Wikipedia

Axial tilt

(Redirected fromObliquity)
"Obliquity" redirects here. For the book, seeObliquity (book).

Inastronomy,axial tilt,also known asobliquity,is theanglebetween an object'srotational axisand itsorbitalaxis, which is the lineperpendicularto itsorbital plane;equivalently, it is the angle between itsequatorialplane and orbital plane.[1]It differs fromorbital inclination.

Thepositivepole of a planet is defined by theright-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.

At an obliquity of 0 degrees, the two axes point in the same direction; that is, the rotational axis is perpendicular to the orbital plane.

The rotational axis ofEarth,for example, is the imaginary line that passes through both theNorth PoleandSouth Pole,whereas the Earth's orbital axis is the line perpendicular to the imaginaryplanethrough which the Earth moves as it revolves around theSun;the Earth's obliquity or axial tilt is the angle between these two lines.

Over the course of anorbital period,the obliquity usually does not change considerably, and theorientation of the axis remains the samerelative to thebackgroundofstars.This causes one pole to be pointed more toward the Sun on one side of the orbit, and more away from the Sun on the other side—the cause of theseasonson Earth.

Standards

edit

There are two standard methods of specifying a planet's tilt. One way is based on the planet'snorth pole,defined in relation to the direction of Earth's north pole, and the other way is based on the planet'spositive pole,defined by theright-hand rule:

  • TheInternational Astronomical Union(IAU) defines thenorth poleof a planet as that which lies on Earth's north side of theinvariable planeof theSolar System;[2]under this system,Venusis tilted 3° and rotatesretrograde,opposite that of most of the other planets.[3][4]
  • The IAU also uses the right-hand rule to define apositive pole[5]for the purpose of determining orientation. Using this convention, Venus is tilted 177° ( "upside down" ) and rotates prograde.

Earth

edit
Further information:Ecliptic § Obliquity of the ecliptic
See also:Earth's rotationandEarth-centered inertial

Earth'sorbital planeis known as theeclipticplane, andEarth's tiltis known to astronomers as theobliquity of the ecliptic,being the angle between the ecliptic and thecelestial equatoron thecelestial sphere.[6]It is denoted by theGreek letterEpsilonε.

Earth currently has an axial tilt of about 23.44°.[7]This value remains about the same relative to a stationary orbital plane throughout the cycles ofaxial precession.[8]But the ecliptic (i.e., Earth's orbit) moves due to planetaryperturbations,and the obliquity of the ecliptic is not a fixed quantity. At present, it is decreasing at a rate of about46.8″[9]percentury(see details inShort termbelow).

History

edit

The ancient Greeks had good measurements of the obliquity since about 350 BCE, whenPytheasof Marseilles measured the shadow of agnomonat the summer solstice.[10]About 830 CE, the CaliphAl-Mamunof Baghdad directed his astronomers to measure the obliquity, and the result was used in the Arab world for many years.[11]In 1437,Ulugh Begdetermined the Earth's axial tilt as 23°30′17″ (23.5047°).[12]

During theMiddle Ages,it was widely believed that both precession and Earth's obliquity oscillated around a mean value, with a period of 672 years, an idea known astrepidationof the equinoxes. Perhaps the first to realize this was incorrect (during historic time) wasIbn al-Shatirin the fourteenth century[13]and the first to realize that the obliquity is decreasing at a relatively constant rate wasFracastoroin 1538.[14]The first accurate, modern, western observations of the obliquity were probably those ofTycho BrahefromDenmark,about 1584,[15]although observations by several others, includingal-Ma'mun,al-Tusi,[16]Purbach,Regiomontanus,andWalther,could have provided similar information.

Seasons

edit
Main article:Season
An illustration ofaxial parallelism.The axis of Earth remains oriented in the same direction with reference to the background stars regardless of where it is in itsorbit.Northern hemisphere summer occurs at the right side of this diagram, where the north pole (red) is directed toward the Sun, winter at the left.

Earth's axis remains tilted in the same direction with reference to the background stars throughout a year (regardless of where it is in itsorbit) – this is known asaxial parallelism.This means that one pole (and the associatedhemisphere 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'sseasons.Summeroccurs in theNorthern hemispherewhen the north pole is directed toward and the south pole away from the Sun. Variations in Earth's axial tilt can influence the seasons and is likely a factor in long-termclimatic change(also seeMilankovitch cycles).

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

Oscillation

edit

Short term

edit
Obliquity of the ecliptic for 20,000 years, fromLaskar(1986). The red point represents the year 2000.

The exact angular value of the obliquity is found by observation of the motions of Earth andplanetsover many years. Astronomers produce newfundamental ephemeridesas the accuracy ofobservationimproves and as the understanding of thedynamicsincreases, and from these ephemerides various astronomical values, including the obliquity, are derived.

Annualalmanacsare published listing the derived values and methods of use. Until 1983, theAstronomical Almanac's angular value of the mean obliquity for any date was calculated based on thework of Newcomb,who analyzed positions of the planets until about 1895:

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

whereεis the obliquity andTistropical centuriesfromB1900.0to the date in question.[17]

From 1984, theJet Propulsion Laboratory's DE seriesof computer-generated ephemerides took over as thefundamental ephemerisof theAstronomical 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+0.001813″T3

where hereafterTisJulian centuriesfromJ2000.0.[18]

JPL's fundamental ephemerides have been continually updated. For instance, according to IAU resolution in 2006 in favor of the P03 astronomical model, theAstronomical Almanacfor 2010 specifies:[19]

ε= 23°26′21.406″ −46.836769″T−0.0001831″T2+0.00200340″T3− 5.76″ × 10−7T4− 4.34″ × 10−8T5

These expressions for the obliquity are intended for high precision over a relatively short time span, perhaps±several centuries.[20]Jacques Laskarcomputed an expression to orderT10good to 0.02″ over 1000 years and severalarcsecondsover 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 heretis multiples of 10,000Julian yearsfromJ2000.0.[21]

These expressions are for the so-calledmeanobliquity, that is, the obliquity free from short-term variations. Periodic motions of the Moon and of Earth in its orbit cause much smaller (9.2arcseconds) short-period (about 18.6 years) oscillations of the rotation axis of Earth, known asnutation,which add a periodic component to Earth's obliquity.[22][23]Thetrueor instantaneous obliquity includes this nutation.[24]

Long term

edit
Main article:Formation and evolution of the Solar System
Main article:Milankovitch cycles

Usingnumerical methodsto simulateSolar Systembehavior over a period of several million years, long-term changes in Earth'sorbit,and hence its obliquity, have been investigated. For the past 5 million years, Earth's obliquity has varied between22°2′33″and24°30′16″,with a mean period of 41,040 years. This cycle is a combination of precession and the largesttermin the motion of theecliptic.For the next 1 million years, the cycle will carry the obliquity between22°13′44″and24°20′50″.[25]

TheMoonhas 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 toorbital resonancesandchaotic behavior of the Solar System,reaching as high as 90° in as little as a few million years (also seeOrbit 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 two billion years. As the Moon continues to recede from Earth due totidal 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; 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.[31]

Solar System bodies

edit
See also:Poles of astronomical bodies § Poles of rotation
Axial tilt of eightplanetsand two dwarf planets,CeresandPluto

All four of the innermost, rocky planets of theSolar Systemmay 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.[32]The rate varies due totidal dissipationandcore-mantleinteraction, among other things. When a planet's precession rate approaches certain values,orbital resonancesmay 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.[32]

MercuryandVenushave most likely been stabilized by the tidal dissipation of the Sun. Earth was stabilized by the Moon, as mentioned above, but before itsformation,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 onperturbationsof the planets.[26][33]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.[3][34]

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.[35][36]

The obliquities of the outer planets are considered relatively stable.

Axis and rotation of selected Solar System bodies
Body NASA,J2000.0[37]epoch IAU,0h 0 January 2010TT[38]epoch
Axial tilt
(degrees) 		North Pole Rotational
period
(hours) 		Axial tilt
(degrees) 		North Pole Rotation
(deg./day)
R.A.(degrees) Dec.(degrees) R.A.(degrees) Dec.(degrees)
Sun 7.25 286.13 63.87 609.12[A] 7.25[B] 286.15 63.89 14.18
Mercury 0.03 281.01 61.41 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 Undefined 90.00 360.99
Moon 6.68 – – 655.73 1.54[C] 270.00 66.54 13.18
Mars 25.19 317.68 52.89 24.62 25.19 317.67 52.88 350.89
Jupiter 3.13 268.06 64.50 9.93[D] 3.12 268.06 64.50 870.54[D]
Saturn 26.73 40.59 83.54 10.66[D] 26.73 40.59 83.54 810.79[D]
Uranus 82.23 257.31 −15.18 −17.24[D] 82.23 257.31 −15.18 −501.16[D]
Neptune 28.32 299.33 42.95 16.11[D] 28.33 299.40 42.95 536.31[D]
Pluto[E] 57.47 312.99[E] 6.16[E] −153.29 60.41 312.99 6.16 −56.36
  1. ^At 16° latitude; the Sun's rotation varies with latitude.
  2. ^With respect to theeclipticof 1850.
  3. ^With respect to the ecliptic; the Moon's orbit is inclined 5.16° to the ecliptic.
  4. ^abcdefghFrom the origin of the radio emissions; the visible clouds generally rotate at different rate.
  5. ^abcNASA lists the coordinates of Pluto's positive pole; noted values have been reinterpreted to correspond to the north/negative pole.

Extrasolar planets

edit

The stellar obliquityψs,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. By 2012, 49 stars have had sky-projected spin-orbit misalignmentλhas been observed,[39]which serves as a lower limit toψs.Most of these measurements rely on theRossiter–McLaughlin effect.Since the launch of space-based telescopes such asKepler space telescope,it has been made possible to determine and estimate the obliquity of an extrasolar planet. The rotational flattening of the planet and the entourage of moons and/or rings, which are traceable with high-precision photometry provide access to planetary obliquity,ψp.Many extrasolar planets have since had their obliquity determined, such asKepler-186fandKepler-413b.[40][41]

Astrophysicists have applied tidal theories to predict the obliquity ofextrasolar planets.It has been shown that the obliquities of exoplanets in thehabitable zonearound low-mass stars tend to be eroded in less than 109years,[42][43]which means that they would not have tilt-induced seasons as Earth has.

See also

edit

References

edit
  1. ^ U.S. Naval Observatory Nautical Almanac Office (1992). P. Kenneth Seidelmann (ed.).Explanatory Supplement to the Astronomical Almanac.University Science Books. p. 733.ISBN978-0-935702-68-2.
  2. ^Explanatory Supplement 1992,p. 384
  3. ^abCorreia, Alexandre C. M.; Laskar, Jacques; de Surgy, Olivier Néron (May 2003)."Long-term evolution of the spin of Venus I. theory"(PDF).Icarus.163(1):1–23.Bibcode:2003Icar..163....1C.doi:10.1016/S0019-1035(03)00042-3.Archived(PDF)from the original on 9 October 2022.
  4. ^Correia, A. C. M.; Laskar, J. (2003)."Long-term evolution of the spin of Venus: II. numerical simulations"(PDF).Icarus.163(1):24–45.Bibcode:2003Icar..163...24C.doi:10.1016/S0019-1035(03)00043-5.Archived(PDF)from the original on 9 October 2022.
  5. ^Seidelmann, P. Kenneth; Archinal, B. A.; a'Hearn, M. F.; Conrad, A.; Consolmagno, G. J.; Hestroffer, D.; Hilton, J. L.; Krasinsky, G. A.; Neumann, G.; Oberst, J.; Stooke, P.; Tedesco, E. F.; Tholen, D. J.; Thomas, P. C.; Williams, I. P. (2007)."Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements: 2006".Celestial Mechanics and Dynamical Astronomy.98(3):155–180.Bibcode:2007CeMDA..98..155S.doi:10.1007/s10569-007-9072-y.
  6. ^ U.S. Naval Observatory Nautical Almanac Office; U.K. Hydrographic Office; H.M. Nautical Almanac Office (2008).The Astronomical Almanac for the Year 2010.US Government Printing Office. p. M11.ISBN978-0-7077-4082-9.
  7. ^"Glossary"inAstronomical Almanac Online.(2023). Washington DC: United States Naval Observatory. s.v. obliquity.
  8. ^ Chauvenet, William (1906).A Manual of Spherical and Practical Astronomy.Vol. 1.J. B. Lippincott.pp.604–605.
  9. ^Ray, Richard D.; Erofeeva, Svetlana Y. (4 February 2014)."Long-period tidal variations in the length of day".Journal of Geophysical Research: Solid Earth.119(2):1498–1509.Bibcode:2014JGRB..119.1498R.doi:10.1002/2013JB010830.
  10. ^ Gore, J. E. (1907).Astronomical Essays Historical and Descriptive.Chatto & Windus. p.61.
  11. ^ Marmery, J. V. (1895).Progress of Science.Chapman and Hall, ld. p.33.
  12. ^Sédillot, L.P.E.A. (1853).Prolégomènes des tables astronomiques d'OlougBeg: Traduction et commentaire.Paris: Firmin Didot Frères. pp. 87 & 253.
  13. ^Saliba, George (1994).A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam.p. 235.
  14. ^ Dreyer, J. L. E. (1890).Tycho Brahe.A. & C. Black. p.355.
  15. ^Dreyer (1890), p. 123
  16. ^ Sayili, Aydin (1981).The Observatory in Islam.p. 78.
  17. ^ U.S. Naval Observatory Nautical Almanac Office; H.M. Nautical Almanac Office (1961).Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac.H.M. Stationery Office.Section 2B.
  18. ^ U.S. Naval Observatory; H.M. Nautical Almanac Office (1989).The Astronomical Almanac for the Year 1990.US Government Printing Office. p. B18.ISBN978-0-11-886934-8.
  19. ^Astronomical Almanac 2010,p. B52
  20. ^ Newcomb, Simon (1906).A Compendium of Spherical Astronomy.MacMillan.pp.226–227.
  21. ^See table 8 and eq. 35 inLaskar, J. (1986). "Secular terms of classical planetary theories using the results of general theory".Astronomy and Astrophysics.157(1):59–70.Bibcode:1986A&A...157...59L.and erratum to article Laskar, J. (1986). "Erratum: 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.Retrieved26 March2015.
  24. ^ Meeus, Jean (1991). "Chapter 21".Astronomical Algorithms.Willmann-Bell.ISBN978-0-943396-35-4.
  25. ^ Berger, A.L. (1976). "Obliquity and Precession for the Last 5000000 Years".Astronomy and Astrophysics.51(1):127–135.Bibcode:1976A&A....51..127B.
  26. ^ab Laskar, J.; Robutel, P. (1993)."The Chaotic Obliquity of the Planets"(PDF).Nature.361(6413):608–612.Bibcode:1993Natur.361..608L.doi:10.1038/361608a0.S2CID4372237.Archived fromthe original(PDF)on 23 November 2012.
  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.S2CID4233758.Archived(PDF)from the original on 9 October 2022.
  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.Archived(PDF)from the original on 8 June 2013.
  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.S2CID119295403.
  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. ^Berger, 1976.
  32. ^abWilliam 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.PMID17730940.S2CID41231503.
  33. ^ 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.PMID17732249.S2CID42933021.Archived(PDF)from the original on 25 June 2010.
  34. ^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.S2CID14778204.
  35. ^Rebecca Boyle (7 October 2017)."Methane burps on young Mars helped it keep its liquid water".New Scientist.
  36. ^Edwin Kite; et al. (2 October 2017)."Methane bursts as a trigger for intermittent lake-forming climates on post-Noachian Mars"(PDF).Nature Geoscience.10(10):737–740.arXiv:1611.01717.Bibcode:2017NatGe..10..737K.doi:10.1038/ngeo3033.S2CID102484593.Archived(PDF)from the original on 23 July 2018.
  37. ^Planetary Fact Sheets,athttp://nssdc.gsfc.nasa.gov
  38. ^Astronomical Almanac 2010,pp. B52, C3, D2, E3, E55
  39. ^ Heller, R."Holt-Rossiter-McLaughlin Encyclopaedia".René Heller.Retrieved24 February2012.
  40. ^Grossman, David (29 June 2018)."Study Shows Exoplanet Has a Stable Axis Just Like Earth".Popular Mechanics.Retrieved26 February2024.
  41. ^"Kepler Finds a Very Wobbly Planet - NASA".4 February 2014.Retrieved26 February2024.
  42. ^ Heller, R.; Leconte, J.; Barnes, R. (2011). "Tidal obliquity evolution of potentially habitable planets".Astronomy and Astrophysics.528:A27.arXiv:1101.2156.Bibcode:2011A&A...528A..27H.doi:10.1051/0004-6361/201015809.S2CID118784209.
  43. ^ Heller, R.; Leconte, J.; Barnes, R. (2011). "Habitability of Extrasolar Planets and Tidal Spin Evolution".Origins of Life and Evolution of Biospheres.41(6):539–43.arXiv:1108.4347.Bibcode:2011OLEB...41..539H.doi:10.1007/s11084-011-9252-3.PMID22139513.S2CID10154158.
edit
Retrieved from "https://en.wikipedia.org/w/index.php?title=Axial_tilt&oldid=1270636100"