Fall comes first, followed by winter, spring, and summer. The Earth's axis is tilted, and that is what gives us the 4 seasons. Since the Earth's axis is tilted, different parts of the globe are oriented towards the Sun at different times of the year.
Day length, or length of day, or length of daytime, is the time each day from the moment the upper limb of the sun's disk appears above the horizon during sunrise to the moment when the upper limb disappears below the horizon during sunset. Because of the diffusion and refraction of sunlight by the atmosphere, there is actually daylight even when the sun is slightly below the horizon. The period when it is still somewhat light even though the sun is below the horizon is called twilight.
In general, the length of a day varies throughout the year, and depends upon latitude. This variation is caused by the tilt of the Earth's axis of rotation with respect to the ecliptic plane of the Earth around the sun. At the solstice occurring about June 20–22, the north pole is tilted toward the sun, and therefore the northern hemisphere has days ranging in duration from just over 12 hours in the southern portion of the Tropic of Cancer to 24 hours in the Arctic Circle, while the southern hemisphere has days ranging in duration from just under 12 hours in the northern portion of the Tropic of Capricorn to zero in the Antarctic Circle. At the equinox occurring about September 22–23, the poles are neither tilted toward nor away from the sun, and the duration of a day is generally about 12 hours all over the Earth. At the solstice occurring about December 20–22, the south pole is tilted toward the sun, and therefore the southern hemisphere has days ranging in duration from just over 12 hours in the northern portion of the Tropic of Capricorn to 24 hours in the Antarctic Circle, whereas the northern hemisphere has days ranging in duration from just under 12 hours in the southern portion of the Tropic of Cancer to zero in the Arctic Circle. At the equinox occurring about March 19–21, the poles are again aligned so that the duration of a day is generally about 12 hours all over the Earth.
In each hemisphere, the higher the latitude, the shorter the day during winter. Between winter and summer solstice, the day's duration increases, and the rate of increase is larger the higher the latitude. A fast increase of day length is what allows a very short day on winter solstice at 60 degrees latitude (either north or south) to reach about 12 hours by the spring equinox, while a slower increase is required for a much longer day on winter solstice at 20 degrees latitude (again, either north or south) to reach 12 hours by the spring equinox. The rate of change of day duration is generally fastest at the equinoxes, although at high latitudes the change is similar for several weeks before and after the equinoxes. The rate of change of day duration at each solstice is zero as the change goes from positive to negative, or vice versa.
Some interesting facts are as follows:
More conveniently, atmospheric refraction is ignored and the center of the sun is often used in place of the upper limb for computing a day's duration. When sunrise and sunset do occur, the day duration can be computed as 2ωo/15°, where ωo is the sunset hour angle in degrees (°) given by the sunset equation. When sunrise and sunset do not occur during the course of a day, the day duration is either 0 or 24 hours.
400 million years ago, years lasted 410 days, meaning that days were 21 hours long. This is because the Earth's speed of rotation was once much faster than it is today. When the Earth formed, a day was around 6 hours long; it has been slowing gradually, but slowed more rapidly when liquid water began to form (~3.5Ga).
See Historical evidence of tidal acceleration
Effect of sun angle on climate
In astronomy, axial tilt, known to astronomers as obliquity, is the angle between an object's rotational axis, and its orbital axis, or, equivalently, the angle between its equatorial plane and orbital plane. It differs from orbital inclination.
Orientation of the axes is established by the right hand rule for both the rotation and the orbital motion. When the fingers of the right hand curl around in the direction of the object's rotation, the thumb points in the direction of its north pole (from which, looking back at the object, it appears to rotate counterclockwise). Similarly, when the fingers of the right hand curl around in the direction of the object's orbital motion, the thumb points in the direction of the north pole of the orbit (from which the object appears to move counter-clockwise in its orbit). The angle between these two poles is the obliquity. At an obliquity of 0°, the axes point in the same direction.
Because the planet Venus has an axial tilt of 177° its rotation can be considered retrograde, opposite that of most of the other planets. The north pole of Venus is "upside down" relative to its orbit. The planet Uranus has a tilt of 97°, hence it rotates "on its side", its north pole being almost in the plane of its orbit.
Over the course of an orbit, the angle of the axial tilt does not change, and the orientation of the axis remains the same relative to the background stars. This causes one pole to be directed toward the Sun on one side of the orbit, and the other pole on the other side, the cause of the seasons on the Earth.
Note that there are two standard methods of specifying tilt. The International Astronomical Union (IAU) defines the north pole as that which lies on the north side of the invariable plane of the Solar System; under this system Venus' tilt is 3°, it rotates retrograde, and the right hand rule does not apply. NASA defines the north pole with the right hand rule, as above; under this system, Venus is tilted 177° ("upside down") and rotates direct. The results are equivalent and neither system is more correct.
The Earth's orbital plane is known as the ecliptic plane, and the Earth's tilt is known to astronomers as the obliquity of the ecliptic, being the angle between the ecliptic and the celestial equator on the celestial sphere. It is denoted by the Greek letter ε.
The Earth currently has an axial tilt of about 23.4°. This value remains approximately the same relative to a stationary orbital plane throughout the cycles of precession. However, because the ecliptic (i.e. the Earth's orbit) moves due to planetary perturbations, the obliquity of the ecliptic is not a fixed quantity. At present, it is decreasing at a rate of about 47" per century (see below).
The exact angular value of the obliquity is found by observation of the motions of the Earth and planets over many years. Astronomers produce new fundamental ephemerides as the accuracy of observation improves and as the understanding of the dynamics increases, and from these ephemerides various astronomical values, including the obliquity, are derived.
Annual almanacs are published listing the derived values and methods of use. Until 1983, the Astronomical Almanac's angular value of the obliquity for any date was calculated based on the work of Newcomb, who analyzed positions of the planets until about 1895:
where is the obliquity and is tropical centuries from B1900.0 to the date in question.
From 1984, the Jet Propulsion Laboratory's DE series of computer-generated ephemerides took over as the fundamental ephemeris of the Astronomical Almanac. Obliquity based on DE200, which analyzed observations from 1911 to 1979, was calculated:
where hereafter is Julian centuries from J2000.0.
JPL's fundamental ephemerides have been continually updated. For instance, the Astronomical Almanac for 2010 specifies:
These expressions for the obliquity are intended for high precision over a relatively short time span, perhaps several centuries. J. Laskar computed an expression to order good to over 1000 years and several arcseconds over 10,000 years:
where here is multiples of 10,000 Julian years from][ J2000.0.
These expressions are for the so-called mean obliquity, that is, the obliquity free from short-term variations. Periodic motions of the Moon and of the Earth in its orbit cause much smaller (a few arcseconds) short-period (about 18.6 years) oscillations of the rotation axis of the Earth, known as nutation, which add a periodic component to Earth's obliquity. The true or instantaneous obliquity includes this nutation.
Using numerical methods to simulate Solar System behavior, long-term changes in Earth's orbit, and hence its obliquity, have been investigated over a period of several million years. For the past 5 million years, Earth's obliquity has varied between 22° 02' 33" and 24° 30' 16", with a mean period of 41,040 years. This cycle is a combination of precession and the largest term in the motion of the ecliptic. For the next 1 million years, the cycle will carry the obliquity between 22° 13' 44" and 24° 20' 50".
The Moon has a stabilizing effect on Earth's obliquity. Frequency map analysis suggests that, in the absence of the Moon, the obliquity can change rapidly due to orbital resonances and chaotic behavior of the Solar System, reaching as high as 90° in as little as a few million years. However, more recent numerical simulations suggest that even in the absence of the Moon, Earth's obliquity could be considerably more stable; varying only by about 20-25°. The Moon's stabilizing effect will continue for less than 2 billion years. If the Moon continues to recede from the Earth due to tidal acceleration, resonances may occur which will cause large oscillations of the obliquity.
The Earth's axis remains tilted in the same direction with reference to the background stars throughout a year (throughout its entire orbit). This means that one pole (and the associated hemisphere of the Earth) will be directed away from the Sun at one side of the orbit, and half an orbit later (half a year later) this pole will be directed towards the Sun. This is the cause of the Earth's seasons.
Variations in Earth's axial tilt can influence the seasons and is likely a factor in long-term climate change.
Earth's obliquity may have been reasonably accurately measured as early as 1100 BCE in India and China. The ancient Greeks had good measurements of the obliquity since about 350 BCE, when Pytheas of Marseilles measured the shadow of a gnomon at the summer solstice. About 830 CE, the Calif Al-Mamun of Baghdad directed his astronomers to measure the obliquity, and the result was used in the Arab world for many years.
It was widely believed, during the Middle Ages, that both precession and Earth's obliquity oscillated around a mean value, with a period of 672 years, an idea known as trepidation of the equinoxes. Perhaps the first to realize this was incorrect and that the obliquity is decreasing at a relatively constant rate (during historic time) was Fracastoro in 1538.
The first accurate, modern, western observations of the obliquity were probably those of Tycho Brahe, about 1584, although observations by several others, including Purbach, Regiomontanus, and Walther, could have provided similar information.
All four of the innermost, rocky planets of the Solar System may have had large variations of their obliquity in the past. Like Earth, all of the rocky planets have a small precessional rotation of their spin axis. This rate varies due to, among other things, tidal dissipation and core-mantle interaction. When each planet reaches certain values of precession, orbital resonances may cause very large, chaotic changes in obliquity. Mercury and Venus have most likely been stabilized by the tidal dissipation of the Sun. The Earth was stabilized by the Moon, as above, but before its capture, the Earth, too, could have passed through times of instability. Mars' obliquity is currently in a chaotic state; it varies as much as 0° to 60° over some millions of years, depending on perturbations of the planets. The obliquities of the outer planets are considered relatively stable. Some authors dispute that Mars' obliquity is chaotic, and show that tidal dissipation and viscous core-mantle coupling are adequate for it to have reached a fully damped state, similar to Mercury and Venus.
The stellar obliquity ψs, i.e. the axial tilt of a star with respect to the orbital plane of one of its planets, has been determined for only a few systems. But for 49 stars as of today, the sky-projected spin-orbit misalignment λ has been observed, which serves as a lower limit to ψs. Most of these measurements rely on the so-called Rossiter-McLaughlin effect. So far, it has not been possible to constrain the obliquity of an extrasolar planet. But the rotational flattening of the planet and the entourage of moons and/or rings, which are traceable with high-precision photometry, e.g. by the space-based Kepler spacecraft, could provide access to ψp in the near future.
Astrophysicists have applied tidal theories to predict the obliquity of extrasolar planets. It has been shown that the obliquities of exoplanets in the habitable zone around low-mass stars tend to be eroded in less than 1 Gyr, which means that they would not have seasons as Earth has.
The amount of heat energy received at any location on the globe is a direct effect of sun angle on climate, as the angle at which sunlight strikes the Earth varies by location, time of day, and season due to the Earth's orbit around the sun and the Earth's rotation around its tilted axis. Seasonal change in the angle of sunlight, caused by the tilt of the Earth's axis, is the basic mechanism that results in warmer weather in summer than in winter. Change in day length is another factor. (See also season.)
When sunlight shines on the earth at a lower angle (sun closer to the horizon), the energy of the sunlight is spread over a larger area, and is therefore weaker than if the sun is higher overhead and the energy is concentrated on a smaller area. (See Figure 1.)
Figure 2 depicts a sunbeam one mile (1.6 km) wide falling on the ground from directly overhead, and another hitting the ground at a 30° angle. Trigonometry tells us that the sine of a 30° angle is 1/2, whereas the sine of a 90° angle is 1. Therefore, the sunbeam hitting the ground at a 30° angle spreads the same amount of light over twice as much area (if we imagine the sun shining from the south at noon, the north-south width doubles; the east-west width does not). Consequently, the amount of light falling on each square mile is only half as much.
The sunbeam entering at the shallower angle must also travel twice as far through the Earth's atmosphere, which reflects some of the energy back into space.
Figure 3 shows the angle of sunlight striking the earth in the Northern and Southern hemispheres when the Earth's northern axis is tilted away from the sun, when it is winter in the north and summer in the south.
Heat energy is not received from the Sun. Radiant energy is received and this results in change in energy level of receiving bodies in Earth's domain. Different materials have different properties for transmitting back received energy in the form of heat energy at different rates. Concrete and tar for example are slow releasers. Most metals are fast releasers.
Orbital plane (astronomy)
Milankovitch theory describes the collective effects of changes in the Earth's movements upon its climate, named after Serbian geophysicist and astronomer Milutin Milanković, who worked on it during First World War internment. Milanković mathematically theorized that variations in eccentricity, axial tilt, and precession of the Earth's orbit determined climatic patterns on Earth through orbital forcing.
The Earth's axis completes one full cycle of precession approximately every 26,000 years. At the same time the elliptical orbit rotates more slowly. The combined effect of the two precessions leads to a 21,000-year period between the astronomical 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.
Similar astronomical theories had been advanced in the 19th century by Joseph Adhemar, James Croll 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, Imbrie, and Shackleton, "Variations in the Earth's Orbit: Pacemaker of the Ice Ages", in Science (1976) did the theory attain its present state.
As the Earth spins around its axis and orbits around the Sun, several quasi-periodic variations occur due to gravitational interactions. Although the curves have a large number of sinusoidal components, a few components are dominant. Milankovitch studied changes in the orbital eccentricity, 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). Changes near the north polar area, about 65 degrees North, are considered important due to the great amount of land. Land masses respond to temperature change more quickly than oceans, which have a higher effective heat capacity, because of the mixing of surface and deep water and the fact that the specific heat of solids is generally lower than that of water.
The Earth's orbit is an ellipse. 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 and Saturn. As the eccentricity of the orbit evolves, the semi-major axis of the orbital ellipse remains unchanged. From the perspective of the perturbation theory used in celestial mechanics to compute the evolution of the orbit, the semi-major axis is an adiabatic invariant. 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, also remains unchanged as the orbit evolves. As the semi-minor 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 four 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). 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.
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.
The angle of the Earth's axial tilt (obliquity of the ecliptic) 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 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 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 11,800 CE ; the last maximum was reached in 8,700 BCE. This trend in forcing, by itself, tends to make winters warmer and summers colder (i.e. milder seasons), as well as cause an overall cooling trend, but the instrumental temperature record shows a comparatively sudden rise in global temperatures in the 20th and 21st centuries attributed to man-made greenhouse gas emissions.
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 (i.e. the north pole is pointed towards the Sun), the northern hemisphere has a greater difference between the seasons while the southern hemisphere has milder seasons. When the axis points away from the Sun in perihelion (i.e. the south pole is pointed towards the Sun), the southern hemisphere has a greater difference between the seasons while the northern hemisphere 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.
In addition, the orbital ellipse itself precesses in space, 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. The total 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.
The inclination 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, the plane that represents the angular momentum of the Solar System, is approximately the orbital plane of Jupiter. The inclination 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 meteors and meteor-related noctilucent clouds.
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.
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.
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 ages. 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, 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.
The stage 5 problem refers to the timing of the penultimate interglacial (in marine isotopic stage 5) that appears to have begun ten thousand years in advance of the solar forcing hypothesized to have caused it (the causality problem).
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) and damping responses (negative feedback).
The unsplit peak problem refers to the fact that eccentricity has cleanly resolved variations at both the 95 and 125 ka periods. A sufficiently long, well-dated record of climate change should be able to resolve both frequencies. However, some researchers][ interpret climate records of the last million years as showing only a single spectral peak at 100 ka periodicity.][
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 41 ka cycle in obliquity. After 1 million years ago, this switched to a 100 ka variation matching eccentricity, for which no reason has been established.][
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 41 ka period for ice ages. Subsequent research][ has shown that the 100 ka eccentricity cycle is more important, resulting in 100,000-year ice age cycles of the Quaternary glaciation over the last million years.][
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 influences climate is not well understood.
The amount of solar radiation (insolation) 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 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 that 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.
Other planets in the Solar System have been discovered to have Milankovitch cycles. Mostly these cycles are not as intense or complex as the Earth's cycles, but do have a global geological impact with respect to the movement of mobile solids like Water or Nitrogen ices or hydrocarbon lakes.
The orbital plane of an object orbiting another is the geometrical plane in which the orbit lies. The orbital plane is defined by two parameters, Inclination (i) and Longitude of the ascending node (Ω). Three non-collinear points in space suffice to determine the orbital plane. A common example would be: the center of the heavier object, the center of the orbiting object and the center of the orbiting object at some later time.
All of the planets, comets, and asteroids in the Solar System are in orbit around the Sun. The orbital planes of all those orbits nearly line up with each other, making a semi-flat disk called the invariable plane of the Solar System.
By definition the inclination of a planet in the solar system is the angle between its orbital plane and the orbital plane of the Earth (the ecliptic). In other cases, for instance a moon orbiting another planet, it is convenient to define the inclination of the moon's orbit as the angle between its orbital plane and the planet's equator.
For launch vehicles and artificial satellites, the orbital plane is a defining parameter of an orbit; as in general, it will take a very large amount of propellant to change the orbital plane of an object. Other parameters, such as the orbital period, the eccentricity of the orbit and the phase of the orbit are more easily changed by propulsion systems.
Orbital planes of satellites are perturbed by the non-spherical nature of the Earth's gravity. This causes the orbital plane of the satellite's orbit to slowly rotate around the Earth, depending on the angle the plane makes with the Earth's equator. For planes that are at a critical angle this can mean that the plane will track the Sun around the Earth, forming a Sun-synchronous orbit.
A launch vehicle's launch window is usually determined by the times when the target orbital plane intersects the launch site.
Earth's rotation is the rotation of the solid Earth around its own axis. The Earth rotates from the west towards the east. As viewed from the North Star or polestar Polaris, the Earth turns counter-clockwise.
The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is the point in the Northern Hemisphere where the Earth's axis of rotation meets its surface. This point is distinct from the Earth's North Magnetic Pole. The South Pole is the other point where the Earth's axis of rotation intersects its surface, in Antarctica.
The Earth rotates once in about 24 hours from the point of view of the sun and once every 23 hours 56 minutes and 4 seconds from the point of view of the stars (see below). Earth's rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tidal effects the Moon has on Earth's rotation. Atomic clocks show that a modern day is longer by about 1.7 milliseconds than a century ago, slowly increasing the rate at which UTC is adjusted by leap seconds.
Earth's rotation period relative to the Sun (true noon to true noon) is its true solar day or apparent solar day. It depends on the Earth's orbital motion and is thus affected by changes in the eccentricity and inclination of Earth's orbit. Both vary over thousands of years so the annual variation of the true solar day also varies. Generally, it is longer than the mean solar day during two periods of the year and shorter during another two. The true solar day tends to be longer near perihelion when the Sun apparently moves along the ecliptic through a greater angle than usual, taking about longer to do so. Conversely, it is about shorter near aphelion. It is about longer near a solstice when the projection of the Sun's apparent movement along the ecliptic onto the celestial equator causes the Sun to move through a greater angle than usual. Conversely, near an equinox the projection onto the equator is shorter by about . Currently, the perihelion and solstice effects combine to lengthen the true solar day near by solar seconds, but the solstice effect is partially cancelled by the aphelion effect near when it is only longer. The effects of the equinoxes shorten it near and by and , respectively.
The average of the true solar day during the course of an entire year is the mean solar day, which contains solar seconds. Currently, each of these seconds is slightly longer than an SI second because Earth's mean solar day is now slightly longer than it was during the 19th century due to tidal friction. The average length of the mean solar day since the introduction of the leap second in 1972 has been about 0 to 2 ms longer than 86,400 SI seconds. Random fluctuations due to core-mantle coupling have an amplitude of about 5 ms. The mean solar second between 1750 and 1892 was chosen in 1895 by Simon Newcomb as the independent unit of time in his Tables of the Sun. These tables were used to calculate the world's ephemerides between 1900 and 1983, so this second became known as the ephemeris second. In 1967 the SI second was made equal to the ephemeris second.
The apparent solar time is a measure of the Earth's rotation and the difference between it and the mean solar time is known as the equation of time.
Earth's rotation period relative to the fixed stars, called its stellar day by the International Earth Rotation and Reference Systems Service (IERS), is seconds of mean solar time (UT1) , mean solar days). Earth's rotation period relative to the precessing or moving mean vernal equinox, misnamed its sidereal day, is seconds of mean solar time (UT1) , mean solar days). Thus the sidereal day is shorter than the stellar day by about .
Both the stellar day and the sidereal day are shorter than the mean solar day by about . The mean solar day in SI seconds is available from the IERS for the periods and .
Recently (1999–2010) the average annual length of the mean solar day in excess of 86,400 SI seconds has varied between and , which must be added to both the stellar and sidereal days given in mean solar time above to obtain their lengths in SI seconds (see Fluctuations in the length of day).
The angular speed of Earth's rotation in inertial space is radians per SI second (mean solar second). Multiplying by (180°/π radians)×(86,400 seconds/mean solar day) yields 360.9856°/mean solar day, indicating that Earth rotates more than 360° relative to the fixed stars in one solar day. Earth's movement along its nearly circular orbit while it is rotating once around its axis requires that Earth rotate slightly more than once relative to the fixed stars before the mean Sun can pass overhead again, even though it rotates only once (360°) relative to the mean Sun. Multiplying the value in rad/s by Earth's equatorial radius of (WGS84 ellipsoid) (factors of 2π radians needed by both cancel) yields an equatorial speed of , or . Some sources state that Earth's equatorial speed is slightly less, or . This is obtained by dividing Earth's equatorial circumference by . However, the use of only one circumference unwittingly implies only one rotation in inertial space, so the corresponding time unit must be a sidereal hour. This is confirmed by multiplying by the number of sidereal days in one mean solar day, , which yields the equatorial speed in mean solar hours given above of .
The tangential speed of Earth's rotation at a point on Earth can be approximated by multiplying the speed at the equator by the cosine of the latitude. For example, the Kennedy Space Center is located at 28.59° North latitude, which yields a speed of: 1,674.4 kilometres per hour (1,040.4 mph) × cos (28.59) = 1,470.23 kilometres per hour (913.56 mph)
In the Earth's rotating frame of reference, a freely moving body follows an apparent path that deviates from the one it would follow in a fixed frame of reference. Because of this Coriolis effect, falling bodies veer eastward from the vertical plumb line below their point of release, and projectiles veer right in the northern hemisphere (and left in the southern) from the direction in which they are shot. The Coriolis effect has many other manifestations, especially in meteorology, where it is responsible for the differing rotation direction of cyclones in the northern and southern hemispheres. Hooke, following a 1679 suggestion from Newton, tried unsuccessfully to verify the predicted eastward deviation of a body dropped from a height of , but definitive results were only obtained later, in the late 18th and early 19th century, by Giovanni Battista Guglielmini in Bologna, Johann Friedrich Benzenberg in Hamburg and Ferdinand Reich in Freiberg, using taller towers and carefully released weights.
The most celebrated test of Earth's rotation is the Foucault pendulum first built by physicist Léon Foucault in 1851, which consisted of a lead-filled brass sphere suspended from the top of the Panthéon in Paris. Because of the Earth's rotation under the swinging pendulum the pendulum's plane of oscillation appears to rotate at a rate depending on latitude. At the latitude of Paris the predicted and observed shift was about clockwise per hour. Foucault pendulums now swing in museums around the world.
The permanent monitoring of the Earth's rotation requires the use of Very Long Baseline Interferometry coordinated with the Global Positioning System, Satellite laser ranging, and other satellite techniques. This provides the absolute reference for the determination of universal time, precession, and nutation.
The Earth's rotation axis moves with respect to the fixed stars (inertial space); the components of this motion are precession and nutation. The Earth's rotation axis also moves with respect to the Earth's crust; this is called polar motion.
Precession is a rotation of the Earth's rotation axis, caused primarily by external torques from the gravity of the Sun, Moon and other bodies. The polar motion is primarily due to free core nutation and the Chandler wobble.
Over millions of years, the rotation is significantly slowed by gravitational interactions with the Moon; both rotational energy and angular momentum are being slowly transferred to the Moon: see tidal acceleration. However some large scale events, such as the 2004 Indian Ocean earthquake, have caused the rotation to speed up by around 3 microseconds by affecting the Earth's moment of inertia. Post-glacial rebound, ongoing since the last Ice age, is also changing the distribution of the Earth's mass thus affecting the moment of inertia of the Earth and, by the conservation of angular momentum, the Earth's rotation period.
The Earth formed as part of the birth of the Solar System: what eventually became the solar system initially existed as a large, rotating cloud of dust, rocks, and gas. It was composed of hydrogen and helium produced in the Big Bang, as well as heavier elements ejected by supernovas. As this interstellar dust is inhomogeneous, any asymmetry during gravitational accretion results in the angular momentum of the eventual planet. The current rotation period of the Earth is the result of this initial rotation and other factors, including tidal friction and the hypothetical impact of Theia.
Units of time
In astronomy, the Earth's orbit is the motion of the Earth around the Sun, from an average distance of approximately 149.59787 million kilometers away. A complete orbit of the earth around the Sun occurs every 365.2563666 mean solar days (1 sidereal year). This motion gives an apparent movement of the Sun with respect to the stars at a rate of about 1°/day (or a Sun or Moon diameter every 12 hours) eastward, as seen from Earth. On average it takes 24 hours—a solar day—for Earth to complete a full rotation about its axis relative to the Sun so that the Sun returns to the meridian. The orbital speed of the Earth around the Sun averages about 30 km/s (108,000 km/h), which is fast enough to cover the planet's diameter (about 12,700 km) in seven minutes, and the distance to the Moon of 384,000 km in four hours.
Viewed from a vantage point above the north poles of both the Sun and the Earth, the Earth would appear to revolve in a counterclockwise direction about the Sun. From the same vantage point both the Earth and the Sun would appear to rotate in a counterclockwise direction about their respective axes.
Approximating Earth's orbit around the sun to be circular, the distance earth travels in one year is roughly 940 million kilometers (585 million miles).
Heliocentrism is the theory that the Sun is at the center of the Solar System. Historically, heliocentrism is opposed to geocentrism, which places the earth at the center. In the 16th century, Nicolaus Copernicus' De revolutionibus presented a full discussion of a heliocentric model of the universe in much the same way as Ptolemy's Almagest had presented his geocentric model in the 2nd century. This 'Copernican revolution' resolved the issue of planetary retrograde motion by arguing that such motion was only perceived and apparent, rather than real...
Because of the axial tilt of the Earth (often known as the obliquity of the ecliptic), the inclination of the Sun's trajectory in the sky (as seen by an observer on Earth's surface) varies over the course of the year. For an observer at a northern latitude, when the northern pole is tilted toward the Sun the day lasts longer and the Sun seems to be climbed higher in the sky. This results in warmer average temperatures from the increase in solar radiation reaching the surface. When the northern pole is tilted away from the Sun, the reverse is true and the climate is generally cooler. Above the arctic circle, an extreme case is reached where there is no daylight at all for part of the year. (This is called a polar night.) This variation in the climate (because of the direction of the Earth's axial tilt) results in the seasons.
By one astronomical convention, the four seasons are determined by flanges, the solstices—the point in the orbit of maximum axial tilt toward or away from the Sun—and the equinoxes, when the direction of the tilt and the direction to the Sun are perpendicular. In the northern hemisphere winter solstice occurs on about December 21, summer solstice is near June 21, spring equinox is around March 20 and autumnal equinox is about September 23. The axial tilt in the southern hemisphere is exactly the opposite of the direction in the northern hemisphere. Thus the seasonal effects in the south are reversed.
In modern times, Earth's perihelion occurs around January 3, and the aphelion around July 4 (for other eras, see precession and Milankovitch cycles). The changing Earth-Sun distance results in an increase of about 6.9% in solar energy reaching the Earth at perihelion relative to aphelion. Since the southern hemisphere is tilted toward the Sun at about the same time that the Earth reaches the closest approach to the Sun, the southern hemisphere receives slightly more energy from the Sun than does the northern over the course of a year. However, this effect is much less significant than the total energy change due to the axial tilt, and most of the excess energy is absorbed by the higher proportion of water in the southern hemisphere.
The Hill sphere (gravitational sphere of influence) of the Earth is about 1.5 Gm (or 1,500,000 kilometers) in radius. This is the maximum distance at which the Earth's gravitational influence is stronger than the more distant Sun and planets. Objects orbiting the Earth must be within this radius, otherwise they can become unbound by the gravitational perturbation of the Sun.
The following diagram shows the relation between the line of solstice and the line of apsides of Earth's elliptical orbit. The orbital ellipse (with eccentricity exaggerated for effect) goes through each of the six Earth images, which are sequentially the perihelion (periapsis—nearest point to the Sun) on anywhere from 2 January to 5 January, the point of March equinox on 20 or 21 March, the point of June solstice on 20 or 21 June, the aphelion (apoapsis—farthest point from the Sun) on anywhere from 4 July to 7 July, the September equinox on 22 or 23 September, and the December solstice on 21 or 22 December. Note that the diagram shows an exaggerated representation of the shape of Earth's orbit. In reality, the actual path of Earth's orbit is not as eccentric as that portrayed in the diagram.
Mathematicians and astronomers (such as Laplace, Lagrange, Gauss, Poincaré, Kolmogorov, Vladimir Arnold, and Jürgen Moser) have searched for evidence for the stability of the planetary motions, and this quest led to many mathematical developments, and several successive 'proofs' of stability for the solar system. By most predictions, Earth's orbit will be relatively stable over long periods.
In 1989, Jacques Laskar's work showed that the Earth's orbit (as well as the orbits of all the inner planets) is chaotic and that an error as small as 15 metres in measuring the initial position of the Earth today would make it impossible to predict where the Earth would be in its orbit in just over 100 million years' time. Modeling the solar system is subject to the n-body problem.
The angle of the Earth's tilt is relatively stable over long periods. However, the tilt does undergo a slight, irregular motion (known as nutation) with a main period of 18.6 years. The orientation (rather than the angle) of the Earth's axis also changes over time, precessing around in a complete circle over each 25,800 year cycle; this precession is the reason for the difference between a sidereal year and a tropical year. Both of these motions are caused by the varying attraction of the Sun and Moon on the Earth's equatorial bulge. From the perspective of the Earth, the poles also migrate a few meters across the surface. This polar motion has multiple, cyclical components, which collectively are termed quasiperiodic motion. In addition to an annual component to this motion, there is a 14-month cycle called the Chandler wobble. The rotational velocity of the Earth also varies in a phenomenon known as length-of-day variation.