# Milankovitch cycles

Last updated on 22 May 2017

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

The Earth's orbit varies between nearly circular and mildly 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, at different times in the year. In addition, the rotational tilt of the Earth (its obliquity), which causes the seasons as the Earth revolves around the Sun, 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 the two precessions is a cycle in which proximity to the Sun occurs during different astronomical seasons. If the Earth is closer to the Sun while the northern or southern hemisphere is tilted toward the Sun (is in summer), then both effects work together to heat that hemisphere. If the Earth is further from the Sun during summer, the greater distance slightly reduces the heat of summer.

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

Now, materials on Earth that have been unchanged for millennia are being studied to indicate the history of Earth's climate. A study of the chronology of Antarctic ice cores using oxygen-nitrogen ratios in air bubbles trapped in the ice, which appear to respond directly to the local insolation, concluded that the climatic response documented in the ice cores was driven by northern hemisphere insolation as proposed by the Milankovitch hypothesis. Analysis of deep-ocean cores and a seminal paper by Hays, Imbrie, and Shackleton provide additional validation of the Milankovitch hypothesis through physical artifacts. However, there are still several observations that the hypothesis does not explain.

Past and future Milankovitch cycles. VSOP allows prediction of past and future orbital parameters with great accuracy.
Shows variations in: obliquity (axial tilt) in blue (ε).
eccentricity in green (e).
longitude of perihelion in purple (sin(ϖ) ).
Precession index in dark red (e sin(ϖ) ), which together with obliquity, controls the seasonal cycle of insolation.
– Calculated daily-averaged insolation at the top of the atmosphere in black (${\displaystyle {\overline {Q}}^{\mathrm {day} }}$ ), on the day of the summer solstice at 65° N latitude.
– Benthic forams in dark red and – Vostok ice core in dark green show two distinct proxies for past global sea level and temperature, from ocean sediment and Antarctic ice respectively.
The vertical gray line shows current conditions, at 2 ky A.D.

## Earth’s movements

The Earth's rotation around its axis, and revolution around the Sun, evolve over time due to gravitational interactions with other bodies in the solar system. The variations are complex, but a few cycles are dominant. Milankovitch studied changes in the orbital eccentricity, obliquity, and precession of the Earth's movements. These changes 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 temperature more quickly than oceans, because of the mixing of surface and deep water and the fact that soil has a lower volumetric heat capacity than water.

### Orbital shape (eccentricity)

Circular orbit, no eccentricity
Orbit with 0.5 eccentricity; Earth's orbit is never this eccentric

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 (with the lowest eccentricity of 0.000055) and mildly elliptical (highest eccentricity of 0.0679) Its geometric or logarithmic mean is 0.0019. The major component of these variations occurs with a period of 413,000 years (eccentricity variation of ±0.012). Other components have 95,000-year and 125,000-year cycles (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 0.017 and decreasing.

Eccentricity varies primarily due to the gravitational pull of Jupiter and Saturn. However, the semi-major axis of the orbital ellipse remains unchanged; according to perturbation theory, which computes the evolution of the orbit, the semi-major axis is invariant. The orbital period (the length of a sidereal year) is also invariant, because according to Kepler's third law, it is determined by the semi-major axis.

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.

The relative increase in solar irradiation at closest approach to the Sun (perihelion) compared to the irradiation at the furthest distance (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% (5.1 million km). Perihelion presently occurs around January 3, while aphelion is around July 4. 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 always so small that the variation in solar irradiation is a minor factor in seasonal climate variation, compared to axial tilt and even compared to the relative ease of heating the larger land masses of the northern hemisphere.

Effect on lengths of seasons
Season durations
Year Northern
Hemisphere
Southern
Hemisphere
Date: GMT Season
duration
2005 Winter solstice Summer solstice 21 December 2005 18:35 88.99 days
2006 Spring equinox Autumn equinox 20 March 2006 18:26 92.75 days
2006 Summer solstice Winter solstice 21 June 2006 12:26 93.65 days
2006 Autumn equinox Spring equinox 23 September 2006 4:03 89.85 days
2006 Winter solstice Summer solstice 22 December 2006 0:22 88.99 days
2007 Spring equinox Autumn equinox 21 March 2007 0:07 92.75 days
2007 Summer solstice Winter solstice 21 June 2007 18:06 93.66 days
2007 Autumn equinox Spring equinox 23 September 2007 9:51 89.85 days
2007 Winter solstice Summer solstice 22 December 2007 06:08

The seasons are quadrants of the Earth's orbit, marked by the two solstices and the two equinoxes. 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. The Earth spends less time near perihelion and more time near aphelion. This means that the lengths of the seasons vary.

Perihelion currently occurs around January 3, so the Earth's greater velocity shortens winter and autumn in the northern hemisphere. Summer in the northern hemisphere is 4.66 days longer than winter, and spring is 2.9 days longer than autumn.

Greater eccentricity increases the variation in the Earth's orbital velocity. However, currently, the Earth's orbit is becoming less eccentric (more nearly circular). This will make the seasons more similar in length.

### Axial tilt (obliquity)

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 BCE. It is now in the decreasing phase of its cycle, and will reach its minimum around the year 11,800 CE.

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.

The current trend of decreasing tilt, by itself, will promote milder seasons (warmer winters and colder summers), as well as an overall cooling trend. Because most of the planet's snow and ice lies at high latitude, decreasing tilt may encourage the onset of an ice age for two reasons: There is less overall summer insolation, and also less insolation at higher latitudes, which melts less of the previous winter's snow and ice.

### Axial precession

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 25,771.5 years. This motion means that eventually Polaris will no longer be the north pole star. It is caused by the tidal forces exerted by the Sun and the Moon on the solid Earth; both contribute roughly equally to this effect.

Currently, perihelion occurs during the southern hemisphere's summer. This means that solar radiation due to (1) axial tilt aiming the southern hemisphere toward the Sun and (2) the Earth's proximity to the Sun, both reach maximum during the summer and both reach minimum during the winter. Their effects on heating are 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 forces work in opposite directions, resulting in less extreme variation.

In about 13,000 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.

### Apsidal precession

Planets orbiting the Sun follow elliptical (oval) orbits that rotate gradually over time (apsidal precession). The eccentricity of this ellipse is exaggerated for visualization. Most orbits in the Solar System have a much smaller eccentricity, making them nearly circular.

In addition, the orbital ellipse itself precesses in space, in an irregular fashion, completing a full cycle every 112,000 years relative to the fixed stars. 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.

Apsidal precession combines with the 25,771.5-year cycle of axial precession (see above) to vary the position in the year that the Earth reaches perihelion. Apsidal precession shortens this period to 23,000 years on average (varying between 20,800 and 29,000 years).

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 above) will affect different seasons. Winter, for instance, will be in a different section of the orbit. When the Earth's apsides 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.

### 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 is 1.57°.

Milankovitch did not study precession. It was discovered more recently and measured, relative to Earth's orbit, to have a period of about 70,000 years.

However, when measured independently of Earth's orbit, but relative to the invariable plane (the plane that represents the angular momentum of the Solar System, approximately the orbital plane of Jupiter), 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.

## Problems

The nature of sediments can vary in a cyclic fashion, and these cycles can be displayed in the sedimentary record. Here, cycles can be observed in the colouration and resistance of different strata.

Artifacts taken from the Earth have been studied to infer the cycles of past climate. These fit so well with the orbital periods that they support Milankovitch's hypothesis that variations in the Earth's orbit influence climate. However, the fit is not perfect, and problems remain reconciling theory with observations.

### 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. However, subsequent research has shown that ice age cycles of the Quaternary glaciation over the last million years have been at a 100,000-year period, which matches the eccentricity cycle.

Various explanations for this discrepancy have been proposed, including frequency modulation or various feedbacks (from carbon dioxide, cosmic rays, or from 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.

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."

Some have argued that the length of the climate record is insufficient to establish a statistically significant relationship between climate and eccentricity variations.

### The transition problem

Variations of Cycle Times, curves determined from ocean sediments

In fact, from 1–3 million years ago, climate cycles did match the 41,000-year cycle in obliquity. After 1 million years ago, this switched to the 100,000-year cycle matching eccentricity. The transition problem refers to the need to explain what changed 1 million years ago.

### The unsplit peak problem

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. However, some researchers say the records do not show these peaks, but only show a single cycle of 100,000 years.

### Stage 5 problem

Deep-sea core samples show that the interglacial interval known as 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.)

### Effect exceeds cause

420,000 years of ice core data from Vostok, Antarctica research station

Artifacts show that the variation in Earth's climate is much more extreme than the variation in the intensity of solar radiation calculated as the Earth's orbit evolves. If orbital forcing causes climate change, science needs to explain why the observed effect is amplified compared to the theoretical effect.

Some climate systems exhibit amplification (positive feedback) and damping responses (negative feedback). An example of amplification would be if, with the land masses around 65° north covered in year-round ice, solar energy were reflected away. Amplification would mean that an ice age induces changes that impede orbital forcing from ending the ice age.

The Earth's current orbital inclination is 1.57° (see above). Earth presently moves through the invariable plane around January 9 and July 9. At these times, there is an increase in meteors and noctilucent clouds. If this is because there is a disk of dust and debris in the invariable plane, then when the Earth's orbital inclination is near 0° and it is orbiting through this dust, materials could be accreted into the atmosphere. This process could explain the narrowness of the 100,000-year climate cycle.

## Present and future conditions

Past and future 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. Blue dot is current conditions, at 2 ky A.D.

Since orbital variations are predictable, any model that relates orbital variations to climate can be run forward to predict future climate.

Astronomical calculations show that 65° N summer insolation should increase gradually over the next 25,000 years. Earth's orbit will become less eccentric for about the next 100,000 years, so changes in 65° N summer insolation will be dominated by changes in obliquity. No declines in this insolation sufficient to cause a glacial period are expected in the next 50,000 years.

An often-cited 1980 orbital model by Imbrie and Imbrie predicted "that the long-term cooling trend that began some 6,000 years ago will continue for the next 23,000 years." More recent work suggests that the current warm climate may last another 50,000 years.

However, the mechanism by which orbital forcing influences climate is not well understood nor definitive:

1. Earth is not homogenous. Milankovitch did not relate Earth's ice ages to the total amount of solar radiation (insolation) reaching Earth but to the insolation striking 65° N in summer, due to the relative ease of heating the larger land masses of the northern hemisphere. Later studies have suggested that insolation hitting ice would simply be reflected away.
2. Earth is not inert. Geology affects climate; not just from the heat of the Earth's core, but from changes to the atmosphere caused by volcanic eruptions. Even the configuration of land masses and ice masses changes over time due to continental drift.
3. The flourishing and industrial activity of humankind may affect climate (may contribute anthropogenic effects) in ways not predicted by orbital models. Many studies have concluded that detectable increases in greenhouse gas in the 20th and 21st centuries would trap energy and result in a warmer climate. A previous theory was that industrial particulate pollution of the atmosphere would block solar radiation and result in cooling.
4. The article Future of earth presents a variety of infrequent events, such as collisions of bodies within the solar system and encounters with bodies outside the solar system, with the potential to make past or future climate deviate from a mathematical model of orbital forcing.

## Effects beyond Earth

Other bodies in the Solar System undergo geological effects associated with orbital fluctuations like the Milankovitch cycles, though not as intense or complex as the Earth's cycles. These cycles cause the movement of elements in the solid state:

Mars

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 polar caps.

Saturn

Saturn's moon Titan has a ~60,000-year cycle that changes the location of the methane lakes.

Neptune

Neptune's moon Triton has a similar variation to Titan with respect to migration of solid nitrogen deposits over long time scales.

Exoplanets

Scientists using computer models to study extreme axial tilts have concluded that high obliquity would cause climate extremes that would threaten Earth-like life. They noted that high obliquity would not likely sterilize a planet completely, but would make it harder for warm-blooded, land-based life to thrive. Although the obliquity they studied is more extreme than Earth ever experiences, there are scenarios 1.5 to 4.5 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.

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