View source for Milankovitch cycles

{{Short description|Global climate cycles}}
{{Use dmy dates|date=December 2022}}

[[File:MilankovitchCyclesOrbitandCores.png|thumb|upright=2|Past and future Milankovitch cycles via [[VSOP (planets)|VSOP]] model{{unordered list
| Graphic shows variations in five orbital elements:
{{legend|#4848FF|border=1px solid #00289E|[[Axial tilt]] or obliquity (ε).}}
{{legend|#229122|border=1px solid #00289E|[[Orbital eccentricity|Eccentricity]] (''e'').}}
{{legend|#922392|border=1px solid #00289E|[[Longitude of the periapsis|Longitude of perihelion]] (sin(ϖ)).}}
{{legend|#FF3232|border=1px solid #00289E|Precession index (''e''&nbsp;sin(ϖ))}}
|Precession index and obliquity control [[insolation]] at each latitude:
{{legend|#323232|border=1px solid #00289E|Daily-average insolation at top of atmosphere on summer solstice (<math display="inline"> \overline{Q}^{\mathrm{day} } </math>) at 65° N }}
|Ocean sediment and Antarctic ice strata [[Proxy (climate)|record]] ancient sea levels and temperatures:
{{legend|#AE3E3E|border=1px solid #00289E|[[Foraminifera|Benthic forams]] (57 widespread locations)}}
{{legend2|#026602|border=1px solid #00289E|[[Vostok_Station#Ice_core_drilling|Vostok ice core (Antarctica)]]}}
|Vertical gray line shows present (2000&nbsp;CE)}}]]

'''Milankovitch cycles''' describe the collective effects of changes in the Earth's movements on its [[climate]] over thousands of years. The term was coined and named after the Serbian [[geophysics|geophysicist]] and [[astronomer]] [[Milutin Milanković]]. In the 1920s, he provided a more definitive and quantitative analysis than [[James Croll]]'s earlier hypothesis that variations in [[eccentricity (orbit)|eccentricity]], [[axial tilt]], and [[precession]] combined to result in cyclical variations in the intra-annual and latitudinal distribution of [[solar radiation]] at the Earth's surface, and that this [[orbital forcing]] strongly influenced the Earth's climatic patterns.<ref>{{cite journal |last1=Kerr |first1=Richard A. |date=14 July 1978 |title=Climate Control: How Large a Role for Orbital Variations? |url=https://www.jstor.org/stable/1746691 |journal=Science |volume=201 |issue=4351 |pages=144–146 |doi=10.1126/science.201.4351.144 |jstor=1746691 |pmid=17801827 |bibcode=1978Sci...201..144K |access-date=29 July 2022}}</ref><ref>{{cite web |title=Why Milankovitch (Orbital) Cycles Can't Explain Earth's Current Warming |last=Buis |first=Alan |date=27 February 2020 |url=https://climate.nasa.gov/ask-nasa-climate/2949/why-milankovitch-orbital-cycles-cant-explain-earths-current-warming/ |publisher=NASA |access-date=29 July 2022}}</ref><ref>{{Cite journal |last=Edwards |first=Kevin J. |date=2022 |title=‘The most remarkable man’: James Croll, Quaternary scientist |url=https://onlinelibrary.wiley.com/doi/10.1002/jqs.3420 |journal=Journal of Quaternary Science |language=en |volume=37 |issue=3 |pages=400–419 |doi=10.1002/jqs.3420 |issn=0267-8179|hdl=2164/18340 |hdl-access=free }}</ref>

==Earth movements==
The [[Earth's rotation]] around its [[Axial tilt|axis]], and revolution around the [[Sun]], evolve over time due to [[Perturbation (astronomy)|gravitational interactions]] with other bodies in the [[Solar System]]. The variations are complex, but a few cycles are dominant.<ref>{{cite thesis |degree=Master of Science |title=A Computational Study on the Evolution of the Dynamics of the Obliquity of the Earth |url=https://etd.ohiolink.edu/ap/10?6433295551748::NO:10:P10_ETD_SUBID:56397 |archive-url=https://archive.today/20140930142332/https://etd.ohiolink.edu/ap/10?6433295551748::NO:10:P10_ETD_SUBID:56397 |url-status=dead |archive-date=30 September 2014 |format=PDF |vauthors=Girkin AM |year=2005 |publisher=Miami University }}</ref>

{{multiple image
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| image1 = Eccentricity zero.svg
| width1 = 200
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| caption1 = Circular orbit, no eccentricity
| image2 = Eccentricity half.svg
| width2 = 200
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| caption2 = Example orbit with 0.5 eccentricity. Earth's orbit is much less eccentric.
| footer =
}}
The [[Earth's orbit]] varies between nearly circular and mildly [[Ellipse|elliptical]] (its eccentricity varies). When the orbit is more elongated, there is more variation in the distance between the Earth and the Sun, and in the amount of [[Solar Radiation|solar radiation]], at different times in the year. In addition, the rotational tilt of the Earth (its [[obliquity]]) changes slightly. A greater tilt makes the seasons more extreme. Finally, the direction in the [[fixed stars]] pointed to by the Earth's axis changes ([[axial precession]]), while the Earth's elliptical orbit around the Sun rotates ([[apsidal precession]]). The combined effect of precession with eccentricity is that proximity to the Sun occurs during different [[Season#Astronomical|astronomical seasons]].<ref>{{cite journal |author= [[Grove Karl Gilbert|G. K. Gilbert]] |journal= [[The Journal of Geology]] |date= February–March 1895 |title= Sedimentary Measurement of Cretaceous Time |publisher= [[University of Chicago Press]] |volume= 3 |issue= 2 |pages= 121–127 |doi= 10.1086/607150 |jstor= 30054556 |bibcode= 1895JG......3..121G |s2cid= 129629329 |quote= As the earth's axis slowly describes its circle on the celestial sphere the relation of the seasons to perihelion is steadily shifted. |doi-access=  }} Note: It is intuitive that if equinoxes and solstices occur in shifting positions on an eccentric orbit, then these astronomical seasons must occur at shifting proximities; and as either eccentricity and tilt vary, the intensities of the effects of these shifts also vary.'l</ref>

Milankovitch studied changes in these movements of the Earth, which alter the amount and location of solar radiation reaching the Earth. This is known as ''solar forcing'' (an example of [[radiative forcing]]). Milankovitch emphasized the changes experienced at 65° north due to the great amount of land at that latitude. Land masses change surface temperature more quickly than oceans, mainly because convective mixing between shallow and deeper waters keeps the ocean surface relatively cooler.  Similarly, the very large [[thermal inertia]] of the global ocean delays changes to Earth's average surface temperature when gradually driven by other forcing factors.<ref name="Scott06">{{cite web |author=Michon Scott |date=24 April 2006 |title=Earth's Big Heat Bucket |url=https://earthobservatory.nasa.gov/features/HeatBucket/heatbucket.php |publisher=NASA Earth Observatory}}</ref>

===Orbital eccentricity===
{{Main|Orbital eccentricity}}
The Earth's orbit approximates an [[ellipse]]. Eccentricity measures the departure of this ellipse from circularity. The shape of the Earth's orbit varies between nearly circular (theoretically the eccentricity can hit zero) and mildly elliptical (highest eccentricity was 0.0679 in the last 250 million years).<ref name=Laskar2010>{{cite journal | vauthors = Laskar J, Fienga A, Gastineau M, Manche H | title=La2010: A New Orbital Solution for the Long-term Motion of the Earth | journal=Astronomy & Astrophysics|year=2011| volume=532| issue=A889| url=http://www.aanda.org/articles/aa/pdf/2011/08/aa16836-11.pdf |doi=10.1051/0004-6361/201116836 |bibcode=2011A&A...532A..89L |pages=A89|arxiv=1103.1084| s2cid=10990456}} See specifically [http://vo.imcce.fr/insola/earth/online/earth/La2010/La2010d_ecc3.dat the downloadable data file].</ref> Its [[Geometric mean|geometric]] or [[logarithmic mean]] is 0.0019. The major component of these variations occurs with a period of 405,000 years<ref name="auto">Laskar2020</ref> (eccentricity variation of ±0.012). Other components have 95,000-year and 124,000-year cycles<ref name="auto"/> (with a beat period of 400,000 years). They loosely combine into a 100,000-year cycle (variation of −0.03 to +0.02). The present eccentricity is 0.0167<ref name="auto"/> and decreasing.

Eccentricity varies primarily due to the gravitational pull of [[Jupiter]] and [[Saturn]]. The [[semi-major axis]] of the orbital ellipse, however, remains unchanged; according to [[perturbation (astronomy)|perturbation theory]], which computes the evolution of the orbit, the semi-major axis is [[adiabatic invariant|invariant]]. The [[orbital period]] (the length of a [[sidereal year]]) is also invariant, because according to [[Kepler's laws of planetary motion#Third law|Kepler's third law]], it is determined by the semi-major axis.<ref>{{cite journal | pmc=6395789 | date=2019 | last1=Vijaya | first1=G. K. | title=Original form of Kepler's Third Law and its misapplication in Propositions XXXII-XXXVII in Newton's Principia (Book I) | journal=Heliyon | volume=5 | issue=2 | pages=e01274 | doi=10.1016/j.heliyon.2019.e01274 | doi-access=free | pmid=30886926 | bibcode=2019Heliy...501274V }}</ref> Longer-term variations are caused by interactions involving the perihelia and nodes of the planets Mercury, Venus, Earth, Mars, and Jupiter.<ref name=Laskar2010/>

====Effect on temperature====
The semi-major axis is a constant. Therefore, when Earth's orbit becomes more eccentric, the [[semi-minor axis]] shortens. This increases the magnitude of seasonal changes.<ref>{{cite journal | vauthors = Berger A, Loutre MF, Mélice JL | title=Equatorial insolation: from precession harmonics to eccentricity frequencies| journal=Climate of the Past Discussions| volume=2 | pages=519–533| year=2006| doi= 10.5194/cpd-2-519-2006| issue=4| url=https://hal.archives-ouvertes.fr/hal-00298053/file/cp-2-131-2006.pdf | doi-access=free}}</ref>

The relative increase in [[solar irradiation]] at closest approach to the Sun ([[perihelion and aphelion|perihelion]]) compared to the irradiation at the furthest distance ([[perihelion and aphelion|aphelion]]) is slightly larger than four times the eccentricity. For Earth's current orbital eccentricity, incoming solar radiation varies by about 6.8%, while the distance from the Sun currently varies by only 3.4% ({{Convert|5.1|e6km|e6mi au|abbr=unit|disp=or}}).<ref>{{cite web |last=Buis |first=Alan |title=Milankovitch (Orbital) Cycles and Their Role in Earth's Climate |url=https://climate.nasa.gov/news/2948/milankovitch-orbital-cycles-and-their-role-in-earths-climate/ |website=NASA's Jet Propulsion Laboratory |date=February 27, 2020 |accessdate=8 January 2024}}
</ref>

Perihelion presently occurs around 3 January, while aphelion is around 4 July. When the orbit is at its most eccentric, the amount of solar radiation at perihelion will be about 23% more than at aphelion. However, the Earth's eccentricity is so small (at least at present) that the variation in solar irradiation is a minor factor in [[Seasonal variation|seasonal climate variation]], compared to axial tilt and even compared to the relative ease of heating the larger land masses of the northern hemisphere.<ref>{{cite web |last=Buis |first=Alan |title=Milankovitch (Orbital) Cycles and Their Role in Earth's Climate |url=https://climate.nasa.gov/news/2948/milankovitch-orbital-cycles-and-their-role-in-earths-climate/ |website=NASA's Jet Propulsion Laboratory |date=February 27, 2020 |accessdate=8 January 2024}}</ref>

====Effect on lengths of seasons====
{| class="wikitable" style="margin: 0 0 1em 1em"
|+ Season durations<ref>Data from [http://aa.usno.navy.mil/data/docs/EarthSeasons.php United States Naval Observatory] {{Webarchive|url=https://web.archive.org/web/20071013000301/http://aa.usno.navy.mil/data/docs/EarthSeasons.php |date=13 October 2007 }}</ref>
|-
!Year
!Northern<br />hemisphere
!Southern<br />hemisphere
!Date ([[UTC]])
!Season<br />duration
|-
|2005
|Winter [[solstice]]
|Summer solstice
|style="text-align:right" | 21 December 2005 18:35
|style="text-align:right" | 88.99 days
|-
|2006
|Spring [[equinox]]
|Autumn equinox
|style="text-align:right" | 20 March 2006 18:26
|style="text-align:right" | 92.75 days
|-
|2006
|Summer solstice
|Winter solstice

|style="text-align:right" | 21 June 2006 12:26
| align="right" | 93.65 days
|-
|2006
|Autumn equinox
|Spring equinox
|style="text-align:right" | 23 September 2006 4:03
|style="text-align:right" | 89.85 days
|-
|2006
|Winter solstice
|Summer solstice
|style="text-align:right" | 22 December 2006 0:22
|style="text-align:right" | 88.99 days
|-
|2007
|Spring equinox
|Autumn equinox
|style="text-align:right" | 21 March 2007 0:07
|style="text-align:right" | 92.75 days
|-
|2007
|Summer solstice
|Winter solstice
|style="text-align:right" | 21 June 2007 18:06
|style="text-align:right" | 93.66 days
|-
|2007
|Autumn equinox
|Spring equinox
|style="text-align:right" | 23 September 2007 9:51
|style="text-align:right" | 89.85 days
|-
|2007
|Winter solstice
|Summer solstice
|style="text-align:right" | 22 December 2007 06:08
|&nbsp;
|}

The seasons are quadrants of the Earth's orbit, marked by the two solstices and the two equinoxes. [[Kepler's laws of planetary motion#Second law|Kepler's second law]] states that a body in orbit traces equal areas over equal times; its orbital velocity is highest around perihelion and lowest around aphelion.<ref name="Wolfram2nd">Bryant, Jeff; Pavlyk, Oleksandr. "[http://demonstrations.wolfram.com/KeplersSecondLaw/ Kepler's Second Law]", ''[[Wolfram Demonstrations Project]]''. Retrieved December 27, 2009.</ref> The Earth spends less time near perihelion and more time near aphelion. This means that the lengths of the seasons vary.<ref name="NASABBuis2021" /> Perihelion currently occurs around 3 January, so the Earth's greater velocity shortens winter and autumn in the northern hemisphere, and summer and spring in the southern hemisphere. Summer in the northern hemisphere is 4.66 days longer than winter, and spring is 2.9 days longer than autumn.<ref name="NASABBuis2021" /> In the southern hemisphere this is the reverse, winter is 4.66 days longer than summer, and autumn is 2.9 days longer than spring. Greater eccentricity increases the variation in the Earth's orbital velocity. Currently, however, the Earth's orbit is becoming less eccentric (more nearly circular). This will make the seasons in the immediate future more similar in length.<ref name="NASABBuis2021" />

===Axial tilt (obliquity)===
{{Main|Axial tilt}}
[[File:Earth obliquity range.svg|thumb|22.1–24.5° range of Earth's obliquity.]]
The angle of the Earth's axial tilt with respect to the orbital plane (the obliquity of the [[ecliptic]]) varies between 22.1° and 24.5°, over a cycle of about 41,000 years. The current tilt is 23.44°, roughly halfway between its extreme values. The tilt last reached its maximum in 8,700 [[Before Common Era|BCE]], which correlates with the beginning of the [[Holocene]], the current geological epoch. It is now in the decreasing phase of its cycle, and will reach its minimum around the year 11,800 [[Common Era|CE]].<ref name= NASABBuis2021 /> Increased tilt increases the amplitude of the seasonal cycle in [[insolation]], providing more solar radiation in each hemisphere's summer and less in winter. However, these effects are not uniform everywhere on the Earth's surface. Increased tilt increases the total annual solar radiation at higher latitudes, and decreases the total closer to the equator.<ref name= NASABBuis2021 >{{cite web |website= climate.nasa.gov |date= 27 February 2020 |publisher= [[NASA]] |access-date= 10 May 2021| title= Milankovitch (Orbital) Cycles and Their Role in Earth's Climate| url= https://climate.nasa.gov/news/2948/milankovitch-orbital-cycles-and-their-role-in-earths-climate/| first= Alan |last=Buis |author2=[[Jet Propulsion Laboratory]] |quote= Over the last million years, it has varied between 22.1 and 24.5 degrees.&nbsp;... The greater Earth's axial tilt angle, the more extreme our seasons are&nbsp;.... Larger tilt angles favor periods of deglaciation (the melting and retreat of glaciers and ice sheets). These effects aren't uniform globally – higher latitudes receive a larger change in total solar radiation than areas closer to the equator.&nbsp;... Earth's axis is currently tilted 23.4 degrees,&nbsp;... As ice cover increases, it reflects more of the Sun's energy back into space, promoting even further cooling. }} Note: See [[Axial tilt]]. Zero obliquity results in minimum (zero) continuous insolation at the poles and maximum continuous insolation at the equator. Any increase of obliquity (to 90 degrees) causes seasonal increase of insolation at the poles and causes decrease of insolation at the equator on any day of the year except an [[equinox]].</ref>

The current trend of decreasing tilt, by itself, will promote milder seasons (warmer winters and colder summers), as well as an overall cooling trend.<ref name= NASABBuis2021 /> Because most of the planet's snow and ice lies at high latitude, ''decreasing'' tilt may encourage the termination of an [[interglacial]] period (and lead to an overall cooler climate) and the onset of a [[glacial period]] for two reasons: 1) there is less overall summer insolation, and 2) there is less insolation at higher latitudes (which melts less of the previous winter's snow and ice).<ref name= NASABBuis2021 />

===Axial precession===
{{Main|Axial precession}}
[[File:Earth precession.svg|thumb|Axial precessional movement.]]
Axial precession is the trend in the direction of the Earth's axis of rotation relative to the fixed stars, with a period of about 25,700 years. Also known as the precession of the equinoxes, this motion means that eventually [[Polaris]] will no longer be the north [[Pole star#Precession of the equinoxes|pole star]].<!-- Axial precession directly implies changing pole stars --> This precession is [[Axial precession#Cause|caused by the tidal forces]] exerted by the Sun and the Moon on the rotating Earth; both contribute roughly equally to this effect.<!-- roughly same order of magnitude -->{{Citation needed|date=December 2022}}

Currently, perihelion occurs during the southern hemisphere's summer. This means that solar radiation due to both the axial tilt inclining the southern hemisphere toward the Sun, and the Earth's proximity to the Sun, will reach maximum during the southern summer and reach minimum during the southern winter. These effects on heating are thus additive, which means that seasonal variation in irradiation of the southern hemisphere is more extreme. In the northern hemisphere, these two factors reach maximum at opposite times of the year: the north is tilted toward the Sun when the Earth is furthest from the Sun. The two effects work in opposite directions, resulting in less extreme variations in insolation.

In about 10,000 years, the north pole will be tilted toward the Sun when the Earth is at perihelion. Axial tilt and orbital eccentricity will both contribute their maximum increase in solar radiation during the northern hemisphere's summer. Axial precession will promote more extreme variation in irradiation of the northern hemisphere and less extreme variation in the south. When the Earth's axis is aligned such that aphelion and perihelion occur near the equinoxes, axial tilt will not be aligned with or against eccentricity.{{Citation needed|date=December 2022}}

===Apsidal precession===
{{Main|Apsidal precession }}

[[File:Precessing Kepler orbit 280frames e0.6 smaller.gif|thumb|Planets orbiting the Sun follow elliptical (oval) orbits that rotate gradually over time (apsidal precession). The eccentricity of this ellipse, as well as the rate of precession, are exaggerated for visualization.]]
The orbital ellipse itself precesses in space, in an irregular fashion, completing a full cycle in about 112,000 years relative to the fixed stars.<ref name=Heuvel>{{cite journal | vauthors = van den Heuvel EP |title=On the Precession as a Cause of Pleistocene Variations of the Atlantic Ocean Water Temperatures|journal=Geophysical Journal International|year=1966| volume=11| issue=3| pages=323–336| bibcode = 1966GeoJ...11..323V | doi = 10.1111/j.1365-246X.1966.tb03086.x | doi-access=free}} Note: The reader may question the number and precision of the periods which the author reports in this early paper.</ref> Apsidal precession occurs in the plane of the ecliptic and alters the orientation of the Earth's orbit relative to the ecliptic. This happens primarily as a result of interactions with Jupiter and Saturn. Smaller contributions are also made by the sun's oblateness and by the effects of [[general relativity]] that are well known for Mercury.<ref>{{cite journal |last1=Barbieri |first1=L. |last2=Talamucci |first2=F. |arxiv=1802.07115 |title=Calculation of Apsidal Precession via Perturbation Theory |journal=Advances in Astrophysics |date= 20 February 2018|volume=4 |issue=3 |doi=10.22606/adap.2019.43003 |s2cid=67784452 }}</ref>

Apsidal precession combines with the 25,700-year cycle of axial precession (see [[#Axial precession|above]]) to vary the position in the year that the Earth reaches perihelion. Apsidal precession shortens this period to about 21,000 years, at present. According to a relatively old source (1965), the average value over the last 300,000 years was 23,000 years, varying between 20,800 and 29,000 years.<ref name=Heuvel/>

[[File:precession and seasons.svg|thumb|upright=1.5|Effects of precession on the seasons (using the [[Northern Hemisphere]] terms)]]
As the orientation of Earth's orbit changes, each season will gradually start earlier in the year. Precession means the Earth's nonuniform motion (see [[#Orbital shape and temperature|above]]) will affect different seasons. Winter, for instance, will be in a different section of the orbit. When the Earth's apsides (extremes of distance from the sun) are aligned with the equinoxes, the length of spring and summer combined will equal that of autumn and winter. When they are aligned with the solstices, the difference in the length of these seasons will be greatest.{{Citation needed|date=December 2022}}

===Orbital inclination===
{{anchor|100,000-year problem}}
{{Main|Orbital inclination }}

The inclination of Earth's orbit drifts up and down relative to its present orbit. This three-dimensional movement is known as "precession of the ecliptic" or "planetary precession". Earth's current inclination relative to the [[invariable plane]] (the plane that represents the [[angular momentum]] of the Solar System—approximately the orbital plane of Jupiter) is 1.57°.{{citation needed|date=April 2021}} Milankovitch did not study planetary precession. It was discovered more recently and measured, relative to Earth's orbit, to have a period of about 70,000 years. When measured independently of Earth's orbit, but relative to the invariable plane, however, precession has a period of about 100,000 years. This period is very similar to the 100,000-year eccentricity period. Both periods closely match the 100,000-year pattern of glacial events.<ref name="pmid11607741">{{cite journal | vauthors = Muller RA, MacDonald GJ | title = Spectrum of 100-kyr glacial cycle: orbital inclination, not eccentricity | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 94 | issue = 16 | pages = 8329–34 | date = August 1997 | pmid = 11607741 | pmc = 33747 | doi = 10.1073/pnas.94.16.8329 | bibcode = 1997PNAS...94.8329M | doi-access = free }}</ref>

==Theory constraints==
[[File:Cyclic deposits.jpg|thumb|upright|left|[[Tabernas Desert]], Spain: Cycles can be observed in the colouration and resistance of different sediment strata]]

Materials taken from the Earth have been studied to infer the cycles of past climate. Antarctic ice cores contain trapped air bubbles whose ratios of different oxygen isotopes are a reliable [[Proxy (climate)#Proxy|proxy]] for global temperatures around the time the ice was formed. Study of this data concluded that the climatic response documented in the ice cores was driven by northern hemisphere insolation as proposed by the Milankovitch hypothesis.<ref>{{cite journal | vauthors = Kawamura K, Parrenin F, Lisiecki L, Uemura R, Vimeux F, Severinghaus JP, Hutterli MA, Nakazawa T, Aoki S, Jouzel J, Raymo ME, Matsumoto K, Nakata H, Motoyama H, Fujita S, Goto-Azuma K, Fujii Y, Watanabe O | display-authors = 6 | title = Northern Hemisphere forcing of climatic cycles in Antarctica over the past 360,000 years | journal = Nature | volume = 448 | issue = 7156 | pages = 912–6 | date = August 2007 | pmid = 17713531 | doi = 10.1038/nature06015 | s2cid = 1784780 | bibcode = 2007Natur.448..912K }}</ref> Similar astronomical hypotheses had been advanced in the 19th century by [[Joseph Adhemar]], [[James Croll]], and others.<ref name="Imbrie Imbrie 1979 p. ">{{cite book | last1=Imbrie | first1=John | last2=Imbrie | first2=Katherine Palmer | title=Ice Ages | publisher=Macmillan Education UK | publication-place=London | date=1979 | isbn=978-1-349-04701-7 | doi=10.1007/978-1-349-04699-7 | page=| doi-broken-date=1 November 2024 }}</ref>

Analysis of deep-ocean cores and of lake depths,<ref>{{cite journal | vauthors = Kerr RA | title = Milankovitch Climate Cycles Through the Ages: Earth's orbital variations that bring on ice ages have been modulating climate for hundreds of millions of years | journal = Science | volume = 235 | issue = 4792 | pages = 973–4 | date = February 1987 | pmid = 17782244 | doi = 10.1126/science.235.4792.973 | bibcode = 1987Sci...235..973K | jstor = 1698758 }}/O</ref><ref>{{cite journal | vauthors = Olsen PE | title = A 40-million-year lake record of early mesozoic orbital climatic forcing | journal = Science | volume = 234 | issue = 4778 | pages = 842–8 | date = November 1986 | pmid = 17758107 | doi = 10.1126/science.234.4778.842 | s2cid = 37659044 | bibcode = 1986Sci...234..842O | jstor = 1698087 }}</ref> and a seminal paper by [[James D. Hays|Hays]], [[John Imbrie|Imbrie]], and [[Nicholas Shackleton|Shackleton]]<ref name=Hays1976>{{cite journal | vauthors = Hays JD, Imbrie J, Shackleton NJ | title = Variations in the Earth's Orbit: Pacemaker of the Ice Ages | journal = Science | volume = 194 | issue = 4270 | pages = 1121–32 | date = December 1976 | pmid = 17790893 | doi = 10.1126/science.194.4270.1121 | s2cid = 667291 | bibcode = 1976Sci...194.1121H | author-link2 = John Imbrie | author-link3 = Nicholas Shackleton | author-link1 = James D. Hays }}</ref> provide additional validation through physical evidence. Climate records contained in a {{Cvt|1700|ft}} core of rock drilled in Arizona show a pattern synchronized with Earth's eccentricity, and cores drilled in New England match it, going back 215 million years.<ref>{{Cite news | url=https://www.nytimes.com/2018/05/21/science/earth-orbit-change.html| title=Every 202,500 Years, Earth Wanders in a New Direction| vauthors = Bakalar N | newspaper=The New York Times| date=21 May 2018| access-date=25 May 2018}}</ref>

{{clear|left}}
===100,000-year issue===
{{Main|100,000-year problem}}

Of all the orbital cycles, Milankovitch believed that obliquity had the greatest effect on climate, and that it did so by varying the summer insolation in northern high latitudes. Therefore, he deduced a 41,000-year period for ice ages.<ref name="Milankovitch">{{cite book | vauthors = Milankovitch M | title=Canon of Insolation and the Ice Age Problem| orig-year=1941| year=1998| publisher=Zavod za Udz̆benike i Nastavna Sredstva |location=Belgrade | isbn=978-86-17-06619-0}}; see also {{cite web | title=Astronomical Theory of Climate Change| url=http://www.ncdc.noaa.gov/paleo/milankovitch.html}}</ref><ref>{{cite book | vauthors = Imbrie J, Imbrie KP |title=Ice Ages: Solving the Mystery |url=https://books.google.com/books?id=GIxRp9fRDGwC&pg=PA158 |year=1986 |publisher=Harvard University Press |isbn=978-0-674-44075-3 |pages=158}}</ref> However, subsequent research<ref name=Hays1976/><ref>{{cite journal | vauthors = Shackleton NJ, Berger A, Peltier WR | author3-link=William Richard Peltier| title=An alternative astronomical calibration of the lower Pleistocene timescale based on ODP Site 677| journal=Transactions of the Royal Society of Edinburgh: Earth Sciences| date=3 November 2011| volume=81| issue=4| pages=251–261| doi=10.1017/S0263593300020782| s2cid=129842704}}</ref><ref>{{cite journal | vauthors = Abe-Ouchi A, Saito F, Kawamura K, Raymo ME, Okuno J, Takahashi K, Blatter H | title = Insolation-driven 100,000-year glacial cycles and hysteresis of ice-sheet volume | journal = Nature | volume = 500 | issue = 7461 | pages = 190–3 | date = August 2013 | pmid = 23925242 | doi = 10.1038/nature12374 | url = https://academiccommons.columbia.edu/doi/10.7916/D8MC994B/download | s2cid = 4408240 | bibcode = 2013Natur.500..190A }}</ref> has shown that [[ice age]] cycles of the [[Quaternary glaciation]] over the last million years have been at a period of 100,000 years, which matches the eccentricity cycle. Various explanations for this discrepancy have been proposed, including [[frequency modulation]]<ref>{{Citation | vauthors = Rial JA | title = Earth's orbital Eccentricity and the rhythm of the Pleistocene ice ages: the concealed pacemaker| journal = Global and Planetary Change| volume = 41| issue = 2| pages = 81–93|date= October 2003| url = http://www.geolab.unc.edu/faculty/rial/GPCRial2.pdf| archive-url =https://web.archive.org/web/20110720092801/http://www.geolab.unc.edu/faculty/rial/GPCRial2.pdf| archive-date =20 July 2011| doi=10.1016/j.gloplacha.2003.10.003| bibcode =2004GPC....41...81R}}</ref> or various feedbacks (from [[Carbon dioxide in Earth's atmosphere|carbon dioxide]], or [[ice sheet dynamics]]). Some models can reproduce the 100,000-year cycles as a result of non-linear interactions between small changes in the Earth's orbit and internal oscillations of the climate system.<ref name="Ghil1994">{{cite journal | vauthors = Ghil M | author-link=Michael Ghil| title=Cryothermodynamics: the chaotic dynamics of paleoclimate| journal=Physica D| volume=77| issue=1–3| year=1994| pages=130–159| doi=10.1016/0167-2789(94)90131-7| bibcode = 1994PhyD...77..130G }}</ref><ref name="Gildor2000">{{cite journal | vauthors=Gildor H, Tziperman E |title=Sea ice as the glacial cycles' climate switch: Role of seasonal and orbital forcing| journal=Paleoceanography| volume=15| issue=6| year=2000| pages=605–615| doi=10.1029/1999PA000461| bibcode=2000PalOc..15..605G| doi-access=free}}</ref> In particular, the mechanism of the [[stochastic resonance]] was originally proposed in order to describe this interaction.<ref>{{Cite journal |last1=Benzi |first1=R |last2=Sutera |first2=A |last3=Vulpiani |first3=A |date=1 November 1981 |title=The mechanism of stochastic resonance |journal=Journal of Physics A: Mathematical and General |volume=14 |issue=11 |pages=L453–L457 |doi=10.1088/0305-4470/14/11/006 |bibcode=1981JPhA...14L.453B |s2cid=123005407 |issn=0305-4470|doi-access=free }}</ref><ref>{{Cite journal |last1=Benzi |first1=Roberto |last2=Parisi |first2=Giorgio |author-link2=Giorgio Parisi |last3=Sutera |first3=Alfonso |last4=Vulpiani |first4=Angelo |date=February 1982 |title=Stochastic resonance in climatic change |url=http://tellusa.net/index.php/tellusa/article/view/10782 |journal=Tellus |language=en |volume=34 |issue=1 |pages=10–16 |doi=10.1111/j.2153-3490.1982.tb01787.x|bibcode=1982Tell...34...10B }}</ref>

Jung-Eun Lee of Brown University proposes that precession changes the amount of energy that Earth absorbs, because the southern hemisphere's greater ability to grow sea ice reflects more energy away from Earth. Moreover, Lee says, "Precession only matters when eccentricity is large. That's why we see a stronger 100,000-year pace than a 21,000-year pace."<ref>{{Cite web | url=https://m.phys.org/news/2017-01-earth-orbital-variations-sea-ice.html |title=Earth's orbital variations and sea ice synch glacial periods | vauthors = Stacey K |publisher=m.phys.org | date=26 January 2017}}</ref><ref>{{cite journal | title=Hemispheric sea ice distribution sets the glacial tempo| vauthors = Lee JE, Shen A, Fox-Kemper B, Ming Y | date=1 January 2017| journal=Geophys. Res. Lett.| pages=1008–1014 |doi=10.1002/2016GL071307| volume=44| issue = 2| bibcode=2017GeoRL..44.1008L| doi-access=free}}</ref> Some others have argued that the length of the climate record is insufficient to establish a statistically significant relationship between climate and eccentricity variations.<ref name="Wunsch2004">{{cite journal | vauthors = Wunsch C | title=Quantitative estimate of the Milankovitch-forced contribution to observed Quaternary climate change| journal=Quaternary Science Reviews| volume=23| year=2004| pages=1001–12| doi=10.1016/j.quascirev.2004.02.014| issue=9–10| bibcode = 2004QSRv...23.1001W | url=https://repositorio.unal.edu.co/handle/unal/80694}}</ref>

===Transition changes===
{{Main|Mid-Pleistocene Transition}}
{{stack|
[[File:Five Myr Climate Change.svg|thumb|upright=1.35|Variations of cycle times, curves determined from ocean sediments.]]
[[File:Vostok 420ky 4curves insolation.jpg|thumb|upright=1.35|420,000 years of ice core data from [[Vostok, Antarctica]] research station, with more recent times on the left.]]
}}

From 1–3&nbsp;million years ago, climate cycles matched the 41,000-year cycle in obliquity. After one million years ago, the [[Mid-Pleistocene Transition]] (MPT) occurred with a switch to the 100,000-year cycle matching eccentricity. The ''transition problem'' refers to the need to explain what changed one million years ago.<ref>{{cite journal | vauthors = Zachos JC, Shackleton NJ, Revenaugh JS, Pälike H, Flower BP | title = Climate response to orbital forcing across the Oligocene-Miocene boundary | journal = Science | volume = 292 | issue = 5515 | pages = 274–8 | date = April 2001 | pmid = 11303100 | doi = 10.1126/science.1058288 | url = http://www.scencemag.org/cgi/pmidlookup?view=long&pmid=11303100 | access-date = 24 October 2010 | url-status = dead | s2cid = 38231747 | bibcode = 2001Sci...292..274Z | archive-url = https://web.archive.org/web/20171203224507/http://scencemag.org/cgi/pmidlookup?view=long&pmid=11303100 | archive-date = 3 December 2017 }}</ref> The MPT can now be reproduced in numerical simulations that include a decreasing trend in [[carbon dioxide]] and glacially induced removal of [[regolith]].<ref name="Willeit">{{cite journal | vauthors = Willeit M, Ganopolski A, Calov R, Brovkin V | title = Mid-Pleistocene transition in glacial cycles explained by declining CO<sub>2</sub> and regolith removal | journal = Science Advances | volume = 5 | issue = 4 | pages = eaav7337 | date = April 2019 | pmid = 30949580 | pmc = 6447376 | doi = 10.1126/sciadv.aav7337 | bibcode = 2019SciA....5.7337W }}</ref>

===Interpretation of unsplit peak variances===
Even the well-dated climate records of the last million years do not exactly match the shape of the eccentricity curve. Eccentricity has component cycles of 95,000 and 125,000 years. Some researchers, however, say the records do not show these peaks, but only indicate a single cycle of 100,000 years.<ref>{{cite web | url=https://www.proquest.com/openview/5d5565735578d40943494a793b71d626/1.pdf?pq-origsite=gscholar| title=Nonlinear coupling between 100 ka periodicity of the paleoclimate records in loess and periodicities of precession and semi-precession| via=ProQuest}}</ref> The split between the two eccentricity components, however, is observed at least once in a drill core from the 500-million year-old Scandinavian Alum Shale.<ref>Sørensen, A.L., Nielsen, A.T., Thibault, N., Zhao, Z., Schovsbo, N.H., Dahl, T.W., 2020. Astronomically forced climate change in the late Cambrian. Earth Planet. Sci. Lett. 548, 116475. https://doi.org/10.1016/j.epsl.2020.116475</ref>

===Unsynced stage five observation===
Deep-sea core samples show that the interglacial interval known as [[Marine isotope stage#Stages|marine isotope stage 5]] began 130,000 years ago. This is 10,000 years before the solar forcing that the Milankovitch hypothesis predicts. (This is also known as the causality problem because the effect precedes the putative cause.)<ref>{{cite journal | vauthors = Karner DB, Muller RA | title = PALEOCLIMATE: A Causality Problem for Milankovitch | journal = Science | volume = 288 | issue = 5474 | pages = 2143–4 | date = June 2000 | pmid = 17758906 | doi = 10.1126/science.288.5474.2143 | s2cid = 9873679 }}</ref>

==Present and future conditions==
[[File:InsolationSummerSolstice65N.png|thumb|upright=1.75|Past and future estimations of daily average insolation at top of the atmosphere on the day of the summer solstice, at 65° N latitude. The green curve is with eccentricity ''e'' hypothetically set to 0. The red curve uses the actual (predicted) value of ''e''; the blue dot indicates current conditions (2000 CE).]]

Since orbital variations are predictable,<ref name="Varadi2003">{{cite journal| vauthors = Varadi F, Runnegar B, Ghil M |author-link3=Michael Ghil |title=Successive Refinements in Long-Term Integrations of Planetary Orbits |journal=The Astrophysical Journal |volume=592 |issue=1 |year=2003 |pages=620–630 |doi=10.1086/375560 |bibcode=2003ApJ...592..620V |doi-access=free }}</ref> any model that relates orbital variations to climate can be run forward to predict future climate, with two caveats: the mechanism by which [[orbital forcing]] influences climate is not definitive; and non-orbital effects can be important (for example, the [[human impact on the environment]] principally increases [[greenhouse gas]]es resulting in [[global warming|a warmer climate]]<ref>{{cite journal | vauthors = Kaufman DS, Schneider DP, McKay NP, Ammann CM, Bradley RS, Briffa KR, Miller GH, Otto-Bliesner BL, Overpeck JT, Vinther BM | display-authors = 6 | title = Recent warming reverses long-term arctic cooling | journal = Science | volume = 325 | issue = 5945 | pages = 1236–9 | date = September 2009 | pmid = 19729653 | doi = 10.1126/science.1173983 | s2cid = 23844037 | citeseerx = 10.1.1.397.8778 | bibcode = 2009Sci...325.1236K }}</ref><ref>{{cite web|title=Arctic Warming Overtakes 2,000 Years of Natural Cooling |url=http://www2.ucar.edu/news/846/arctic-warming-overtakes-2000-years-natural-cooling |publisher=UCAR |date=3 September 2009 |access-date=19 May 2011 |url-status=dead |archive-url=https://web.archive.org/web/20110427235538/http://www2.ucar.edu/news/846/arctic-warming-overtakes-2000-years-natural-cooling |archive-date=27 April 2011 }}</ref><ref>{{cite news| vauthors = Bello D |title=Global Warming Reverses Long-Term Arctic Cooling |url=http://www.scientificamerican.com/article.cfm?id=global-warming-reverses-arctic-cooling |work=Scientific American |date=4 September 2009 |access-date=19 May 2011 }}</ref>).

An often-cited 1980 orbital model by [[John Imbrie|Imbrie]] predicted "the long-term cooling trend that began some 6,000 years ago will continue for the next 23,000 years."<ref name="Imbriel1980">{{cite journal | vauthors = Imbrie J, Imbrie JZ | title = Modeling the climatic response to orbital variations | journal = Science | volume = 207 | issue = 4434 | pages = 943–53 | date = February 1980 | pmid = 17830447 | doi = 10.1126/science.207.4434.943 | s2cid = 7317540 | bibcode = 1980Sci...207..943I }}</ref> Another work<ref>{{Cite journal |last1=Mukherjee |first1=Pami |last2=Sinha |first2=Nitesh |last3=Chakraborty |first3=Supriyo |date=2017-07-10 |title=Investigating the dynamical behavior of the Intertropical Convergence Zone since the last glacial maximum based on terrestrial and marine sedimentary records |url=https://www.sciencedirect.com/science/article/pii/S1040618216300143 |journal=Quaternary International |series=Third Pole: The Last 20,000 Years - Part 1 |language=en |volume=443 |pages=49–57 |doi=10.1016/j.quaint.2016.08.030 |bibcode=2017QuInt.443...49M |issn=1040-6182}}</ref> suggests that [[Solar irradiance|solar insolation]] at 65°&nbsp;N will reach a peak of 460 W·m<sup>−2</sup> in around 6,500 years, before decreasing back to current levels (450 W·m<sup>−2</sup>)<ref>{{Cite web |title=Energy resources: solar energy |url=https://www.open.edu/openlearn/nature-environment/environmental-studies/energy-resources-solar-energy/nature-environment/environmental-studies/energy-resources-solar-energy |access-date=2023-06-17 |website=Energy resources: solar energy |language=en }}{{Dead link|date=April 2024 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> in around 16,000 years. Earth's orbit will become less eccentric for about the next 100,000 years, so changes in this insolation will be dominated by changes in obliquity, and should not decline enough to permit a [[next glacial period|new glacial period]] in the next 50,000 years.<ref name="Berger2002">{{cite journal | vauthors = Berger A, Loutre MF | title = Climate. An exceptionally long interglacial ahead? | journal = Science | volume = 297 | issue = 5585 | pages = 1287–8 | date = August 2002 | pmid = 12193773 | doi = 10.1126/science.1076120 | s2cid = 128923481 }}</ref><ref>{{cite journal | vauthors = Ganopolski A, [[Ricarda Winkelmann|Winkelmann R]], Schellnhuber HJ | title = Critical insolation-CO2 relation for diagnosing past and future glacial inception | journal = Nature | volume = 529 | issue = 7585 | pages = 200–3 | date = January 2016 | pmid = 26762457 | doi = 10.1038/nature16494 | s2cid = 4466220 | bibcode = 2016Natur.529..200G }}</ref>

==Other celestial bodies==
===Mars===
Since 1972, speculation sought a relationship between the formation of Mars' alternating bright and dark layers in the polar layered deposits, and the planet's orbital climate forcing. In 2002, Laska, Levard, and Mustard showed ice-layer radiance, as a function of depth, correlate with the insolation variations in summer at the Martian north pole, similar to palaeoclimate variations on Earth. They also showed Mars' precession had a period of about 51 [[kyr]], obliquity had a period of about 120 kyr, and eccentricity had a period ranging between 95 and 99 kyr. In 2003, Head, Mustard, Kreslavsky, Milliken, and Marchant proposed Mars was in an interglacial period for the past 400 kyr, and in a glacial period between 400 and 2100 kyr, due to Mars' obliquity exceeding 30°. At this extreme obliquity, insolation is dominated by the regular periodicity of Mars' obliquity variation.<ref name="pmid12353029">{{cite journal | author3-link = John F. Mustard | vauthors = Laskar J, Levrard B, Mustard JF | title = Orbital forcing of the martian polar layered deposits | journal = Nature | volume = 419 | issue = 6905 | pages = 375–7 | date = September 2002 | pmid = 12353029 | doi = 10.1038/nature01066 | bibcode = 2002Natur.419..375L | s2cid = 4380705 | url = http://www.planetary.brown.edu/pdfs/2839.pdf | access-date = 11 December 2020 | archive-date = 19 July 2011 | archive-url = https://web.archive.org/web/20110719160258/http://www.planetary.brown.edu/pdfs/2839.pdf | url-status = dead }}</ref><ref name="pmid14685228">{{cite journal | vauthors = Head JW, Mustard JF, Kreslavsky MA, Milliken RE, Marchant DR | title = Recent ice ages on Mars | journal = Nature | volume = 426 | issue = 6968 | pages = 797–802 | date = December 2003 | pmid = 14685228 | doi = 10.1038/nature02114 | bibcode = 2003Natur.426..797H | s2cid = 2355534 | url = http://planetary.brown.edu/planetary/documents/2957.pdf | archive-date = 15 April 2021 | access-date = 11 December 2020 | archive-url = https://web.archive.org/web/20210415202634/http://planetary.brown.edu/planetary/documents/2957.pdf | url-status = dead }}</ref> [[Fourier analysis]] of Mars' orbital elements, show an obliquity period of 128 kyr, and a precession index period of 73 kyr.<ref>{{cite journal | vauthors = Brzostowski M |title=Martian Milankovic Cycles, a Constraint for Understanding Martian Geology? |journal=Western Pacific Geophysics Meeting, Supplement to Eos, Transactions, American Geophysical Union |year=2004 |volume=85 |issue=28 |page=WP11}}</ref><ref>{{cite web | vauthors = Brzostowski M |title=Milankovic Cycles on Mars and the Impact on Economic Exploration |url=https://ace.aapg.org/2020/technical-program/program/wednesday-presentations |website=ACE 2020 |publisher=American Association of Petroleum Geologists |access-date=11 December 2020 |year=2020}}</ref>

[[Mars]] has no moon large enough to stabilize its obliquity, which has varied from 10 to 70 degrees. This would explain recent observations of its surface compared to evidence of different conditions in its past, such as the extent of its [[Martian polar ice caps|polar caps]].<ref>{{Cite journal | bibcode=2008GeoRL..3518201S| title=Temperature response of Mars to Milankovitch cycles| journal=Geophysical Research Letters| volume=35| issue=18| pages=L18201| vauthors = Schorghofer N | s2cid=16598911| year=2008| doi=10.1029/2008GL034954| doi-access=}}</ref><ref>{{cite web | url=http://ams.confex.com/ams/90annual/techprogram/paper_165827.htm| title=3.5 Modeling Milankovitch cycles on Mars (2010 – 90; Annual Symp Planet Atmos)| publisher= Confex}}</ref>

===Outer Solar system===
Saturn's moon [[Titan (moon)|Titan]] has a cycle of approximately 60,000 years that could change the location of the [[methane]] lakes.<ref>{{cite web | url=http://www.universetoday.com/46308/lake-asymmetry-on-titan-explained/| title=Lake Asymmetry on Titan Explained| last=Wethington |first=Nicholos |date=30 November 2009}}</ref> Neptune's moon [[Triton (moon)|Triton]] has a variation similar to Titan's, which could cause its solid [[nitrogen]] deposits to migrate over long time scales.<ref>{{cite web | url=http://www.livescience.com/1349-sun-blamed-warming-earth-worlds.html| title=Sun Blamed for Warming of Earth and Other Worlds| work=LiveScience.com| date=12 March 2007}}</ref>

===Exoplanets===
Scientists using computer models to study extreme axial tilts have concluded that high obliquity could cause extreme climate variations, and while that would probably not render a planet uninhabitable, it could pose difficulty for land-based life in affected areas. Most such planets would nevertheless allow development of both simple and more complex lifeforms.<ref>{{cite journal| vauthors=Williams DM, Pollard P| title=Earth-like worlds on eccentric orbits: excursions beyond the habitable zone| journal=Inter. J. Astrobio.| volume=1| issue=1| pages=21–9| year=2002| url=http://physics.bd.psu.edu/faculty/williams/3DEarthClimate/ija2003.pdf| doi=10.1017/s1473550402001064| bibcode=2002IJAsB...1...61W| s2cid=37593615| access-date=17 September 2009| archive-date=22 August 2013| archive-url=https://web.archive.org/web/20130822060604/http://physics.bd.psu.edu/faculty/williams/3DEarthClimate/ija2003.pdf| url-status=dead}}</ref> Although the obliquity they studied is more extreme than Earth ever experiences, there are scenarios 1.5 to 4.5&nbsp;billion years from now, as the Moon's stabilizing effect lessens, where obliquity could leave its current range and the poles could eventually point almost directly at the Sun.<ref>{{cite journal | vauthors = Neron de Surgy O, Laskar J | title=On the long term evolution of the spin of the Earth | journal=Astronomy and Astrophysics | volume=318 | pages=975–989 |date=February 1997 | bibcode=1997A&A...318..975N }}</ref>

== See also ==
* {{slink|Cenomanian-Turonian boundary event|Milankovitch cycles}}
* {{slink|Supercontinent|Milankovitch cycles}}

== References ==
{{reflist}}

== Bibliography ==
{{refbegin}}
* {{cite journal|vauthors=Edvardsson S, Karlsson KG, Engholm M |title=Accurate spin axes and solar system dynamics: Climatic variations for the Earth and Mars|journal=[[Astronomy and Astrophysics]]|volume=384|year=2002|pages=689–701|doi=10.1051/0004-6361:20020029|issue=2|bibcode = 2002A&A...384..689E |doi-access=free}} ''This is the first work that investigated the derivative of the ice volume in relation to insolation (page 698).''
*[https://news.climate.columbia.edu/2018/05/07/milankovitch-cycles-deep-time In Ancient Rocks Scientists See a Climate Cycle Working Across Deep Time (Columbia Climate School, Kevin Krajick, May 7, 2018)] 
* {{cite journal | vauthors = Kaufmann RK, Juselius K | title= Testing competing forms of the Milankovitch hypothesis | journal= [[Paleoceanography (journal)|Paleoceanography]] | year= 2016 | volume=31| issue= 2 | doi= 10.1002/2014PA002767 | pages=286–297| bibcode= 2016PalOc..31..286K | doi-access= free }}.
* {{cite journal | vauthors = Pälike H, Norris RD, Herrle JO, Wilson PA, Coxall HK, Lear CH, Shackleton NJ, Tripati AK, Wade BS | display-authors = 6 | title = The heartbeat of the Oligocene climate system | journal = Science | volume = 314 | issue = 5807 | pages = 1894–8 | date = December 2006 | pmid = 17185595 | doi = 10.1126/science.1133822 | url = https://eprints.soton.ac.uk/42935/2/Paelike_etal_Science2006_supplMat.pdf | quote = A 13-million-year continuous record of [[Oligocene]] climate from the equatorial Pacific reveals a pronounced "heartbeat" in the global carbon cycle and periodicity of glaciations. | s2cid = 32334205 | bibcode = 2006Sci...314.1894P }}
* {{cite journal| vauthors = Roe G|s2cid=13230658|title=In defense of Milankovitch|journal=[[Geophysical Research Letters]]|volume=33|year=2006|pages=L24703|doi=10.1029/2006GL027817|issue=24|bibcode=2006GeoRL..3324703R|doi-access=free}} ''This shows that Milankovitch theory fits the data extremely well, over the past million years, provided that we consider derivatives.''
* The oldest reference for Milankovitch cycles is: {{cite book | vauthors = Milankovitch M |title=Mathematische Klimalehre und Astronomische Theorie der Klimaschwankungen |series=Handbuch der Klimatologie |volume=1 Teil A |publisher=von Gebrüder Borntraeger |year=1930 |oclc=490063906}}
*[https://physicstoday.scitation.org/doi/10.1063/PT.3.4474 Tying celestial mechanics to Earth's ice age (Physics Today 73 (5), Maslin M. A. 01 May 2020)] 
* {{cite journal | vauthors = Zachos J, Pagani M, Sloan L, Thomas E, Billups K | title = Trends, rhythms, and aberrations in global climate 65 Ma to present | journal = Science | volume = 292 | issue = 5517 | pages = 686–93 | date = April 2001 | pmid = 11326091 | doi = 10.1126/science.1059412 | s2cid = 2365991 | bibcode = 2001Sci...292..686Z | url = http://doc.rero.ch/record/13508/files/PAL_E304.pdf }}<br />''This review article discusses cycles and great-scale changes in the global climate during the [[Cenozoic]] Era.''
{{refend}}

== External links ==
{{Commons-inline|Milankovitch cycles}}

{{Wikibooks-inline|Historical Geology|Milankovitch cycles}}
* Campisano, C. J. (2012) [https://www.nature.com/scitable/knowledge/library/milankovitch-cycles-paleoclimatic-change-and-hominin-evolution-68244581 Milankovitch Cycles, Paleoclimatic Change, and Hominin Evolution]. Nature Education Knowledge 4(3):5
* [https://web.archive.org/web/20121011002043/http://channel.nationalgeographic.com/channel/videos/ice-age-cycles/ Ice Age – Milankovitch Cycles – National Geographic Channel]
* [https://web.archive.org/web/20080729060933/http://www.agu.org/revgeophys/overpe00/node6.html The Milankovitch band], Internet Archive of [[American Geophysical Union]] lecture

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[[Category:Paleoclimatology]]
[[Category:Climate forcing]]
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[[Category:Periodic phenomena]]