Axial tilt

Source: Wikipedia, the free encyclopedia.
"Obliquity" redirects here. For the book, see Obliquity (book).
orbital plane; equivalently, it is 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; that is, the rotational axis is perpendicular to the orbital plane.

The rotational axis of

plane through which the Earth moves as it revolves around the Sun
; the Earth's obliquity or axial tilt is the angle between these two lines.

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 pointed more toward the Sun on one side of the orbit, and more away from the Sun on the other side—the cause of the seasons on Earth.

Standards

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

Earth

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

Greek letter ε
.

Earth currently has an axial tilt of about 23.44°.

46.8″[9] per century (see details in Short term
below).

History

The ancient Greeks had good measurements of the obliquity since about 350 BCE, when

Al-Mamun of Baghdad directed his astronomers to measure the obliquity, and the result was used in the Arab world for many years.[11] In 1437, Ulugh Beg determined the Earth's axial tilt as 23°30′17″ (23.5047°).[12]

During the

Purbach, Regiomontanus, and Walther
, could have provided similar information.

Seasons

Main article: Season
The axis of Earth remains oriented in the same direction with reference to the background stars regardless of where it is in its orbit. 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.

climatic change (also see Milankovitch cycles
).

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

Oscillation

Short term

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

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 + 0.00181″ T3

where ε is the obliquity and T is tropical centuries from B1900.0 to the date in question.[17]

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 + 0.001813″ T3

where hereafter T is Julian centuries from J2000.0.[18]

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

ε = 23°26′21.406″ − 46.836769″ T − 0.0001831″ T2 + 0.00200340″ T3 − 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.

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

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

Using

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 could 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 two 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.)

Solar System bodies

See also: Poles of astronomical bodies § Poles of rotation
Axial tilt of eight planets and two dwarf planets, Ceres and Pluto

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 formation, 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.[3][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
J2000.0[36]
epoch
TT[37]
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 the ecliptic of 1850.
  3. ^ With respect to the ecliptic; the Moon's orbit is inclined 5.16° to the ecliptic.
  4. ^ a b c d e f g h From the origin of the radio emissions; the visible clouds generally rotate at different rate.
  5. ^ a b c NASA lists the coordinates of Pluto's positive pole; noted values 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. By 2012, 49 stars have had 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. Since the launch of space-based telescopes such as Kepler 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 as Kepler-186f and Kepler-413b.[39][40]

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,[41][42]
which means that they would not have tilt-induced seasons as Earth has.

See also

References

  1. ^ U.S. Naval Observatory Nautical Almanac Office (1992). P. Kenneth Seidelmann (ed.). Explanatory Supplement to the Astronomical Almanac. University Science Books. p. 733.
    ISBN 978-0-935702-68-2
    .
  2. ^ Explanatory Supplement 1992, p. 384
  3. ^
    doi:10.1016/S0019-1035(03)00042-3. Archived
    (PDF) from the original on 9 October 2022.
  4. doi:10.1016/S0019-1035(03)00043-5. Archived
    (PDF) from the original on 9 October 2022.
  5. 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.
    ISBN 978-0-7077-4082-9
    .
  7. ^ "Glossary" in Astronomical 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. 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.
    ISBN 978-0-11-886934-8
    .
  19. ^ Astronomical Almanac 2010, p. B52
  20. ^ Newcomb, Simon (1906). A Compendium of Spherical Astronomy. MacMillan. pp. 226–227.
  21. 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. Retrieved 26 March 2015.
  24. ^ Meeus, Jean (1991). "Chapter 21". Astronomical Algorithms. Willmann-Bell.
    ISBN 978-0-943396-35-4
    .
  25. ^ Berger, A.L. (1976). "Obliquity and Precession for the Last 5000000 Years".
    Bibcode:1976A&A....51..127B
    .
  26. ^ a b Laskar, J.; Robutel, P. (1993). "The Chaotic Obliquity of the Planets" (PDF).
    S2CID 4372237. Archived from the 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.
    S2CID 4233758. 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).
    doi:10.1016/j.icarus.2011.10.013. Archived
    (PDF) from the original on 8 June 2013.
  29. S2CID 119295403
    .
  30. ^ Ward, W.R. (1982). "Comments on the Long-Term Stability of the Earth's Obliquity".
    doi:10.1016/0019-1035(82)90134-8
    .
  31. ^
    S2CID 41231503
    .
  32. ^ Touma, J.; Wisdom, J. (1993). "The Chaotic Obliquity of Mars" (PDF).
    S2CID 42933021. Archived
    (PDF) from the original on 25 June 2010.
  33. S2CID 14778204
    .
  34. ^ Rebecca Boyle (7 October 2017). "Methane burps on young Mars helped it keep its liquid water". New Scientist.
  35. S2CID 102484593. Archived
    (PDF) from the original on 23 July 2018.
  36. ^ Planetary Fact Sheets, at http://nssdc.gsfc.nasa.gov
  37. ^ Astronomical Almanac 2010, pp. B52, C3, D2, E3, E55
  38. ^ Heller, R. "Holt-Rossiter-McLaughlin Encyclopaedia". René Heller. Retrieved 24 February 2012.
  39. ^ Grossman, David (29 June 2018). "Study Shows Exoplanet Has a Stable Axis Just Like Earth". Popular Mechanics. Retrieved 26 February 2024.
  40. ^ "Kepler Finds a Very Wobbly Planet - NASA". 4 February 2014. Retrieved 26 February 2024.
  41. ^ Heller, R.; Leconte, J.; Barnes, R. (2011). "Tidal obliquity evolution of potentially habitable planets".
    S2CID 118784209
    .
  42. ^ 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.
    S2CID 10154158
    .

External links
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