McLaughlin effect. 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 spacecraft, could provide access to ψp in the near future.

Astrophysicists have applied tidal theories to predict the obliquity of extrasolar planets. It has been shown that the obliquities of exoplanets in the habitable zone around low-mass stars tend to be eroded in less than 109 years,[39][40] which means that they would not have seasons as Earth has.

See also


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  3. ^ Explanatory Supplement 1992, p. 384
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  20. ^ Newcomb, Simon (1906). A Compendium of Spherical Astronomy. MacMillan. pp. 226–227.
  21. ^ See table 8 and eq. 35 in Laskar, J. (1986). "Secular Terms of Classical Planetary Theories Using the Results of General Relativity". Astronomy and Astrophysics. 157: 59–70. Bibcode:1986A&A...157...59L. and erratum to article Laskar, J. (1986). "Errratum: Secular terms of classical planetary theories using the results of general theory". Astronomy and Astrophysics. 164: 437. Bibcode:1986A&A...164..437L. Units in article are arcseconds, which may be more convenient.
  22. ^ Explanatory Supplement (1961), sec. 2C
  23. ^ "Basics of Space Flight, Chapter 2". Jet Propulsion Laboratory/NASA. 29 October 2013. Retrieved 26 March 2015.
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  27. ^ Laskar, J.; Joutel, F.; Robutel, P. (1993). "Stabilization of the Earth's Obliquity by the Moon" (PDF). Nature. 361 (6413): 615–617. Bibcode:1993Natur.361..615L. doi:10.1038/361615a0.
  28. ^ Lissauer, J.J.; Barnes, J.W.; Chambers, J.E. (2011). "Obliquity variations of a moonless Earth" (PDF). Icarus. 217 (1): 77–87. Bibcode:2012Icar..217...77L. doi:10.1016/j.icarus.2011.10.013.
  29. ^ Li, Gongjie; Batygin, Konstantin (20 July 2014). "On the Spin-axis Dynamics of a Moonless Earth". Astrophysical Journal. 790 (1): 69–76. arXiv:1404.7505. Bibcode:2014ApJ...790...69L. doi:10.1088/0004-637X/790/1/69.
  30. ^ Ward, W.R. (1982). "Comments on the Long-Term Stability of the Earth's Obliquity". Icarus. 50 (2–3): 444–448. Bibcode:1982Icar...50..444W. doi:10.1016/0019-1035(82)90134-8.
  31. ^ a b William Ward (20 July 1973). "Large-Scale Variations in the Obliquity of Mars". Science. 181 (4096): 260–262. Bibcode:1973Sci...181..260W. doi:10.1126/science.181.4096.260. PMID 17730940.
  32. ^ Touma, J.; Wisdom, J. (1993). "The Chaotic Obliquity of Mars" (PDF). Science. 259 (5099): 1294–1297. Bibcode:1993Sci...259.1294T. doi:10.1126/science.259.5099.1294. PMID 17732249.
  33. ^ Correia, Alexandre C.M; Laskar, Jacques (2009). "Mercury's capture into the 3/2 spin-orbit resonance including the effect of core-mantle friction". Icarus. 201 (1): 1–11. arXiv:0901.1843. Bibcode:2009Icar..201....1C. doi:10.1016/j.icarus.2008.12.034.
  34. ^ Rebecca Boyle (7 October 2017). "Methane burps on young Mars helped it keep its liquid water". New Scientist.
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  36. ^ Planetary Fact Sheets, at
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  38. ^ Heller, R. "Holt-Rossiter-McLaughlin Encyclopaedia". René Heller. Retrieved 24 February 2012.
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External links

Abu-Mahmud Khojandi

Abu Mahmud Hamid ibn Khidr Khojandi (known as Abu Mahmood Khojandi, Alkhujandi or al-Khujandi, Persian: ابومحمود خجندی, c. 940 - 1000) was a Central Asian astronomer and mathematician who lived in the late 10th century and helped build an observatory, near the city of Ray (near today's Tehran), in Iran. He was born in Khujand; a bronze bust of the astronomer is present in a park in modern-day Khujand, now part of Tajikistan.


In astronomy, an analemma (; from Greek ἀνάλημμα analēmma "support") is a diagram showing the position of the Sun in the sky, as seen from a fixed location on Earth at the same mean solar time, as that position varies over the course of a year. The diagram will resemble the figure 8. Globes of Earth often display an analemma.

The north–south component of the analemma results from the change in the Sun's declination due to the tilt of Earth's axis of rotation. The east–west component results from the nonuniform rate of change of the Sun's right ascension, governed by combined effects of Earth's axial tilt and orbital eccentricity.

One can photograph an analemma by keeping a camera at a fixed location and orientation and taking multiple exposures throughout the year, always at the same time of day (disregarding daylight saving time, if applicable).

Diagrams of analemmas frequently carry marks that show the position of the Sun at various closely spaced dates throughout the year. Analemmas with date marks can be used for various practical purposes.

Analemmas (as they are known today) have been used in conjunction with sundials since the 18th century to convert between apparent and mean solar time. Prior to this, the term referred to any tool or method used in the construction of sundials.Although the term analemma usually refers to Earth's solar analemma, it can be applied to other celestial bodies as well.

Antarctic Circle

The Antarctic Circle is the most southerly of the five major circles of latitude that mark maps of the 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 midnight) and the centre of the sun is below the horizon for 24 continuous hours at least once per year (and therefore not visible at noon); this is also true within the equivalent polar circle in the Northern Hemisphere, the Arctic Circle.

The position of the Antarctic Circle is not fixed; as of 17 February 2019, it runs 66°33′47.5″ south of the Equator. 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 15 m (49 ft) per year.

Arctic Circle

The Arctic Circle is the most northerly of the five major circles of latitude as shown on maps of Earth. It marks the northernmost point at which the centre of the noon sun is just visible on the December solstice and the southernmost point at which the centre of the midnight sun is just visible on the June solstice. The region north of this circle is known as the Arctic, and the zone just to the south is called the Northern Temperate Zone.

As seen from the Arctic, the Sun is above the horizon for 24 continuous hours at least once per year (and therefore visible at midnight) and below the horizon for 24 continuous hours at least once per year (and therefore not visible at noon). This is also true in the Antarctic region, south of the equivalent Antarctic Circle.

The position of the Arctic Circle is not fixed; as of 21 February 2019, it runs 66°33′47.5″ north of the Equator. 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 Arctic Circle is currently drifting northwards at a speed of about 15 metres (49 feet) per year.

Astronomy on Mars

In many cases astronomical phenomena viewed from the planet Mars are the same or similar to those seen from Earth but sometimes (as with the view of Earth as an evening/morning star) they can be quite different. For example, because the atmosphere of Mars does not contain an ozone layer, it is also possible to make UV observations from the surface of Mars.

Celestial equator

The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. This plane of reference bases the equatorial coordinate system. In other words, the celestial equator is an abstract projection of the terrestrial equator into outer space. Due to Earth's axial tilt, the celestial equator is currently inclined by about 23.44° with respect to the ecliptic (the plane of Earth's orbit).

An observer standing on Earth's equator visualizes the celestial equator as a semicircle passing through the zenith, the point directly overhead. As the observer moves north (or south), the celestial equator tilts towards the opposite horizon. The celestial equator is defined to be infinitely distant (since it is on the celestial sphere); thus, the ends of the semicircle always intersect the horizon due east and due west, regardless of the observer's position on Earth. (At the poles, the celestial equator coincides with the astronomical horizon.) At all latitudes, the celestial equator is a uniform arc or circle because the observer is only finitely far from the plane of the celestial equator, but infinitely far from the celestial equator itself.Astronomical objects near the celestial equator appear above the horizon from most places on earth, but they culminate (reach the meridian) highest near the equator. The celestial equator currently passes through these constellations:

These, by definition, are the most globally visible constellations.

Celestial bodies other than Earth also have similarly defined celestial equators.

Chao Meng-Fu (crater)

Chao Meng-Fu is a 167 kilometer-diameter crater on Mercury named after the Chinese painter and calligrapher Zhao Mengfu (1254–1322). Due to its location near Mercury's south pole (132.4° west, 87.3° south) and the planet's small axial tilt, an estimated 40% of the crater lies in permanent shadow. This combined with bright radar echoes from the location of the crater leads scientists to suspect that it may shelter large quantities of ice protected against sublimation into the near-vacuum by the constant -171 °C temperatures.

Circumpolar constellation

In astronomy, a circumpolar constellation is a constellation (group of stars) that never sets below the horizon, as viewed from a location on Earth. Due to Earth's rotation and axial tilt with respect to the Sun, the stars and constellations can be divided into two categories. Those stars and constellations that never rise or set are called circumpolar. The rest are divided into seasonal stars and constellations.

The stars and constellations that are circumpolar depends on the observer's latitude. In the Northern Hemisphere, certain stars and constellations will always be visible in the northern circumpolar sky. The same holds true in the Southern Hemisphere, where certain stars and constellations will always be visible in the southern circumpolar sky. The celestial north pole, currently marked by Polaris less than 1° away, always has an azimuth equal to zero. The pole's altitude for a given latitude Ø is fixed, and its value is given by the following formula: A = 90° - Ø. All stars with a declination less than A are not circumpolar.As viewed from the North Pole, all fully visible constellations north of the celestial equator are circumpolar, and likewise for constellations south of the celestial equator as viewed from the South Pole. As viewed from the Equator, no circumpolar constellations are visible. As viewed from mid-northern latitudes (40–50° N), circumpolar constellations may include Ursa Major, Ursa Minor, Draco, Cepheus, Cassiopeia, and the less-known Camelopardalis.

Crater of eternal darkness

A crater of eternal darkness is a depression on a body in the Solar System within which lies a point that is always in darkness. Such a crater must be located at high latitude (close to a pole) and be on a body with very small axial tilt.

Craters of eternal darkness might be advantageous for space exploration and colonization, as they could potentially preserve sources of water ice.

Earth's orbit

Earth orbits the Sun at an average distance of 149.60 million km (92.96 million mi), and one complete orbit takes 365.256 days (1 sidereal year), during which time Earth has traveled 940 million km (584 million mi). Earth's orbit has an eccentricity of 0.0167. Since the Sun constitutes 99.76% of the mass of the Sun–Earth system, the center of the orbit is extremely close to the center of the Sun.

As seen from Earth, the planet's orbital prograde motion makes the Sun appear to move with respect to other stars at a rate of about 1° (or a Sun or Moon diameter every 12 hours) eastward per solar day. Earth's orbital speed averages about 30 km/s (108,000 km/h; 67,000 mph), which is fast enough to cover the planet's diameter in 7 minutes and the distance to the Moon in 4 hours.From a vantage point above the north pole of either the Sun or Earth, Earth would appear to revolve in a counterclockwise direction around the Sun. From the same vantage point, both the Earth and the Sun would appear to rotate also in a counterclockwise direction about their respective axes.

Habitability of natural satellites

The habitability of natural satellites is a measure of the potential of natural satellites to have environments hospitable to life. Habitable environments do not necessarily harbor life. Planetary habitability is an emerging study which is considered important to astrobiology for several reasons, foremost being that natural satellites are predicted to greatly outnumber planets and that it is hypothesized that habitability factors are likely to be similar to those of planets. There are, however, key environmental differences which have a bearing on moons as potential sites for extraterrestrial life.

The strongest candidates for natural satellite habitability are currently icy satellites such as those of Jupiter and Saturn—Europa and Enceladus respectively, although if life exists in either place, it would probably be confined to subsurface habitats. Historically, life on Earth was thought to be strictly a surface phenomenon, but recent studies have shown that up to half of Earth's biomass could live below the surface. Europa and Enceladus exist outside the circumstellar habitable zone which has historically defined the limits of life within the Solar System as the zone in which water can exist as liquid at the surface. In the Solar System's habitable zone, there are only three natural satellites—the Moon, and Mars's moons Phobos and Deimos (although some estimates show Mars and its moons to be slightly outside the habitable zone) —none of which sustain an atmosphere or water in liquid form. Tidal forces are likely to play as significant a role providing heat as stellar radiation in the potential habitability of natural satellites.Exomoons are not yet confirmed to exist. Detecting them is extremely difficult, because current methods are limited to transit timing. It is possible that some of their attributes could be determined by similar methods as those of transiting planets. Despite this, some scientists estimate that there are as many habitable exomoons as habitable exoplanets. Given the general planet-to-satellite(s) mass ratio of 10,000, large Saturn or Jupiter sized gas planets in the habitable zone are thought to be the best candidates to harbour Earth-like moons.

Milankovitch cycles

Milankovitch cycles describe the collective effects of changes in the Earth's movements on its climate over thousands of years. The term is named for Serbian geophysicist and astronomer Milutin Milanković. In the 1920s, he hypothesized that variations in eccentricity, axial tilt, and precession of the Earth's orbit resulted in cyclical variation in the solar radiation reaching the Earth, and that this orbital forcing strongly influenced climatic patterns on Earth.

Similar astronomical hypotheses had been advanced in the 19th century by Joseph Adhemar, James Croll and others, but verification was difficult because there was no reliably dated evidence, and because it was unclear which periods were important.

Now, materials on Earth that have been unchanged for millennia (obtained via ice, rock, and deep ocean cores) are being studied to indicate the history of Earth's climate. Though they are consistent with the Milankovitch hypothesis, there are still several observations that the hypothesis does not explain.

Northern Hemisphere

The Northern Hemisphere is the half of Earth that is north of the Equator. For other planets in the Solar System, north is defined as being in the same celestial hemisphere relative to the invariable plane of the solar system as Earth's North Pole.Owing to the Earth's axial tilt, winter in the Northern Hemisphere lasts from the December solstice (typically December 21 UTC) to the March equinox (typically March 20 UTC), while summer lasts from the June solstice through to the September equinox (typically September 23 UTC). The dates vary each year due to the difference between the calendar year and the astronomical year.

Its surface is 60.7% water, compared with 80.9% water in the case of the Southern Hemisphere, and it contains 67.3% of Earth's land.

Polar circle

A polar circle is either the Arctic Circle or the Antarctic Circle. On Earth, the Arctic Circle is located at a latitude of 66°33′47.5″ N, and the Antarctic Circle is located at a latitude of 66°33′47.5″ S.Areas inside each polar circle and its associated pole (North Pole or South Pole), known geographically as the frigid zones, would theoretically experience at least one 24-hour period when the center of the sun is continuously above the horizon and at least one 24-hour period when the center of the sun is continuously below the horizon annually. However, due to atmospheric refraction and the Sun being an extended object rather than a point source, the continuous daylight area is somewhat extended while the continuous darkness area is somewhat reduced.

The latitude of the polar circles is 90 degrees minus the axial tilt of the Earth's axis of daily rotation relative to the ecliptic, the plane of the Earth's orbit. This tilt varies slightly, a phenomenon described as nutation. Therefore, the latitudes noted above are calculated by averaging values of tilt observed over many years. The axial tilt also exhibits long-term variations as described in the reference article (a difference of 1 second of arc in the tilt is equivalent to change of about 31 metres north or south in the positions of the polar circles on the Earth's surface).

Retrograde and prograde motion

Retrograde motion in astronomy is, in general, orbital or rotational motion of an object in the direction opposite the rotation of its primary, that is the central object (right figure). It may also describe other motions such as precession or nutation of the object's rotational axis. Prograde or direct motion is motion in the same direction as the primary rotates. Rotation is determined by an inertial frame of reference, such as distant fixed stars. However, retrograde and prograde can also refer to an object other than the primary if so described.

In our Solar System, the orbits about the Sun of all planets and most other objects, except many comets, are prograde, i.e. in the same direction as the Sun rotates. The rotations of most planets, except Venus and Uranus, are also prograde. Most natural satellites have prograde orbits about their planets. Prograde satellites of Uranus orbit in the direction Uranus rotates, which is retrograde to the Sun. Retrograde satellites are generally small and distant from their planets, except Neptune's satellite Triton, which is large and close. All retrograde satellites are thought to have formed separately before being captured by their planets.


A season is a division of the year marked by changes in weather, ecology, and amount of daylight. On Earth, seasons result from Earth's orbit around the Sun and Earth's axial tilt relative to the ecliptic plane. In temperate and polar regions, the seasons are marked by changes in the intensity of sunlight that reaches the Earth's surface, variations of which may cause animals to undergo hibernation or to migrate, and plants to be dormant. Various cultures define the number and nature of seasons based on regional variations.

During May, June, and July, the Northern Hemisphere is exposed to more direct sunlight because the hemisphere faces the Sun. The same is true of the Southern Hemisphere in November, December, and January. It is Earth's axial tilt that causes the Sun to be higher in the sky during the summer months, which increases the solar flux. However, due to seasonal lag, June, July, and August are the warmest months in the Northern Hemisphere while December, January, and February are the warmest months in the Southern Hemisphere.

In temperate and subpolar regions, four seasons based on the Gregorian calendar are generally recognized: spring, summer, autumn or fall, and winter. The definition of seasons is also cultural. In India from the ancient times, six seasons or Ritu based on south Asian religious or culteral calendars are recognised and identified even today for the purposes such as agriculture and trade. Ecologists often use a six-season model for temperate climate regions which are not tied to any fixed calendar dates: prevernal, vernal, estival, serotinal, autumnal, and hibernal. Many tropical regions have two seasons: the rainy, wet, or monsoon season and the dry season. Some have a third cool, mild, or harmattan season. Seasons often held special significance for agrarian societies, whose lives revolved around planting and harvest times, and the change of seasons was often attended by ritual.

In some parts of the world, some other "seasons" capture the timing of important ecological events such as hurricane season, tornado season, and wildfire season. The most historically important of these are the three seasons—flood, growth, and low water—which were previously defined by the former annual flooding of the Nile in Egypt.

Solar eclipses on Neptune

Solar eclipses on Neptune occur when any of the natural satellites of Neptune pass in front of the Sun as seen from the planet.

For bodies which appear smaller in angular diameter than the Sun, the proper term would be a transit and bodies which are larger than the apparent size of the Sun, the proper term would be an occultation.

All of Neptune's inner moons and Triton can eclipse the Sun as seen from Neptune.

All other satellites of Neptune are too small and/or too distant to produce an umbra.

From this distance, the Sun's angular diameter is reduced to one and a quarter arcminutes across. Here are the angular diameters of the moons that are large enough to fully eclipse the Sun: Naiad, 7–13'; Thalassa, 8–14'; Despina, 14–22'; Galatea, 13–18'; Larissa, 10–14'; Proteus, 13–16'; Triton, 26–28'.

Just because the moons are large enough to fully eclipse the Sun does not necessarily mean that they will do so. Eclipses of the Sun from Neptune are rare due to the planet's long orbital period and large axial tilt of 28 degrees. In addition, the largest moon, Triton, has an orbital inclination of about 25 degrees to Neptune's equator. This makes eclipses of the Sun by Triton rare. Even when such an eclipse does occur, it passes rather quickly, as Triton moves in the opposite direction of Neptune's spin.


The tropics are the region of the Earth surrounding the Equator. They are delimited in latitude by The Tropic of Cancer in the Northern Hemisphere at 23°26′12.5″ (or 23.4368°) N and the Tropic of Capricorn in

the Southern Hemisphere at 23°26′12.5″ (or 23.4368°) S; these latitudes correspond to the axial tilt of the Earth. The tropics are also referred to as the tropical zone and the torrid zone (see geographical zone). The tropics include all the areas on the Earth where the Sun contacts a point directly overhead at least once during the solar year (which is a subsolar point) - thus the latitude of the tropics is roughly equal to the angle of the Earth's axial tilt.

The tropics are distinguished from the other climatic and biomatic regions of Earth, which are the middle latitudes and the polar regions on either side of the equatorial zone.

The tropics comprise 40% of the Earth's surface area and contain 36% of the Earth's landmass. As of 2014, the region is home to 40% of the world population, and this figure is projected to reach 50% by the late 2030s.


Wobble or wobbles may refer to:

"Wobble" (song), a single by V.I.C.

Wobbles (equine disorder), a disorder of the nervous system in dogs and horses

Wobble base pair, a type of base pairing in genetics

Jah Wobble (born 1958), British musician

Milankovitch wobble, change in the Earth's axial tilt, axial precession and orbital eccentricity

Speed wobble, a quick oscillation of primarily just the steerable wheel(s) of a vehicle

A metasyntactic variable, commonly used alongside wibble, wubble, and flob

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