Editing Axial tilt (section)

==== Long term ====
{{main|Formation and evolution of the Solar System}}
{{main|Milankovitch cycles}}

Using [[numerical methods]] to simulate [[Solar System]] behavior over a period of several million years, long-term changes in Earth's [[orbit]], and hence its obliquity, have been investigated. For the past 5 million years, Earth's obliquity has varied between {{nowrap|22°2′33″}} and {{nowrap|24°30′16″}}, with a mean period of 41,040 years. This cycle is a combination of precession and the largest [[Addend|term]] in the motion of the [[ecliptic]]. For the next 1 million years, the cycle will carry the obliquity between {{nowrap|22°13′44″}} and {{nowrap|24°20′50″}}.<ref>
{{cite journal
 |last=Berger |first=A.L.
 |date=1976
 |title=Obliquity and Precession for the Last 5000000 Years
 |journal=[[Astronomy and Astrophysics]]
 |volume=51 |issue= 1|pages=127–135
 |bibcode=1976A&A....51..127B
}}</ref>

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 resonance]]s and [[Stability of the Solar System|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]]'').<ref name="LaskarRobutel">
{{cite journal
 |author1=Laskar, J.
 |author2=Robutel, P.
 |date=1993
 |title=The Chaotic Obliquity of the Planets
 |url=http://bugle.imcce.fr/fr/presentation/equipes/ASD/person/Laskar/misc_files/Laskar_Robutel_1993.pdf
 |journal=[[Nature (journal)|Nature]]
 |volume=361 |issue=6413 |pages=608–612
 |bibcode=1993Natur.361..608L
 |doi=10.1038/361608a0
 |s2cid=4372237
 |url-status=dead
 |archive-url=https://web.archive.org/web/20121123093109/http://bugle.imcce.fr/fr/presentation/equipes/ASD/person/Laskar/misc_files/Laskar_Robutel_1993.pdf
 |archive-date=23 November 2012
}}</ref><ref>
{{cite journal
 |author1=Laskar, J.
 |author2=Joutel, F.
 |author3=Robutel, P.
 |date=1993
 |title=Stabilization of the Earth's Obliquity by the Moon
 |url=http://www.imcce.fr/Equipes/ASD/person/Laskar/misc_files/Laskar_Joutel_Robutel_1993.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.imcce.fr/Equipes/ASD/person/Laskar/misc_files/Laskar_Joutel_Robutel_1993.pdf |archive-date=9 October 2022 |url-status=live
 |journal=Nature
 |volume=361 |issue= 6413 |pages=615–617
 |bibcode=1993Natur.361..615L
 |doi=10.1038/361615a0
 |s2cid=4233758
}}</ref> However, more recent numerical simulations<ref>
{{cite journal
 |author1=Lissauer, J.J.
 |author2=Barnes, J.W.
 |author3=Chambers, J.E.
 |date=2011
 |title=Obliquity variations of a moonless Earth
 |url=http://barnesos.net/publications/papers/2012.01.Icarus.Barnes.Moonless.Earth.pdf |archive-url=https://web.archive.org/web/20130608154841/http://barnesos.net/publications/papers/2012.01.Icarus.Barnes.Moonless.Earth.pdf |archive-date=8 June 2013 |url-status=live
 |journal=[[Icarus (journal)|Icarus]]
 |volume=217 |issue= 1 |pages=77–87
 |doi=10.1016/j.icarus.2011.10.013
 |bibcode = 2012Icar..217...77L
}}</ref> 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°.<ref>{{Cite journal|last1=Li|first1=Gongjie|last2=Batygin|first2=Konstantin|date=20 July 2014|title=On the Spin-axis Dynamics of a Moonless Earth|journal=Astrophysical Journal|volume=790|issue=1|pages=69–76|arxiv=1404.7505|bibcode=2014ApJ...790...69L|doi=10.1088/0004-637X/790/1/69|s2cid=119295403}}</ref> 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.<ref>
{{cite journal
 |author1=Ward, W.R.
 |date=1982
 |title=Comments on the Long-Term Stability of the Earth's Obliquity
 |journal=[[Icarus (journal)|Icarus]]
 |volume=50 |issue= 2–3 |pages=444–448
 |bibcode=1982Icar...50..444W
 |doi=10.1016/0019-1035(82)90134-8
}}</ref>

{{multiple image
 |direction = horizontal
 |align= center
 |width1= 264
 |width2= 272
 |image1=Obliquity berger -5000000 to 0.png
 |image2=Obliquity berger 0 to 1000000.png
 |footer=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&nbsp;million years; note the approx. 41,000-year period of variation. In both graphs, the red point represents the year 1850.<ref>Berger, 1976.</ref>
}}