Milankovitch cycles
Encyclopedia
Milankovitch theory describes the collective effects of changes in the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

's movements upon its climate, named after Serbia
Serbia
Serbia , officially the Republic of Serbia , is a landlocked country located at the crossroads of Central and Southeast Europe, covering the southern part of the Carpathian basin and the central part of the Balkans...

n civil engineer
Civil engineering
Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works like roads, bridges, canals, dams, and buildings...

and mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

Milutin Milanković
Milutin Milankovic
Milutin Milanković was a Serbian geophysicist and civil engineer, best known for his theory of ice ages, suggesting a relationship between Earth's long-term climate changes and periodic changes in its orbit, now known as Milankovitch cycles. Milanković gave two fundamental contributions to global...

, who worked on it during First World War internment. Milanković mathematically theorized that variations in eccentricity, axial tilt
Axial tilt
In astronomy, axial tilt is the angle between an object's rotational axis, and a line perpendicular to its orbital plane...

, and precession
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...

of the Earth's orbit determined climatic patterns on Earth through orbital forcing
Orbital forcing
Orbital forcing is the effect on climate of slow changes in the tilt of the Earth's axis and shape of the orbit . These orbital changes change the total amount of sunlight reaching the Earth by up to 25% at mid-latitudes...

.

The Earth's axis completes one full cycle of precession
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...

approximately every 26,000 years. At the same time the elliptical orbit rotates
Apsidal precession
In celestial mechanics, perihelion precession, apsidal precession or orbital precession is the precession of the orbit of a celestial body. More precisely it is the gradual rotation of the line joining the apsides of an orbit, which are the points of closest and farthest approach...

more slowly. The combined effect of the two precessions leads to a 21,000-year period between the seasons and the orbit. In addition, the angle between Earth's rotational axis and the normal to the plane of its orbit (obliquity) oscillates between 22.1 and 24.5 degrees on a 41,000-year cycle. It is currently 23.44 degrees and decreasing.

Joseph Alphonse Adhemar was a French mathematician. He was the first to suggest that ice ages were controlled by astronomical forces in his 1842 book Revolutions of the Sea....

, James Croll
James Croll
James Croll was a 19th century Scottish scientist who developed a theory of climate change based on changes in the Earth's orbit.-Life:...

and others, but verification was difficult due to the absence of reliably dated evidence and doubts as to exactly which periods were important. Not until the advent of deep-ocean cores and a seminal paper by Hays
James Hays
James D. Hays is a professor of Earth and environmental sciences at Columbia University's Lamont-Doherty Earth Observatory. Hays founded and led the CLIMAP project, which collected sea floor sediment data to study surface sea temperatures and paleoclimatological conditions 18,000 years ago.Hays is...

, Imbrie
John Imbrie
John Imbrie is an American paleoceanographer best known for his work on the theory of ice ages.After serving with the 10th Mountain Division in Italy during World War II, Imbrie earned his bachelor's degree from Princeton University. He then went on to receive a Ph.D. from Yale University in 1951...

, and Shackleton
Nicholas Shackleton
Sir Nicholas John Shackleton FRS was a British geologist and climatologist who specialised in the Quaternary Period...

, "Variations in the Earth's Orbit: Pacemaker of the Ice Ages", in Science
Science (journal)
Science is the academic journal of the American Association for the Advancement of Science and is one of the world's top scientific journals....

(1976) did the theory attain its present state.

## Earth’s movements

As the Earth spins around its axis and orbits around the Sun, several quasi-periodic variations occur due to gravitational interactions
Perturbation (astronomy)
Perturbation is a term used in astronomy in connection with descriptions of the complex motion of a massive body which is subject to appreciable gravitational effects from more than one other massive body....

. Although the curves have a large number of sinusoidal components, a few components are dominant. Milankovitch studied changes in the orbital eccentricity
Orbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...

, obliquity, and precession of Earth's movements. Such changes in movement and orientation alter the amount and location of solar radiation reaching the Earth. This is known as solar forcing (an example of radiative forcing
In climate science, radiative forcing is generally defined as the change in net irradiance between different layers of the atmosphere. Typically, radiative forcing is quantified at the tropopause in units of watts per square meter. A positive forcing tends to warm the system, while a negative...

). Changes near the north polar area, about 65 degrees North, are considered important due to the great amount of land, which reacts to such changes quicker than the oceans do. Land masses respond to temperature change more quickly than oceans which self cool by mixing of surface and deep water, the movement of cool and warm currents and suface evaporation, and the fact that the specific heat of solids is generally lower than that of water (i.e., it takes a smaller change in the amount of heat a given mass of a solid contains to change its temperature by the same number of degrees than it would take to change the same mass of water's temperature by the same number of degrees.)

### Orbital shape (eccentricity)

The Earth's orbit is an ellipse
Ellipse
In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...

. The eccentricity is a measure of the departure of this ellipse from circularity. The shape of the Earth's orbit varies in time between nearly circular (low eccentricity of 0.005) and mildly elliptical (high eccentricity of 0.058) with the mean eccentricity of 0.028. The major component of these variations occurs on a period of 413,000 years (eccentricity variation of ±0.012). A number of other terms vary between components 95,000 and 125,000 years (with a beat period 400,000 years), and loosely combine into a 100,000-year cycle (variation of −0.03 to +0.02). The present eccentricity is 0.017.

If the Earth were the only planet orbiting our Sun, the eccentricity of its orbit would not perceptibly vary even over a period of a million years. The Earth's eccentricity varies primarily due to interactions with the gravitational fields of Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...

and Saturn
Saturn
Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...

. As the eccentricity of the orbit evolves, the semi-major axis
Semi-major axis
The major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape...

of the orbital ellipse remains unchanged. From the perspective of the perturbation theory
Perturbation (astronomy)
Perturbation is a term used in astronomy in connection with descriptions of the complex motion of a massive body which is subject to appreciable gravitational effects from more than one other massive body....

used in celestial mechanics to compute the evolution of the orbit, the semi-major axis is an adiabatic invariant
An adiabatic invariant is a property of a physical system that stays constant when changes occur slowly.In thermodynamics, an adiabatic process is a change that occurs without heat flow, and slowly compared to the time to reach equilibrium. In an adiabatic process, the system is in equilibrium at...

. According to Kepler's third law the period of the orbit is determined by the semi-major axis. It follows that the Earth's orbital period, the length of a sidereal year
Sidereal year
A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. Hence it is also the time taken for the Sun to return to the same position with respect to the fixed stars after apparently travelling once around the ecliptic. It was equal to at noon 1 January...

, also remains unchanged as the orbit evolves. As the semi-minor axis
Semi-minor axis
In geometry, the semi-minor axis is a line segment associated with most conic sections . One end of the segment is the center of the conic section, and it is at right angles with the semi-major axis...

is decreased with the eccentricity increase, the seasonal changes increase. But the mean solar irradiation for the planet changes only slightly for small eccentricity, due to Kepler's second law.

The same average irradiation does not correspond to the average of corresponding temperatures (due to non-linearity of the Stefan–Boltzmann law). For an irradiation with corresponding temperature 20°C and its symmetric variation ±50% (e.g. from the seasons change) we obtain asymmetric variation of corresponding temperatures with their average 16°C (i.e. deviation −4°C). And for the irradiation variation during a day (with its average corresponding also to 20°C) we obtain the average temperature (for zero thermal capacity) −113°C.

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 4 times the eccentricity. For the current orbital eccentricity this amounts to a variation in incoming solar radiation of about 6.8%, while the current difference between perihelion and aphelion is only 3.4% (5.1 million km
Kilometre
The kilometre is a unit of length in the metric system, equal to one thousand metres and is therefore exactly equal to the distance travelled by light in free space in of a second...

). Perihelion presently occurs around January 3, while aphelion is around July 4. When the orbit is at its most elliptical, the amount of solar radiation at perihelion will be about 23% more than at aphelion.
Season (northern hemisphere) durations
Year Date: GMT Season duration
2005 Winter solstice 12/21/2005 18:35 88.99 days
2006 Spring equinox 3/20/2006 18:26 92.75 days
2006 Summer solstice 6/21/2006 12:26 93.65 days
2006 Autumn equinox 9/23/2006 4:03 89.85 days
2006 Winter solstice 12/22/2006 0:22 88.99 days
2007 Spring equinox 3/21/2007 0:07 92.75 days
2007 Summer solstice 6/21/2007 18:06 93.66 days
2007 Autumn equinox 9/23/2007 9:51 89.85 days
2007 Winter solstice 12/22/2007 06:08

Orbital mechanics requires that the length of the seasons be proportional to the areas of the seasonal quadrants, so when the eccentricity is extreme, the Earth's orbital motion becomes more nonuniform and the lengths of the seasons change. When autumn and winter occur at closest approach, as is the case currently in the northern hemisphere, the earth is moving at its maximum velocity and therefore autumn and winter are slightly shorter than spring and summer. Thus, summer in the northern hemisphere is 4.66 days longer than winter and spring is 2.9 days longer than autumn. But as the orientation of Earth's orbit changes relative to the Vernal Equinox due to apsidal precession the way the length of the seasons are altered by the nonuniform motion changes since different sections of the orbit are involved. When the Earth's apsides are aligned with the equinoxes the length of Spring and Summer (together) equals that of Autumn and Winter. When they are aligned with the solstices either Spring and Summer or Autumn and Winter will be at its longest. Increasing the eccentricity lengthens the time spent near aphelion and shortens the time near perihelion.

Changes to the eccentricity do not by themselves change the length of the anomalistic year or the Earth's mean motion along its orbit since they are both functions of the semi-major axis.

### Axial tilt (obliquity)

The angle of the Earth's axial tilt (obliquity of the ecliptic
Ecliptic
The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...

) varies with respect to the plane of the Earth's orbit. These slow 2.4° obliquity variations are roughly periodic, taking approximately 41,000 years to shift between a tilt of 22.1° and 24.5° and back again. When the obliquity increases, the amplitude of the seasonal cycle in insolation
Insolation
Insolation is a measure of solar radiation energy received on a given surface area in a given time. It is commonly expressed as average irradiance in watts per square meter or kilowatt-hours per square meter per day...

increases, with summers in both hemispheres receiving more radiative flux from the Sun, and winters less. Conversely, when the obliquity decreases, summers receive less insolation and winters more.

But these changes of opposite sign in summer and winter are not of the same magnitude everywhere on the Earth's surface. At high latitude the annual mean insolation increases with increasing obliquity, while lower latitudes experience a reduction in insolation. Cooler summers are suspected of encouraging the onset of an ice age
Ice age
An ice age or, more precisely, glacial age, is a generic geological period of long-term reduction in the temperature of the Earth's surface and atmosphere, resulting in the presence or expansion of continental ice sheets, polar ice sheets and alpine glaciers...

by melting less of the previous winter's precipitation. Because most of the planet's snow and ice lies at high latitude, it can be argued that lower obliquity favors ice ages for two reasons: the reduction in overall summer insolation and the additional reduction in mean insolation at high latitude.

Scientists using computer models to study more extreme tilts than those that actually occur have concluded that climate extremes at high obliquity would be particularly threatening to advanced forms of life that presently exist on Earth. They noted that high obliquity would not likely sterilize a planet completely, but would make it harder for fragile, warm-blooded land-based life to thrive as it does today.

Currently the Earth is tilted at 23.44 degrees from its orbital plane, roughly halfway between its extreme values. The tilt is in the decreasing phase of its cycle, and will reach its minimum value around the year 10,000 CE
Common Era
Common Era ,abbreviated as CE, is an alternative designation for the calendar era originally introduced by Dionysius Exiguus in the 6th century, traditionally identified with Anno Domini .Dates before the year 1 CE are indicated by the usage of BCE, short for Before the Common Era Common Era...

. This trend, by itself, tends to make winters warmer and summers colder with an overall cooling trend leading to an ice age, but the 20th century instrumental temperature record
Instrumental temperature record
The instrumental temperature record shows fluctuations of the temperature of the global land surface and oceans. This data is collected from several thousand meteorological stations, Antarctic research stations and satellite observations of sea-surface temperature. Currently, the longest-running...

shows a sudden rise in global temperatures and a concurring glacial melt has led some to attribute recent changes to greenhouse gas
Greenhouse gas
A greenhouse gas is a gas in an atmosphere that absorbs and emits radiation within the thermal infrared range. This process is the fundamental cause of the greenhouse effect. The primary greenhouse gases in the Earth's atmosphere are water vapor, carbon dioxide, methane, nitrous oxide, and ozone...

emissions.

### Axial precession

Precession is the trend in the direction of the Earth's axis of rotation relative to the fixed stars, with a period of roughly 26,000 years. This gyroscopic motion is due to the tidal forces exerted by the sun and the moon on the solid Earth, which has the shape of an oblate spheroid rather than a sphere. The sun and moon contribute roughly equally to this effect.

When the axis points toward the Sun in perihelion, one polar hemisphere has a greater difference between the seasons while the other has milder seasons. The hemisphere that is in summer at perihelion receives much of the corresponding increase in solar radiation, but that same hemisphere in winter at aphelion has a colder winter. The other hemisphere will have a relatively warmer winter and cooler summer.

When the Earth's axis is aligned such that aphelion and perihelion occur near the equinoxes, the Northern and Southern Hemispheres will have similar contrasts in the seasons.

At present, perihelion occurs during the southern hemisphere's summer, and aphelion is reached during the southern winter. Thus the southern hemisphere seasons are somewhat more extreme than the northern hemisphere seasons, when other factors are equal.

### Apsidal precession

In addition, the orbital ellipse itself precesses in space, primarily as a result of interactions with Jupiter and Saturn. This orbital precession is in the same sense to the gyroscopic motion of the axis of rotation, shortening the period of the precession of the equinoxes with respect to the perihelion from 25,771.5 to ~21,636 years. Apsidal precession occurs in the plane of the Ecliptic and alters the orientation of the Earth's orbit relative to the Ecliptic. In combination with changes to the eccentricity it alters the length of the seasons.

### Orbital inclination

The inclination
Inclination
Inclination in general is the angle between a reference plane and another plane or axis of direction.-Orbits:The inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit...

of Earth's orbit drifts up and down relative to its present orbit. Milankovitch did not study this three-dimensional movement. This movement is known as "precession of the ecliptic" or "planetary precession".

More recent researchers noted this drift and that the orbit also moves relative to the orbits of the other planets. The invariable plane
Invariable plane
The invariable plane of a planetary system, also called Laplace's invariable plane, is the plane passing through its barycenter perpendicular to its angular momentum vector. In the Solar System, about 98% of this effect is contributed by the orbital angular momenta of the four jovian planets...

, the plane that represents the angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

of the solar system, is approximately the orbital plane of Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...

. The inclination
Inclination
Inclination in general is the angle between a reference plane and another plane or axis of direction.-Orbits:The inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit...

of Earth's orbit drifts up and down relative to its present orbit with a cycle having a period of about 70,000 years. The inclination of the Earth's orbit has a 100,000 year cycle relative to the invariable plane. This is very similar to the 100,000 year eccentricity period. This 100,000-year cycle closely matches the 100,000-year pattern of ice ages.

It has been proposed that a disk of dust and other debris exists in the invariable plane, and this affects the Earth's climate through several possible means. The Earth presently moves through this plane around January 9 and July 9, when there is an increase in radar-detected meteor
METEOR
METEOR is a metric for the evaluation of machine translation output. The metric is based on the harmonic mean of unigram precision and recall, with recall weighted higher than precision...

s and meteor-related noctilucent cloud
Noctilucent cloud
Night clouds or Noctilucent clouds are tenuous cloud-like phenomena that are the "ragged-edge" of a much brighter and pervasive polar cloud layer called polar mesospheric clouds in the upper atmosphere, visible in a deep twilight. They are made of crystals of water ice. The name means roughly night...

s.

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 (Kawamura et al., Nature, 23 August 2007, vol 448, pp 912–917). This is an additional validation of the Milankovitch hypothesis by a relatively novel method, and is inconsistent with the "inclination" theory of the 100,000-year cycle.

## Problems

Because the observed periodicities of climate fit so well with the orbital periods, the orbital theory has overwhelming support. Nonetheless, there are several difficulties in reconciling theory with observations.

### 100,000-year problem

The 100,000-year problem is that the eccentricity variations have a significantly smaller impact on solar forcing than precession or obliquity and hence might be expected to produce the weakest effects.
The greatest observed response is at the 100,000-year timescale, while the theoretical forcing is smaller at this scale, in regard to the ice age
Ice age
An ice age or, more precisely, glacial age, is a generic geological period of long-term reduction in the temperature of the Earth's surface and atmosphere, resulting in the presence or expansion of continental ice sheets, polar ice sheets and alpine glaciers...

s.
However, observations show that during the last 1 million years, the strongest climate signal is the 100,000-year cycle. In addition, despite the relatively great 100,000-year cycle, some have argued that the length of the climate record is insufficient to establish a statistically significant relationship between climate and eccentricity variations. Various explanations for this discrepancy have been proposed, including frequency modulation or various feedbacks (from carbon dioxide
Carbon dioxide
Carbon dioxide is a naturally occurring chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom...

, cosmic rays, or from ice sheet dynamics
Ice sheet dynamics
Ice sheet dynamics describe the motion within large bodies of ice, such those currently on Greenland and Antarctica. Ice motion is dominated by the movement of glaciers, whose gravity-driven activity is controlled by two main variable factors: the temperature and strength of their bases...

).
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.

### 400,000-year problem

The 400,000-year problem is that the eccentricity variations have a strong 400,000-year cycle. That cycle is only clearly present in climate records older than the last million years. If the 100ka variations are having such a strong effect, the 400ka variations might also be expected to be apparent. This is also known as the stage 11 problem, after the interglacial in marine isotopic stage
Marine isotopic stage
Marine isotope stages , marine oxygen-isotope stages, or oxygen isotope stages , are alternating warm and cool periods in the Earth's paleoclimate, deduced from oxygen isotope data reflecting changes in temperature derived from data from deep sea core samples...

11 which would be unexpected if the 400,000-year cycle has an impact on climate. The relative absence of this periodicity in the marine isotopic record may be due, at least in part, to the response times of the climate system components involved—in particular, the carbon cycle
Carbon cycle
The carbon cycle is the biogeochemical cycle by which carbon is exchanged among the biosphere, pedosphere, geosphere, hydrosphere, and atmosphere of the Earth...

.

### Stage 5 problem

The stage 5 problem refers to the timing of the penultimate interglacial (in marine isotopic stage
Marine isotopic stage
Marine isotope stages , marine oxygen-isotope stages, or oxygen isotope stages , are alternating warm and cool periods in the Earth's paleoclimate, deduced from oxygen isotope data reflecting changes in temperature derived from data from deep sea core samples...

5) which appears to have begun ten thousand years in advance of the solar forcing hypothesized to have caused it (the causality problem).

### Effect exceeds cause

The effects of these variations are primarily believed to be due to variations in the intensity of solar radiation upon various parts of the globe. Observations show climate behavior is much more intense than the calculated variations. Various internal characteristics of climate systems are believed to be sensitive to the insolation changes, causing amplification (positive feedback
Positive feedback
Positive feedback is a process in which the effects of a small disturbance on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system that responds to a perturbation in a way that reduces its effect is...

) and damping responses (negative feedback
Negative feedback
Negative feedback occurs when the output of a system acts to oppose changes to the input of the system, with the result that the changes are attenuated. If the overall feedback of the system is negative, then the system will tend to be stable.- Overview :...

).

### The unsplit peak problem

The unsplit peak problem refers to the fact that eccentricity has cleanly resolved variations at both the 95 and 125ka periods. A sufficiently long, well-dated record of climate change should be able to resolve both frequencies, but some researchers interpret climate records of the last million years as showing only a single spectral peak at 100ka periodicity. It is debatable whether the quality of existing data ought to be sufficient to resolve both frequencies over the last million years.

### The transition problem

The transition problem refers to the switch in the frequency of climate variations 1 million years ago. From 1–3 million years, climate had a dominant mode matching the 41ka cycle in obliquity. After 1 million years ago, this switched to a 100ka variation matching eccentricity, for which no reason has been established.

### Identifying dominant factor

Milankovitch believed that decreased summer insolation in northern high latitudes was the dominant factor leading to glaciation, which led him to (incorrectly) deduce an approximate 41ka period for ice ages. Subsequent research has shown that the 100ka eccentricity cycle is more important, resulting in 100,000-year ice age
Ice age
An ice age or, more precisely, glacial age, is a generic geological period of long-term reduction in the temperature of the Earth's surface and atmosphere, resulting in the presence or expansion of continental ice sheets, polar ice sheets and alpine glaciers...

cycles of the Quaternary glaciation
Quaternary glaciation
Quaternary glaciation, also known as the Pleistocene glaciation, the current ice age or simply the ice age, refers to the period of the last few million years in which permanent ice sheets were established in Antarctica and perhaps Greenland, and fluctuating ice sheets have occurred elsewhere...

over the last few million years.

## Present and future conditions

As mentioned above, at present, perihelion occurs during the southern hemisphere's summer and aphelion during the southern winter. Thus the southern hemisphere seasons should tend to be somewhat more extreme than the northern hemisphere seasons. The relatively low eccentricity of the present orbit results in a 6.8% difference in the amount of solar radiation during summer in the two hemispheres.

Since orbital variations are predictable, if one has a model that relates orbital variations to climate, it is possible to run such a model forward to "predict" future climate. Two caveats are necessary: that anthropogenic effects may modify or even overwhelm orbital effects; and that the mechanism by which orbital forcing
Orbital forcing
Orbital forcing is the effect on climate of slow changes in the tilt of the Earth's axis and shape of the orbit . These orbital changes change the total amount of sunlight reaching the Earth by up to 25% at mid-latitudes...

influences climate is not well understood.

The amount of solar radiation (insolation
Insolation
Insolation is a measure of solar radiation energy received on a given surface area in a given time. It is commonly expressed as average irradiance in watts per square meter or kilowatt-hours per square meter per day...

) in the Northern Hemisphere at 65° N seems to be related to occurrence of an ice age. Astronomical calculations show that 65° N summer insolation should increase gradually over the next 25,000 years. A regime of eccentricity lower than the current value will last for about the next 100,000 years. Changes in northern hemisphere summer insolation will be dominated by changes in obliquity ε. No declines in 65° N summer insolation, sufficient to cause a glacial period, are expected in the next 50,000 years.

An often-cited 1980 study by Imbrie
John Imbrie
John Imbrie is an American paleoceanographer best known for his work on the theory of ice ages.After serving with the 10th Mountain Division in Italy during World War II, Imbrie earned his bachelor's degree from Princeton University. He then went on to receive a Ph.D. from Yale University in 1951...

and Imbrie determined that, "Ignoring anthropogenic and other possible sources of variation acting at frequencies higher than one cycle per 19,000 years, this model predicts that the long-term cooling trend which began some 6,000 years ago will continue for the next 23,000 years."

More recent work by Berger and Loutre suggests that the current warm climate may last another 50,000 years.

The best chances for a decline in northern hemisphere summer insolation that would be sufficient for triggering a glacial period is at 130,000 years or possibly as far out at 620,000 years.