172-604: The sky is an unobstructed view upward from the surface of the Earth . It includes the atmosphere and outer space . It may also be considered a place between the ground and outer space, thus distinct from outer space. In the field of astronomy , the sky is also called the celestial sphere . This is an abstract sphere, concentric to the Earth, on which the Sun , Moon , planets , and stars appear to be drifting . The celestial sphere
344-475: A 1 and a 2 denote the amplitude of the wave in the two components of the electric field vector, while θ 1 and θ 2 represent the phases. The product of a Jones vector with a complex number of unit modulus gives a different Jones vector representing the same ellipse, and thus the same state of polarization. The physical electric field, as the real part of the Jones vector, would be altered but
516-421: A birefringent substance, electromagnetic waves of different polarizations travel at different speeds ( phase velocities ). As a result, when unpolarized waves travel through a plate of birefringent material, one polarization component has a shorter wavelength than the other, resulting in a phase difference between the components which increases the further the waves travel through the material. The Jones matrix
688-540: A circumstellar disk , and then the planets grow out of that disk with the Sun. A nebula contains gas, ice grains, and dust (including primordial nuclides ). According to nebular theory , planetesimals formed by accretion , with the primordial Earth being estimated as likely taking anywhere from 70 to 100 million years to form. Estimates of the age of the Moon range from 4.5 Ga to significantly younger. A leading hypothesis
860-411: A marine layer , an indication of a stable atmosphere. Rainy conditions are preceded by wind or clouds which prevent fog formation. The approach of a line of thunderstorms could indicate the approach of a cold front . Cloud-free skies are indicative of fair weather for the near future. The use of sky cover in weather prediction has led to various weather lore over the centuries. Within 36 hours of
1032-492: A common barycenter every 27.32 days relative to the background stars. When combined with the Earth–Moon system's common orbit around the Sun, the period of the synodic month , from new moon to new moon, is 29.53 days. Viewed from the celestial north pole , the motion of Earth, the Moon, and their axial rotations are all counterclockwise . Viewed from a vantage point above the Sun and Earth's north poles, Earth orbits in
1204-400: A coordinate system and viewing the polarization ellipse in terms of the x and y polarization components, corresponds to the definition of the Jones vector (below) in terms of those basis polarizations. Axes are selected to suit a particular problem, such as x being in the plane of incidence. Since there are separate reflection coefficients for the linear polarizations in and orthogonal to
1376-548: A counterclockwise direction about the Sun. The orbital and axial planes are not precisely aligned: Earth's axis is tilted some 23.44 degrees from the perpendicular to the Earth–Sun plane (the ecliptic ), and the Earth-Moon plane is tilted up to ±5.1 degrees against the Earth–Sun plane. Without this tilt, there would be an eclipse every two weeks, alternating between lunar eclipses and solar eclipses . The Hill sphere , or
1548-455: A day, and the primary cause of these properties differs as well. When the Sun is well above the horizon , direct scattering of sunlight ( Rayleigh scattering ) is the overwhelmingly dominant source of light. However, during twilight , the period between sunset and night or between night and sunrise , the situation is more complex. Green flashes and green rays are optical phenomena that occur shortly after sunset or before sunrise, when
1720-1253: A dielectric, η is real and has the value η 0 / n , where n is the refractive index and η 0 is the impedance of free space . The impedance will be complex in a conducting medium. Note that given that relationship, the dot product of E and H must be zero: E → ( r → , t ) ⋅ H → ( r → , t ) = e x h x + e y h y + e z h z = e x ( − e y η ) + e y ( e x η ) + 0 ⋅ 0 = 0 , {\displaystyle {\begin{aligned}{\vec {E}}\left({\vec {r}},t\right)\cdot {\vec {H}}\left({\vec {r}},t\right)&=e_{x}h_{x}+e_{y}h_{y}+e_{z}h_{z}\\&=e_{x}\left(-{\frac {e_{y}}{\eta }}\right)+e_{y}\left({\frac {e_{x}}{\eta }}\right)+0\cdot 0\\&=0,\end{aligned}}} indicating that these vectors are orthogonal (at right angles to each other), as expected. Knowing
1892-399: A frequency of f = c/λ where c is the speed of light), let us take the direction of propagation as the z axis. Being a transverse wave the E and H fields must then contain components only in the x and y directions whereas E z = H z = 0 . Using complex (or phasor ) notation, the instantaneous physical electric and magnetic fields are given by the real parts of
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#17327984019722064-420: A full rotation about its axis so that the Sun returns to the meridian . The orbital speed of Earth averages about 29.78 km/s (107,200 km/h; 66,600 mph), which is fast enough to travel a distance equal to Earth's diameter, about 12,742 km (7,918 mi), in seven minutes, and the distance from Earth to the Moon, 384,400 km (238,900 mi), in about 3.5 hours. The Moon and Earth orbit
2236-403: A given path on those two components is most easily characterized in the form of a complex 2 × 2 transformation matrix J known as a Jones matrix : e ′ = J e . {\displaystyle \mathbf {e'} =\mathbf {J} \mathbf {e} .} The Jones matrix due to passage through a transparent material is dependent on the propagation distance as well as
2408-421: A globe-spanning mid-ocean ridge system. At Earth's polar regions , the ocean surface is covered by seasonally variable amounts of sea ice that often connects with polar land, permafrost and ice sheets , forming polar ice caps . Earth's land covers 29.2%, or 149 million km (58 million sq mi) of Earth's surface. The land surface includes many islands around the globe, but most of
2580-526: A green spot is visible above the Sun, usually for no more than a second or two, or it may resemble a green ray shooting up from the sunset point. Green flashes are a group of phenomena that stem from different causes, most of which occur when there is a temperature inversion (when the temperature increases with altitude rather than the normal decrease in temperature with altitude). Green flashes may be observed from any altitude (even from an aircraft). They are usually seen above an unobstructed horizon, such as over
2752-425: A liquid outer core that generates a magnetosphere capable of deflecting most of the destructive solar winds and cosmic radiation . Earth has a dynamic atmosphere , which sustains Earth's surface conditions and protects it from most meteoroids and UV-light at entry . It has a composition of primarily nitrogen and oxygen . Water vapor is widely present in the atmosphere, forming clouds that cover most of
2924-483: A more general formulation with propagation not restricted to the +z direction, then the spatial dependence kz is replaced by k → ∙ r → where k → is called the wave vector , the magnitude of which is the wavenumber. Thus the leading vectors e and h each contain up to two nonzero (complex) components describing the amplitude and phase of the wave's x and y polarization components (again, there can be no z polarization component for
3096-622: A plane wave with those given parameters can then be used to predict its response to a more general case, since a wave with any specified spatial structure can be decomposed into a combination of plane waves (its so-called angular spectrum ). Incoherent states can be modeled stochastically as a weighted combination of such uncorrelated waves with some distribution of frequencies (its spectrum ), phases, and polarizations. Electromagnetic waves (such as light), traveling in free space or another homogeneous isotropic non-attenuating medium, are properly described as transverse waves , meaning that
3268-434: A plane wave's electric field vector E and magnetic field H are each in some direction perpendicular to (or "transverse" to) the direction of wave propagation; E and H are also perpendicular to each other. By convention, the "polarization" direction of an electromagnetic wave is given by its electric field vector. Considering a monochromatic plane wave of optical frequency f (light of vacuum wavelength λ has
3440-402: A polarized transverse wave is vibrations traveling along a taut string (see image) , for example, in a musical instrument like a guitar string . Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves , such as sound waves in a liquid or gas, the displacement of
3612-419: A purely polarized monochromatic wave the electric field vector over one cycle of oscillation traces out an ellipse. A polarization state can then be described in relation to the geometrical parameters of the ellipse, and its "handedness", that is, whether the rotation around the ellipse is clockwise or counter clockwise. One parameterization of the elliptical figure specifies the orientation angle ψ , defined as
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#17327984019723784-426: A random mixture of waves having different spatial characteristics, frequencies (wavelengths), phases, and polarization states. However, for understanding electromagnetic waves and polarization in particular, it is easier to just consider coherent plane waves ; these are sinusoidal waves of one particular direction (or wavevector ), frequency, phase, and polarization state. Characterizing an optical system in relation to
3956-431: A significant imaginary part (or " extinction coefficient ") such as metals; these fields are also not strictly transverse. Surface waves or waves propagating in a waveguide (such as an optical fiber ) are generally not transverse waves, but might be described as an electric or magnetic transverse mode , or a hybrid mode. Even in free space, longitudinal field components can be generated in focal regions, where
4128-536: A superposition of right and left circularly polarized states, with equal amplitude and phases synchronized to give oscillation in a plane. Polarization is an important parameter in areas of science dealing with transverse waves, such as optics , seismology , radio , and microwaves . Especially impacted are technologies such as lasers , wireless and optical fiber telecommunications , and radar . Most sources of light are classified as incoherent and unpolarized (or only "partially polarized") because they consist of
4300-598: A surface. According to quantum mechanics , electromagnetic waves can also be viewed as streams of particles called photons . When viewed in this way, the polarization of an electromagnetic wave is determined by a quantum mechanical property of photons called their spin . A photon has one of two possible spins: it can either spin in a right hand sense or a left hand sense about its direction of travel. Circularly polarized electromagnetic waves are composed of photons with only one type of spin, either right- or left-hand. Linearly polarized waves consist of photons that are in
4472-457: A transverse wave in the + z direction). For a given medium with a characteristic impedance η , h is related to e by: h y = e x η h x = − e y η . {\displaystyle {\begin{aligned}h_{y}&={\frac {e_{x}}{\eta }}\\h_{x}&=-{\frac {e_{y}}{\eta }}.\end{aligned}}} In
4644-514: Is rounded into an ellipsoid with a circumference of about 40,000 km. It is the densest planet in the Solar System . Of the four rocky planets , it is the largest and most massive. Earth is about eight light-minutes away from the Sun and orbits it , taking a year (about 365.25 days) to complete one revolution. Earth rotates around its own axis in slightly less than a day (in about 23 hours and 56 minutes). Earth's axis of rotation
4816-534: Is a unitary matrix : | g 1 | = | g 2 | = 1 . Media termed diattenuating (or dichroic in the sense of polarization), in which only the amplitudes of the two polarizations are affected differentially, may be described using a Hermitian matrix (generally multiplied by a common phase factor). In fact, since any matrix may be written as the product of unitary and positive Hermitian matrices, light propagation through any sequence of polarization-dependent optical components can be written as
4988-456: Is a chemically distinct silicate solid crust, which is underlain by a highly viscous solid mantle. The crust is separated from the mantle by the Mohorovičić discontinuity . The thickness of the crust varies from about 6 kilometres (3.7 mi) under the oceans to 30–50 km (19–31 mi) for the continents. The crust and the cold, rigid, top of the upper mantle are collectively known as
5160-483: Is approximately 9.8 m/s (32 ft/s ). Local differences in topography, geology, and deeper tectonic structure cause local and broad regional differences in Earth's gravitational field, known as gravity anomalies . The main part of Earth's magnetic field is generated in the core, the site of a dynamo process that converts the kinetic energy of thermally and compositionally driven convection into electrical and magnetic field energy. The field extends outwards from
5332-423: Is common, with sudden increases in wind accompanied by rain showers or thunderstorms. Within six hours of the center's arrival, rain becomes continuous. Within an hour of the center, the rain becomes very heavy and the highest winds within the tropical cyclone are experienced. When the center arrives with a strong tropical cyclone, weather conditions improve and the sun becomes visible as the eye moves overhead. Once
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5504-443: Is commonly referred to as transverse-magnetic (TM), and has also been termed pi-polarized or π -polarized , or tangential plane polarized . S -polarization is also called transverse-electric (TE), as well as sigma-polarized or σ-polarized , or sagittal plane polarized . Degree of polarization ( DOP ) is a quantity used to describe the portion of an electromagnetic wave which is polarized. DOP can be calculated from
5676-529: Is contained in 3.45 billion-year-old Australian rocks showing fossils of microorganisms . During the Neoproterozoic , 1000 to 539 Ma , much of Earth might have been covered in ice. This hypothesis has been termed " Snowball Earth ", and it is of particular interest because it preceded the Cambrian explosion , when multicellular life forms significantly increased in complexity. Following
5848-419: Is conventionally divided into designated areas called constellations . Usually, the term sky informally refers to a perspective from the Earth's surface; however, the meaning and usage can vary. An observer on the surface of the Earth can see a small part of the sky, which resembles a dome (sometimes called the sky bowl ) appearing flatter during the day than at night . In some cases, such as in discussing
6020-434: Is dependent on the polarization state of a wave, properties known as birefringence and polarization dichroism (or diattenuation ) respectively, then the polarization state of a wave will generally be altered. In such media, an electromagnetic wave with any given state of polarization may be decomposed into two orthogonally polarized components that encounter different propagation constants . The effect of propagation over
6192-416: Is depicted in the animation on the right. Note that circular or elliptical polarization can involve either a clockwise or counterclockwise rotation of the field, depending on the relative phases of the components. These correspond to distinct polarization states, such as the two circular polarizations shown above. The orientation of the x and y axes used in this description is arbitrary. The choice of such
6364-792: Is enabled by Earth being an ocean world , the only one in the Solar System sustaining liquid surface water . Almost all of Earth's water is contained in its global ocean, covering 70.8% of Earth's crust . The remaining 29.2% of Earth's crust is land, most of which is located in the form of continental landmasses within Earth's land hemisphere . Most of Earth's land is at least somewhat humid and covered by vegetation , while large sheets of ice at Earth's polar deserts retain more water than Earth's groundwater , lakes, rivers and atmospheric water combined. Earth's crust consists of slowly moving tectonic plates , which interact to produce mountain ranges, volcanoes , and earthquakes. Earth has
6536-457: Is farthest out from its center of mass at its equatorial bulge, the summit of the volcano Chimborazo in Ecuador (6,384.4 km or 3,967.1 mi) is its farthest point out. Parallel to the rigid land topography the ocean exhibits a more dynamic topography . To measure the local variation of Earth's topography, geodesy employs an idealized Earth producing a geoid shape. Such a shape
6708-516: Is gained if the ocean is idealized, covering Earth completely and without any perturbations such as tides and winds. The result is a smooth but irregular geoid surface, providing a mean sea level (MSL) as a reference level for topographic measurements. Earth's surface is the boundary between the atmosphere, and the solid Earth and oceans. Defined in this way, it has an area of about 510 million km (197 million sq mi). Earth can be divided into two hemispheres : by latitude into
6880-413: Is identical to one of those basis polarizations. Since the phase shift, and thus the change in polarization state, is usually wavelength-dependent, such objects viewed under white light in between two polarizers may give rise to colorful effects, as seen in the accompanying photograph. Circular birefringence is also termed optical activity , especially in chiral fluids, or Faraday rotation , when due to
7052-426: Is liquid under normal atmospheric pressure. Differences in the amount of captured energy between geographic regions (as with the equatorial region receiving more sunlight than the polar regions) drive atmospheric and ocean currents , producing a global climate system with different climate regions , and a range of weather phenomena such as precipitation , allowing components such as nitrogen to cycle . Earth
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7224-439: Is more commonly called in astronomy to avoid confusion with the horizontal coordinate system ) corresponding to due north. Another coordinate system frequently used relates to the plane of incidence . This is the plane made by the incoming propagation direction and the vector perpendicular to the plane of an interface, in other words, the plane in which the ray travels before and after reflection or refraction. The component of
7396-402: Is normally not even mentioned. On the other hand, sound waves in a bulk solid can be transverse as well as longitudinal, for a total of three polarization components. In this case, the transverse polarization is associated with the direction of the shear stress and displacement in directions perpendicular to the propagation direction, while the longitudinal polarization describes compression of
7568-513: Is now slightly longer than it was during the 19th century due to tidal deceleration , each day varies between 0 and 2 ms longer than the mean solar day. Earth's rotation period relative to the fixed stars , called its stellar day by the International Earth Rotation and Reference Systems Service (IERS), is 86,164.0989 seconds of mean solar time ( UT1 ), or 23 56 4.0989 . Earth's rotation period relative to
7740-532: Is passed through an ideal polarizer (where g 1 = 1 and g 2 = 0 ) exactly half of its initial power is retained. Practical polarizers, especially inexpensive sheet polarizers, have additional loss so that g 1 < 1 . However, in many instances the more relevant figure of merit is the polarizer's degree of polarization or extinction ratio , which involve a comparison of g 1 to g 2 . Since Jones vectors refer to waves' amplitudes (rather than intensity ), when illuminated by unpolarized light
7912-627: Is polarized. In a vacuum , the components of the electric field propagate at the speed of light , so that the phase of the wave varies in space and time while the polarization state does not. That is, the electric field vector e of a plane wave in the + z direction follows: e ( z + Δ z , t + Δ t ) = e ( z , t ) e i k ( c Δ t − Δ z ) , {\displaystyle \mathbf {e} (z+\Delta z,t+\Delta t)=\mathbf {e} (z,t)e^{ik(c\Delta t-\Delta z)},} where k
8084-622: Is rare, though the alternative spelling Gaia has become common due to the Gaia hypothesis , in which case its pronunciation is / ˈ ɡ aɪ . ə / rather than the more classical English / ˈ ɡ eɪ . ə / . There are a number of adjectives for the planet Earth. The word "earthly" is derived from "Earth". From the Latin Terra comes terran / ˈ t ɛr ə n / , terrestrial / t ə ˈ r ɛ s t r i ə l / , and (via French) terrene / t ə ˈ r iː n / , and from
8256-465: Is stronger at the shorter (bluer) end of the visible spectrum , meaning that the scattered light is bluer than its source: the Sun . The remaining direct sunlight, having lost some of its shorter-wavelength components, appears slightly less blue. Scattering also occurs even more strongly in clouds. Individual water droplets refract white light into a set of colored rings . If a cloud is thick enough, scattering from multiple water droplets will wash out
8428-487: Is that it was formed by accretion from material loosed from Earth after a Mars -sized object with about 10% of Earth's mass, named Theia , collided with Earth. It hit Earth with a glancing blow and some of its mass merged with Earth. Between approximately 4.1 and 3.8 Ga , numerous asteroid impacts during the Late Heavy Bombardment caused significant changes to the greater surface environment of
8600-446: Is the wavenumber . As noted above, the instantaneous electric field is the real part of the product of the Jones vector times the phase factor e − i ω t {\displaystyle e^{-i\omega t}} . When an electromagnetic wave interacts with matter, its propagation is altered according to the material's (complex) index of refraction . When the real or imaginary part of that refractive index
8772-453: Is the basis for the astronomical unit (AU) and is equal to roughly 8.3 light minutes or 380 times Earth's distance to the Moon . Earth orbits the Sun every 365.2564 mean solar days , or one sidereal year . With an apparent movement of the Sun in Earth's sky at a rate of about 1°/day eastward, which is one apparent Sun or Moon diameter every 12 hours. Due to this motion, on average it takes 24 hours—a solar day—for Earth to complete
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#17327984019728944-429: Is the main sky god and also the creator god. In Iroquois mythology , Atahensic was a sky goddess who fell down to the ground during the creation of the Earth. Many cultures have drawn constellations between stars in the sky, using them in association with legends and mythology about their deities. Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life . This
9116-402: Is the wavelength in the medium (whose refractive index is n ) and T = 1/ f is the period of the wave. Here e x , e y , h x , and h y are complex numbers. In the second more compact form, as these equations are customarily expressed, these factors are described using the wavenumber k = 2π n / λ 0 and angular frequency (or "radian frequency") ω = 2π f . In
9288-457: Is tied to that of the Sun. Over the next 1.1 billion years , solar luminosity will increase by 10%, and over the next 3.5 billion years by 40%. Earth's increasing surface temperature will accelerate the inorganic carbon cycle , possibly reducing CO 2 concentration to levels lethally low for current plants ( 10 ppm for C4 photosynthesis ) in approximately 100–900 million years . A lack of vegetation would result in
9460-455: Is tilted with respect to the perpendicular to its orbital plane around the Sun, producing seasons . Earth is orbited by one permanent natural satellite , the Moon , which orbits Earth at 384,400 km (1.28 light seconds) and is roughly a quarter as wide as Earth. The Moon's gravity helps stabilize Earth's axis, causes tides and gradually slows Earth's rotation . Tidal locking has made
9632-583: The Milky Way and orbits about 28,000 light-years from its center. It is about 20 light-years above the galactic plane in the Orion Arm . The axial tilt of Earth is approximately 23.439281° with the axis of its orbit plane, always pointing towards the Celestial Poles . Due to Earth's axial tilt, the amount of sunlight reaching any given point on the surface varies over the course of
9804-583: The Old Norse sky , meaning 'cloud, abode of God '. The Norse term is also the source of the Old English scēo , which shares the same Indo-European base as the classical Latin obscūrus , meaning 'obscure'. In Old English, the term heaven was used to describe the observable expanse above the earth. During the period of Middle English , "heaven" began shifting toward its current, religious meaning. Except for direct sunlight , most of
9976-759: The Pacific , North American , Eurasian , African , Antarctic , Indo-Australian , and South American . Other notable plates include the Arabian Plate , the Caribbean Plate , the Nazca Plate off the west coast of South America and the Scotia Plate in the southern Atlantic Ocean. The Australian Plate fused with the Indian Plate between 50 and 55 Ma . The fastest-moving plates are
10148-463: The Stokes parameters . A perfectly polarized wave has a DOP of 100%, whereas an unpolarized wave has a DOP of 0%. A wave which is partially polarized, and therefore can be represented by a superposition of a polarized and unpolarized component, will have a DOP somewhere in between 0 and 100%. DOP is calculated as the fraction of the total power that is carried by the polarized component of
10320-419: The asthenosphere , the solid but less-viscous part of the upper mantle that can flow and move along with the plates. As the tectonic plates migrate, oceanic crust is subducted under the leading edges of the plates at convergent boundaries. At the same time, the upwelling of mantle material at divergent boundaries creates mid-ocean ridges. The combination of these processes recycles the oceanic crust back into
10492-408: The astronomical twilight , defined as the period between −12° and −18°. When the Sun drops more than 18° below the horizon, the sky generally attains its minimum brightness. Several sources can be identified as the source of the intrinsic brightness of the sky, namely airglow , indirect scattering of sunlight, scattering of starlight , and artificial light pollution . The term night sky refers to
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#173279840197210664-415: The celestial equator , this is equivalent to an apparent diameter of the Sun or the Moon every two minutes; from Earth's surface, the apparent sizes of the Sun and the Moon are approximately the same. Earth orbits the Sun, making Earth the third-closest planet to the Sun and part of the inner Solar System . Earth's average orbital distance is about 150 million km (93 million mi), which
10836-405: The electric displacement D and magnetic flux density B still obey the above geometry but due to anisotropy in the electric susceptibility (or in the magnetic permeability ), now given by a tensor , the direction of E (or H ) may differ from that of D (or B ). Even in isotropic media, so-called inhomogeneous waves can be launched into a medium whose refractive index has
11008-405: The ellipticity angle , χ = arctan b / a {\textstyle \chi =\arctan b/a} = arctan 1 / ε {\textstyle =\arctan 1/\varepsilon } as is shown in the figure. The angle χ is also significant in that the latitude (angle from the equator) of the polarization state as represented on
11180-403: The light in the daytime sky is caused by scattering , which is dominated by a small-particle limit called Rayleigh scattering . The scattering due to molecule-sized particles (as in air) is greater in the directions both toward and away from the source of light than it is in directions perpendicular to the incident path. Scattering is significant for light at all visible wavelengths, but
11352-488: The lunar sky black even when the Sun is visible. Sky luminance distribution models have been recommended by the International Commission on Illumination (CIE) for the design of daylighting schemes. Recent developments relate to "all sky models" for modelling sky luminance under weather conditions ranging from clear to overcast. The brightness and color of the sky vary greatly over the course of
11524-479: The observing site permit a clear view of the horizon, the shadow's fringe appears as a dark or dull bluish band just above the horizon, in the low part of the sky opposite of the (setting or rising) Sun's direction. A related phenomenon is the Belt of Venus (or antitwilight arch), a pinkish band that is visible above the bluish band of Earth's shadow in the same part of the sky. No defined line divides Earth's shadow and
11696-408: The ocean floor form the top of Earth's crust , which together with parts of the upper mantle form Earth's lithosphere . Earth's crust may be divided into oceanic and continental crust. Beneath the ocean-floor sediments, the oceanic crust is predominantly basaltic , while the continental crust may include lower density materials such as granite , sediments and metamorphic rocks. Nearly 75% of
11868-430: The precessing or moving mean March equinox (when the Sun is at 90° on the equator), is 86,164.0905 seconds of mean solar time (UT1) (23 56 4.0905 ) . Thus the sidereal day is shorter than the stellar day by about 8.4 ms. Apart from meteors within the atmosphere and low-orbiting satellites, the main apparent motion of celestial bodies in Earth's sky is to the west at a rate of 15°/h = 15'/min. For bodies near
12040-413: The sphere of gravitational influence , of Earth is about 1.5 million km (930,000 mi) in radius. This is the maximum distance at which Earth's gravitational influence is stronger than that of the more distant Sun and planets. Objects must orbit Earth within this radius, or they can become unbound by the gravitational perturbation of the Sun. Earth, along with the Solar System, is situated in
12212-427: The xy -plane, along the page, with the wave propagating in the z direction, perpendicular to the page. The first two diagrams below trace the electric field vector over a complete cycle for linear polarization at two different orientations; these are each considered a distinct state of polarization (SOP). The linear polarization at 45° can also be viewed as the addition of a horizontally linearly polarized wave (as in
12384-464: The "last ice age", covered large parts of the continents, to the middle latitudes, in ice and ended about 11,700 years ago. Chemical reactions led to the first self-replicating molecules about four billion years ago. A half billion years later, the last common ancestor of all current life arose. The evolution of photosynthesis allowed the Sun's energy to be harvested directly by life forms. The resultant molecular oxygen ( O 2 ) accumulated in
12556-403: The "polarization" of electromagnetic waves refers to the direction of the electric field. In linear polarization , the fields oscillate in a single direction. In circular or elliptical polarization , the fields rotate at a constant rate in a plane as the wave travels, either in the right-hand or in the left-hand direction. Light or other electromagnetic radiation from many sources, such as
12728-484: The Belt of Venus; one colored band fades into the other in the sky. Twilight is divided into three stages according to the Sun's depth below the horizon, measured in segments of 6°. After sunset, the civil twilight sets in; it ends when the Sun drops more than 6° below the horizon. This is followed by the nautical twilight , when the Sun is between 6° and 12° below the horizon (depth between −6° and −12°), after which comes
12900-484: The Cambrian explosion, 535 Ma , there have been at least five major mass extinctions and many minor ones. Apart from the proposed current Holocene extinction event, the most recent was 66 Ma , when an asteroid impact triggered the extinction of non-avian dinosaurs and other large reptiles, but largely spared small animals such as insects, mammals , lizards and birds. Mammalian life has diversified over
13072-654: The Earth. Terra is also the name of the planet in some Romance languages , languages that evolved from Latin , like Italian and Portuguese , while in other Romance languages the word gave rise to names with slightly altered spellings, like the Spanish Tierra and the French Terre . The Latinate form Gæa or Gaea ( English: / ˈ dʒ iː . ə / ) of the Greek poetic name Gaia ( Γαῖα ; Ancient Greek : [ɡâi̯.a] or [ɡâj.ja] )
13244-421: The Jones matrix can be written as J = T [ g 1 0 0 g 2 ] T − 1 , {\displaystyle \mathbf {J} =\mathbf {T} {\begin{bmatrix}g_{1}&0\\0&g_{2}\end{bmatrix}}\mathbf {T} ^{-1},} where g 1 and g 2 are complex numbers describing the phase delay and possibly
13416-533: The Latin Tellus comes tellurian / t ɛ ˈ l ʊər i ə n / and telluric . The oldest material found in the Solar System is dated to 4.5682 +0.0002 −0.0004 Ga (billion years) ago. By 4.54 ± 0.04 Ga the primordial Earth had formed. The bodies in the Solar System formed and evolved with the Sun. In theory, a solar nebula partitions a volume out of a molecular cloud by gravitational collapse, which begins to spin and flatten into
13588-758: The Moon always face Earth with the same side. Earth, like most other bodies in the Solar System, formed 4.5 billion years ago from gas and dust in the early Solar System . During the first billion years of Earth's history , the ocean formed and then life developed within it. Life spread globally and has been altering Earth's atmosphere and surface, leading to the Great Oxidation Event two billion years ago. Humans emerged 300,000 years ago in Africa and have spread across every continent on Earth. Humans depend on Earth's biosphere and natural resources for their survival, but have increasingly impacted
13760-426: The Moon and, by inference, to that of Earth. Earth's atmosphere and oceans were formed by volcanic activity and outgassing . Water vapor from these sources condensed into the oceans, augmented by water and ice from asteroids, protoplanets , and comets . Sufficient water to fill the oceans may have been on Earth since it formed. In this model, atmospheric greenhouse gases kept the oceans from freezing when
13932-465: The Moon, planets, and stars are similarly visible in the sky. Some of the natural phenomena seen in the sky are clouds, rainbows , and aurorae . Lightning and precipitation are also visible in the sky. Certain birds and insects, as well as human inventions like aircraft and kites , can fly in the sky. Due to human activities , smog during the day and light pollution during the night are often seen above large cities. The word sky comes from
14104-463: The Poincaré sphere (see below) is equal to ±2 χ . The special cases of linear and circular polarization correspond to an ellipticity ε of infinity and unity (or χ of zero and 45°) respectively. Full information on a completely polarized state is also provided by the amplitude and phase of oscillations in two components of the electric field vector in the plane of polarization. This representation
14276-458: The Solar System's planetary-sized objects, Earth is the object with the highest density . Earth's mass is approximately 5.97 × 10 kg ( 5.970 Yg ). It is composed mostly of iron (32.1% by mass ), oxygen (30.1%), silicon (15.1%), magnesium (13.9%), sulfur (2.9%), nickel (1.8%), calcium (1.5%), and aluminium (1.4%), with the remaining 1.2% consisting of trace amounts of other elements. Due to gravitational separation ,
14448-403: The Sun when the star reaches its maximum radius, otherwise, with tidal effects, it may enter the Sun's atmosphere and be vaporized. Earth has a rounded shape , through hydrostatic equilibrium , with an average diameter of 12,742 kilometres (7,918 mi), making it the fifth largest planetary sized and largest terrestrial object of the Solar System . Due to Earth's rotation it has
14620-408: The Sun, distant clouds or snowy mountaintops may appear yellow. The effect is not very obvious on clear days, but is very pronounced when clouds cover the line of sight, reducing the blue hue from scattered sunlight. At higher altitudes, the sky tends toward darker colors since scattering is reduced due to lower air density . An extreme example is the Moon, where no atmospheric scattering occurs, making
14792-404: The amount of ambient lighting. With the advent of artificial light sources, however, light pollution has been a growing problem for viewing the night sky. Special filters and modifications to light fixtures can help to alleviate this problem, but for the best views, both professional and amateur optical astronomers seek viewing sites located far from major urban areas. Along with pressure tendency,
14964-427: The amplitude attenuation due to propagation in each of the two polarization eigenmodes . T is a unitary matrix representing a change of basis from these propagation modes to the linear system used for the Jones vectors; in the case of linear birefringence or diattenuation the modes are themselves linear polarization states so T and T can be omitted if the coordinate axes have been chosen appropriately. In
15136-439: The angle between the major axis of the ellipse and the x -axis along with the ellipticity ε = a/b , the ratio of the ellipse's major to minor axis. (also known as the axial ratio ). The ellipticity parameter is an alternative parameterization of an ellipse's eccentricity e = 1 − b 2 / a 2 , {\textstyle e={\sqrt {1-b^{2}/a^{2}}},} or
15308-425: The atmosphere and due to interaction with ultraviolet solar radiation, formed a protective ozone layer ( O 3 ) in the upper atmosphere. The incorporation of smaller cells within larger ones resulted in the development of complex cells called eukaryotes . True multicellular organisms formed as cells within colonies became increasingly specialized. Aided by the absorption of harmful ultraviolet radiation by
15480-462: The belief that relationships between heavenly bodies influence or convey information about events on Earth. The scientific study of the night sky and bodies observed within it, meanwhile, takes place in the science of astronomy. Within visible-light astronomy , the visibility of celestial objects in the night sky is affected by light pollution. The presence of the Moon in the night sky has historically hindered astronomical observation by increasing
15652-451: The birefringence. The birefringence (as well as the average refractive index) will generally be dispersive , that is, it will vary as a function of optical frequency (wavelength). In the case of non-birefringent materials, however, the 2 × 2 Jones matrix is the identity matrix (multiplied by a scalar phase factor and attenuation factor), implying no change in polarization during propagation. For propagation effects in two orthogonal modes,
15824-480: The case of linear birefringence (with two orthogonal linear propagation modes) with an incoming wave linearly polarized at a 45° angle to those modes. As a differential phase starts to accrue, the polarization becomes elliptical, eventually changing to purely circular polarization (90° phase difference), then to elliptical and eventually linear polarization (180° phase) perpendicular to the original polarization, then through circular again (270° phase), then elliptical with
15996-450: The center, the temperature may be up to 6,000 °C (10,830 °F), and the pressure could reach 360 GPa (52 million psi ). Because much of the heat is provided by radioactive decay, scientists postulate that early in Earth's history, before isotopes with short half-lives were depleted, Earth's heat production was much higher. At approximately 3 Gyr , twice the present-day heat would have been produced, increasing
16168-1575: The complex quantities occurring in the following equations. As a function of time t and spatial position z (since for a plane wave in the + z direction the fields have no dependence on x or y ) these complex fields can be written as: E → ( z , t ) = [ e x e y 0 ] e i 2 π ( z λ − t T ) = [ e x e y 0 ] e i ( k z − ω t ) {\displaystyle {\vec {E}}(z,t)={\begin{bmatrix}e_{x}\\e_{y}\\0\end{bmatrix}}\;e^{i2\pi \left({\frac {z}{\lambda }}-{\frac {t}{T}}\right)}={\begin{bmatrix}e_{x}\\e_{y}\\0\end{bmatrix}}\;e^{i(kz-\omega t)}} and H → ( z , t ) = [ h x h y 0 ] e i 2 π ( z λ − t T ) = [ h x h y 0 ] e i ( k z − ω t ) , {\displaystyle {\vec {H}}(z,t)={\begin{bmatrix}h_{x}\\h_{y}\\0\end{bmatrix}}\;e^{i2\pi \left({\frac {z}{\lambda }}-{\frac {t}{T}}\right)}={\begin{bmatrix}h_{x}\\h_{y}\\0\end{bmatrix}}\;e^{i(kz-\omega t)},} where λ = λ 0 / n
16340-432: The condition of the sky is one of the more important parameters used to forecast weather in mountainous areas. Thickening of cloud cover or the invasion of a higher cloud deck is indicative of rain in the near future. At night, high thin cirrostratus clouds can lead to halos around the Moon, which indicate the approach of a warm front and its associated rain. Morning fog portends fair conditions and can be associated with
16512-454: The continental crust , particularly during the early stages of Earth's history. New continental crust forms as a result of plate tectonics , a process ultimately driven by the continuous loss of heat from Earth's interior. Over the period of hundreds of millions of years, tectonic forces have caused areas of continental crust to group together to form supercontinents that have subsequently broken apart. At approximately 750 Ma , one of
16684-616: The continental surfaces are covered by sedimentary rocks, although they form about 5% of the mass of the crust. Earth's surface topography comprises both the topography of the ocean surface , and the shape of Earth's land surface. The submarine terrain of the ocean floor has an average bathymetric depth of 4 km, and is as varied as the terrain above sea level. Earth's surface is continually being shaped by internal plate tectonic processes including earthquakes and volcanism ; by weathering and erosion driven by ice, water, wind and temperature; and by biological processes including
16856-419: The core are chaotic; the magnetic poles drift and periodically change alignment. This causes secular variation of the main field and field reversals at irregular intervals averaging a few times every million years. The most recent reversal occurred approximately 700,000 years ago. The extent of Earth's magnetic field in space defines the magnetosphere . Ions and electrons of the solar wind are deflected by
17028-527: The core is primarily composed of the denser elements: iron (88.8%), with smaller amounts of nickel (5.8%), sulfur (4.5%), and less than 1% trace elements. The most common rock constituents of the crust are oxides . Over 99% of the crust is composed of various oxides of eleven elements, principally oxides containing silicon (the silicate minerals ), aluminium, iron, calcium, magnesium, potassium, or sodium. The major heat-producing isotopes within Earth are potassium-40 , uranium-238 , and thorium-232 . At
17200-463: The core, through the mantle, and up to Earth's surface, where it is, approximately, a dipole . The poles of the dipole are located close to Earth's geographic poles. At the equator of the magnetic field, the magnetic-field strength at the surface is 3.05 × 10 T , with a magnetic dipole moment of 7.79 × 10 Am at epoch 2000, decreasing nearly 6% per century (although it still remains stronger than its long time average). The convection movements in
17372-428: The crystal. It was this effect that provided the first discovery of polarization, by Erasmus Bartholinus in 1669. Media in which transmission of one polarization mode is preferentially reduced are called dichroic or diattenuating . Like birefringence, diattenuation can be with respect to linear polarization modes (in a crystal) or circular polarization modes (usually in a liquid). Devices that block nearly all of
17544-539: The days shorter. Above the Arctic Circle and below the Antarctic Circle there is no daylight at all for part of the year, causing a polar night , and this night extends for several months at the poles themselves. These same latitudes also experience a midnight sun , where the sun remains visible all day. By astronomical convention, the four seasons can be determined by the solstices—the points in
17716-412: The different propagation of waves in two such components in circularly birefringent media (see below) or signal paths of coherent detectors sensitive to circular polarization. Regardless of whether polarization state is represented using geometric parameters or Jones vectors, implicit in the parameterization is the orientation of the coordinate frame. This permits a degree of freedom, namely rotation about
17888-611: The earliest known supercontinents, Rodinia , began to break apart. The continents later recombined to form Pannotia at 600–540 Ma , then finally Pangaea , which also began to break apart at 180 Ma . The most recent pattern of ice ages began about 40 Ma , and then intensified during the Pleistocene about 3 Ma . High- and middle-latitude regions have since undergone repeated cycles of glaciation and thaw, repeating about every 21,000, 41,000 and 100,000 years. The Last Glacial Period , colloquially called
18060-406: The electric field parallel to this plane is termed p-like (parallel) and the component perpendicular to this plane is termed s-like (from senkrecht , German for 'perpendicular'). Polarized light with its electric field along the plane of incidence is thus denoted p-polarized , while light whose electric field is normal to the plane of incidence is called s-polarized . P -polarization
18232-544: The equally large area of land under permafrost ) or deserts (33%). The pedosphere is the outermost layer of Earth's land surface and is composed of soil and subject to soil formation processes. Soil is crucial for land to be arable. Earth's total arable land is 10.7% of the land surface, with 1.3% being permanent cropland. Earth has an estimated 16.7 million km (6.4 million sq mi) of cropland and 33.5 million km (12.9 million sq mi) of pastureland. The land surface and
18404-576: The ground. The engineering aspects of flight are studied in aerospace engineering which is subdivided into aeronautics , which is the study of vehicles that travel through the air, and astronautics , the study of vehicles that travel through space, and in ballistics , the study of the flight of projectiles. While human beings have been capable of flight via hot air balloons since 1783, other species have used flight for significantly longer. Animals, such as birds, bats, and insects are capable of flight. Spores and seeds from plants use flight, via use of
18576-638: The growth and decomposition of biomass into soil . Earth's mechanically rigid outer layer of Earth's crust and upper mantle , the lithosphere , is divided into tectonic plates . These plates are rigid segments that move relative to each other at one of three boundaries types: at convergent boundaries , two plates come together; at divergent boundaries , two plates are pulled apart; and at transform boundaries , two plates slide past one another laterally. Along these plate boundaries, earthquakes, volcanic activity , mountain-building , and oceanic trench formation can occur. The tectonic plates ride on top of
18748-404: The heat in Earth is lost through plate tectonics, by mantle upwelling associated with mid-ocean ridges . The final major mode of heat loss is through conduction through the lithosphere, the majority of which occurs under the oceans. The gravity of Earth is the acceleration that is imparted to objects due to the distribution of mass within Earth. Near Earth's surface, gravitational acceleration
18920-426: The horizon travels through as much as 38 times the air mass as does light from the zenith , causing a blue gradient looking vivid at the zenith and pale near the horizon. Red light is also scattered if there is enough air between the source and the observer, causing parts of the sky to change color as the Sun rises or sets. As the air mass nears infinity, scattered daylight appears whiter and whiter. Apart from
19092-406: The land surface is taken by the four continental landmasses , which are (in descending order): Africa-Eurasia , America (landmass) , Antarctica , and Australia (landmass) . These landmasses are further broken down and grouped into the continents . The terrain of the land surface varies greatly and consists of mountains, deserts , plains , plateaus , and other landforms . The elevation of
19264-513: The land surface varies from a low point of −418 m (−1,371 ft) at the Dead Sea , to a maximum altitude of 8,848 m (29,029 ft) at the top of Mount Everest . The mean height of land above sea level is about 797 m (2,615 ft). Land can be covered by surface water , snow, ice, artificial structures or vegetation. Most of Earth's land hosts vegetation, but considerable amounts of land are ice sheets (10%, not including
19436-414: The leftmost figure) and a vertically polarized wave of the same amplitude in the same phase . [REDACTED] [REDACTED] [REDACTED] Now if one were to introduce a phase shift in between those horizontal and vertical polarization components, one would generally obtain elliptical polarization as is shown in the third figure. When the phase shift is exactly ±90°, and the amplitudes are
19608-506: The length of the vector measured from the center of the sphere. Unpolarized light is light with a random, time-varying polarization . Natural light, like most other common sources of visible light, is produced independently by a large number of atoms or molecules whose emissions are uncorrelated . Unpolarized light can be produced from the incoherent combination of vertical and horizontal linearly polarized light, or right- and left-handed circularly polarized light. Conversely,
19780-399: The lithosphere, which is divided into independently moving tectonic plates. Beneath the lithosphere is the asthenosphere , a relatively low-viscosity layer on which the lithosphere rides. Important changes in crystal structure within the mantle occur at 410 and 660 km (250 and 410 mi) below the surface, spanning a transition zone that separates the upper and lower mantle. Beneath
19952-410: The loss of oxygen in the atmosphere, making current animal life impossible. Due to the increased luminosity, Earth's mean temperature may reach 100 °C (212 °F) in 1.5 billion years, and all ocean water will evaporate and be lost to space, which may trigger a runaway greenhouse effect , within an estimated 1.6 to 3 billion years. Even if the Sun were stable, a fraction of the water in
20124-456: The lowercase when it is preceded by "the", such as "the atmosphere of the earth". It almost always appears in lowercase in colloquial expressions such as "what on earth are you doing?" The name Terra / ˈ t ɛr ə / occasionally is used in scientific writing and especially in science fiction to distinguish humanity's inhabited planet from others, while in poetry Tellus / ˈ t ɛ l ə s / has been used to denote personification of
20296-497: The magnetosphere. During magnetic storms and substorms , charged particles can be deflected from the outer magnetosphere and especially the magnetotail, directed along field lines into Earth's ionosphere , where atmospheric atoms can be excited and ionized, causing an aurora . Earth's rotation period relative to the Sun—its mean solar day—is 86,400 seconds of mean solar time ( 86,400.0025 SI seconds ). Because Earth's solar day
20468-409: The magnetosphere; solar wind pressure compresses the day-side of the magnetosphere, to about 10 Earth radii, and extends the night-side magnetosphere into a long tail. Because the velocity of the solar wind is greater than the speed at which waves propagate through the solar wind, a supersonic bow shock precedes the day-side magnetosphere within the solar wind. Charged particles are contained within
20640-483: The magnetosphere; the plasmasphere is defined by low-energy particles that essentially follow magnetic field lines as Earth rotates. The ring current is defined by medium-energy particles that drift relative to the geomagnetic field, but with paths that are still dominated by the magnetic field, and the Van Allen radiation belts are formed by high-energy particles whose motion is essentially random, but contained in
20812-417: The mantle, an extremely low viscosity liquid outer core lies above a solid inner core . Earth's inner core may be rotating at a slightly higher angular velocity than the remainder of the planet, advancing by 0.1–0.5° per year, although both somewhat higher and much lower rates have also been proposed. The radius of the inner core is about one-fifth of that of Earth. The density increases with depth. Among
20984-612: The mantle. Due to this recycling, most of the ocean floor is less than 100 Ma old. The oldest oceanic crust is located in the Western Pacific and is estimated to be 200 Ma old. By comparison, the oldest dated continental crust is 4,030 Ma , although zircons have been found preserved as clasts within Eoarchean sedimentary rocks that give ages up to 4,400 Ma , indicating that at least some continental crust existed at that time. The seven major plates are
21156-548: The modern oceans will descend to the mantle , due to reduced steam venting from mid-ocean ridges. The Sun will evolve to become a red giant in about 5 billion years . Models predict that the Sun will expand to roughly 1 AU (150 million km; 93 million mi), about 250 times its present radius. Earth's fate is less clear. As a red giant, the Sun will lose roughly 30% of its mass, so, without tidal effects, Earth will move to an orbit 1.7 AU (250 million km; 160 million mi) from
21328-399: The mother of Thor . Historically, "Earth" has been written in lowercase. Beginning with the use of Early Middle English , its definite sense as "the globe" was expressed as "the earth". By the era of Early Modern English , capitalization of nouns began to prevail , and the earth was also written the Earth , particularly when referenced along with other heavenly bodies. More recently,
21500-424: The name is sometimes simply given as Earth , by analogy with the names of the other planets , though "earth" and forms with "the earth" remain common. House styles now vary: Oxford spelling recognizes the lowercase form as the more common, with the capitalized form an acceptable variant. Another convention capitalizes "Earth" when appearing as a name, such as a description of the "Earth's atmosphere", but employs
21672-425: The newly forming Sun had only 70% of its current luminosity . By 3.5 Ga , Earth's magnetic field was established, which helped prevent the atmosphere from being stripped away by the solar wind . As the molten outer layer of Earth cooled it formed the first solid crust , which is thought to have been mafic in composition. The first continental crust , which was more felsic in composition, formed by
21844-593: The ocean may have covered Earth completely. The world ocean is commonly divided into the Pacific Ocean, Atlantic Ocean, Indian Ocean, Antarctic or Southern Ocean , and Arctic Ocean, from largest to smallest. The ocean covers Earth's oceanic crust , with the shelf seas covering the shelves of the continental crust to a lesser extent. The oceanic crust forms large oceanic basins with features like abyssal plains , seamounts , submarine volcanoes , oceanic trenches , submarine canyons , oceanic plateaus , and
22016-418: The ocean, but are also seen above clouds and mountains. Green flashes may also be observed at the horizon in association with the Moon and bright planets, including Venus and Jupiter . Earth's shadow is the shadow that the planet casts through its atmosphere and into outer space. This atmospheric phenomenon is visible during civil twilight (after sunset and before sunrise). When the weather conditions and
22188-670: The oceanic plates, with the Cocos Plate advancing at a rate of 75 mm/a (3.0 in/year) and the Pacific Plate moving 52–69 mm/a (2.0–2.7 in/year). At the other extreme, the slowest-moving plate is the South American Plate, progressing at a typical rate of 10.6 mm/a (0.42 in/year). Earth's interior, like that of the other terrestrial planets, is divided into layers by their chemical or physical ( rheological ) properties. The outer layer
22360-599: The orbit of maximum axial tilt toward or away from the Sun—and the equinoxes , when Earth's rotational axis is aligned with its orbital axis. In the Northern Hemisphere, winter solstice currently occurs around 21 December; summer solstice is near 21 June, spring equinox is around 20 March and autumnal equinox is about 22 or 23 September. In the Southern Hemisphere, the situation is reversed, with
22532-472: The original azimuth angle, and finally back to the original linearly polarized state (360° phase) where the cycle begins anew. In general the situation is more complicated and can be characterized as a rotation in the Poincaré sphere about the axis defined by the propagation modes. Examples for linear (blue), circular (red), and elliptical (yellow) birefringence are shown in the figure on the left. The total intensity and degree of polarization are unaffected. If
22704-475: The overall magnitude and phase of that wave. Specifically, the intensity of the light wave is proportional to the sum of the squared magnitudes of the two electric field components: I = ( | e x | 2 + | e y | 2 ) 1 2 η {\displaystyle I=\left(\left|e_{x}\right|^{2}+\left|e_{y}\right|^{2}\right)\,{\frac {1}{2\eta }}} However,
22876-649: The ozone layer, life colonized Earth's surface. Among the earliest fossil evidence for life is microbial mat fossils found in 3.48 billion-year-old sandstone in Western Australia , biogenic graphite found in 3.7 billion-year-old metasedimentary rocks in Western Greenland , and remains of biotic material found in 4.1 billion-year-old rocks in Western Australia. The earliest direct evidence of life on Earth
23048-474: The partial melting of this mafic crust. The presence of grains of the mineral zircon of Hadean age in Eoarchean sedimentary rocks suggests that at least some felsic crust existed as early as 4.4 Ga , only 140 Ma after Earth's formation. There are two main models of how this initial small volume of continental crust evolved to reach its current abundance: (1) a relatively steady growth up to
23220-483: The particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves , gravitational waves , and transverse sound waves ( shear waves ) in solids. An electromagnetic wave such as light consists of a coupled oscillating electric field and magnetic field which are always perpendicular to each other; by convention,
23392-436: The passage of a tropical cyclone 's center, the pressure begins to fall and a veil of white cirrus clouds approaches from the cyclone's direction. Within 24 hours of the closest approach to the center, low clouds begin to move in, also known as the bar of a tropical cyclone, as the barometric pressure begins to fall more rapidly and the winds begin to increase. Within 18 hours of the center's approach, squally weather
23564-501: The past 66 Mys , and several million years ago, an African ape species gained the ability to stand upright. This facilitated tool use and encouraged communication that provided the nutrition and stimulation needed for a larger brain, which led to the evolution of humans . The development of agriculture , and then civilization , led to humans having an influence on Earth and the nature and quantity of other life forms that continues to this day. Earth's expected long-term future
23736-447: The path length in the birefringent medium is sufficient, the two polarization components of a collimated beam (or ray ) can exit the material with a positional offset, even though their final propagation directions will be the same (assuming the entrance face and exit face are parallel). This is commonly viewed using calcite crystals , which present the viewer with two slightly offset images, in opposite polarizations, of an object behind
23908-545: The phase of e x is zero; in other words e x is a real number while e y may be complex. Under these restrictions, e x and e y can be represented as follows: e x = 1 + Q 2 e y = 1 − Q 2 e i ϕ , {\displaystyle {\begin{aligned}e_{x}&={\sqrt {\frac {1+Q}{2}}}\\e_{y}&={\sqrt {\frac {1-Q}{2}}}\,e^{i\phi },\end{aligned}}} where
24080-458: The plane of incidence ( p and s polarizations, see below), that choice greatly simplifies the calculation of a wave's reflection from a surface. Any pair of orthogonal polarization states may be used as basis functions, not just linear polarizations. For instance, choosing right and left circular polarizations as basis functions simplifies the solution of problems involving circular birefringence (optical activity) or circular dichroism. For
24252-409: The plane wave approximation breaks down. An extreme example is radially or tangentially polarized light, at the focus of which the electric or magnetic field respectively is entirely longitudinal (along the direction of propagation). For longitudinal waves such as sound waves in fluids , the direction of oscillation is by definition along the direction of travel, so the issue of polarization
24424-478: The planet's environment . Humanity's current impact on Earth's climate and biosphere is unsustainable , threatening the livelihood of humans and many other forms of life, and causing widespread extinctions . The Modern English word Earth developed, via Middle English , from an Old English noun most often spelled eorðe . It has cognates in every Germanic language , and their ancestral root has been reconstructed as * erþō . In its earliest attestation,
24596-400: The planet. The water vapor acts as a greenhouse gas and, together with other greenhouse gases in the atmosphere, particularly carbon dioxide (CO 2 ), creates the conditions for both liquid surface water and water vapor to persist via the capturing of energy from the Sun's light . This process maintains the current average surface temperature of 14.76 °C (58.57 °F), at which water
24768-421: The polar Northern and Southern hemispheres; or by longitude into the continental Eastern and Western hemispheres. Most of Earth's surface is ocean water: 70.8% or 361 million km (139 million sq mi). This vast pool of salty water is often called the world ocean , and makes Earth with its dynamic hydrosphere a water world or ocean world . Indeed, in Earth's early history
24940-457: The polarization of a coherent wave cannot be described simply using a Jones vector, as we have just done. Just considering electromagnetic waves, we note that the preceding discussion strictly applies to plane waves in a homogeneous isotropic non-attenuating medium, whereas in an anisotropic medium (such as birefringent crystals as discussed below) the electric or magnetic field may have longitudinal as well as transverse components. In those cases
25112-481: The polarization state is now fully parameterized by the value of Q (such that −1 < Q < 1 ) and the relative phase ϕ . In addition to transverse waves, there are many wave motions where the oscillation is not limited to directions perpendicular to the direction of propagation. These cases are far beyond the scope of the current article which concentrates on transverse waves (such as most electromagnetic waves in bulk media), but one should be aware of cases where
25284-403: The polarization state itself is independent of absolute phase . The basis vectors used to represent the Jones vector need not represent linear polarization states (i.e. be real ). In general any two orthogonal states can be used, where an orthogonal vector pair is formally defined as one having a zero inner product . A common choice is left and right circular polarizations, for example to model
25456-420: The presence of a magnetic field along the direction of propagation. When linearly polarized light is passed through such an object, it will exit still linearly polarized, but with the axis of polarization rotated. A combination of linear and circular birefringence will have as basis polarizations two orthogonal elliptical polarizations; however, the term "elliptical birefringence" is rarely used. One can visualize
25628-495: The present day, which is supported by the radiometric dating of continental crust globally and (2) an initial rapid growth in the volume of continental crust during the Archean , forming the bulk of the continental crust that now exists, which is supported by isotopic evidence from hafnium in zircons and neodymium in sedimentary rocks. The two models and the data that support them can be reconciled by large-scale recycling of
25800-500: The product of these two basic types of transformations. In birefringent media there is no attenuation, but two modes accrue a differential phase delay. Well known manifestations of linear birefringence (that is, in which the basis polarizations are orthogonal linear polarizations) appear in optical wave plates /retarders and many crystals. If linearly polarized light passes through a birefringent material, its state of polarization will generally change, unless its polarization direction
25972-418: The propagation direction ( + z in this case) and η , one can just as well specify the wave in terms of just e x and e y describing the electric field. The vector containing e x and e y (but without the z component which is necessarily zero for a transverse wave) is known as a Jones vector . In addition to specifying the polarization state of the wave, a general Jones vector also specifies
26144-420: The propagation direction. When considering light that is propagating parallel to the surface of the Earth, the terms "horizontal" and "vertical" polarization are often used, with the former being associated with the first component of the Jones vector, or zero azimuth angle. On the other hand, in astronomy the equatorial coordinate system is generally used instead, with the zero azimuth (or position angle, as it
26316-437: The radiation in one mode are known as polarizing filters or simply " polarizers ". This corresponds to g 2 = 0 in the above representation of the Jones matrix. The output of an ideal polarizer is a specific polarization state (usually linear polarization) with an amplitude equal to the input wave's original amplitude in that polarization mode. Power in the other polarization mode is eliminated. Thus if unpolarized light
26488-493: The rates of mantle convection and plate tectonics, and allowing the production of uncommon igneous rocks such as komatiites that are rarely formed today. The mean heat loss from Earth is 87 mW m , for a global heat loss of 4.42 × 10 W . A portion of the core's thermal energy is transported toward the crust by mantle plumes , a form of convection consisting of upwellings of higher-temperature rock. These plumes can produce hotspots and flood basalts . More of
26660-461: The remaining power in the unwanted polarization will be ( g 2 / g 1 ) of the power in the intended polarization. In addition to birefringence and dichroism in extended media, polarization effects describable using Jones matrices can also occur at (reflective) interface between two materials of different refractive index . These effects are treated by the Fresnel equations . Part of the wave
26832-413: The same, then circular polarization is produced (fourth and fifth figures). Circular polarization can be created by sending linearly polarized light through a quarter-wave plate oriented at 45° to the linear polarization to create two components of the same amplitude with the required phase shift. The superposition of the original and phase-shifted components causes a rotating electric field vector, which
27004-410: The set of colored rings and create a washed-out white color. The sky can turn a multitude of colors such as red, orange, purple, and yellow (especially near sunset or sunrise) when the light must travel a much longer path (or optical depth ) through the atmosphere. Scattering effects also partially polarize light from the sky and are most pronounced at an angle 90° from the Sun. Scattered light from
27176-522: The shape of an ellipsoid , bulging at its Equator ; its diameter is 43 kilometres (27 mi) longer there than at its poles . Earth's shape also has local topographic variations; the largest local variations, like the Mariana Trench (10,925 metres or 35,843 feet below local sea level), shortens Earth's average radius by 0.17% and Mount Everest (8,848 metres or 29,029 feet above local sea level) lengthens it by 0.14%. Since Earth's surface
27348-412: The sky (in the absence of moon and city lights) absolutely dark, one would not be able to see the silhouette of an object against the sky. The night sky and studies of it have a historical place in both ancient and modern cultures. In the past, for instance, farmers have used the state of the night sky as a calendar to determine when to plant crops. The ancient belief in astrology is generally based on
27520-431: The sky as seen at night. The term is usually associated with skygazing and astronomy , with reference to views of celestial bodies such as stars, the Moon, and planets that become visible on a clear night after the Sun has set. Natural light sources in a night sky include moonlight, starlight, and airglow, depending on location and timing. The fact that the sky is not completely dark at night can be easily observed. Were
27692-505: The solid and vibration along the direction of propagation. The differential propagation of transverse and longitudinal polarizations is important in seismology . Polarization can be defined in terms of pure polarization states with only a coherent sinusoidal wave at one optical frequency. The vector in the adjacent diagram might describe the oscillation of the electric field emitted by a single-mode laser (whose oscillation frequency would be typically 10 times faster). The field oscillates in
27864-413: The summer and winter solstices exchanged and the spring and autumnal equinox dates swapped. Polarization (waves) Polarization ( also polarisation ) is a property of transverse waves which specifies the geometrical orientation of the oscillations . In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of
28036-643: The sun, flames, and incandescent lamps , consists of short wave trains with an equal mixture of polarizations; this is called unpolarized light . Polarized light can be produced by passing unpolarized light through a polarizer , which allows waves of only one polarization to pass through. The most common optical materials do not affect the polarization of light, but some materials—those that exhibit birefringence , dichroism , or optical activity —affect light differently depending on its polarization. Some of these are used to make polarizing filters. Light also becomes partially polarized when it reflects at an angle from
28208-586: The system departs, winds reverse and, along with the rain, suddenly increase. One day after the center's passage, the low overcast is replaced with a higher overcast, and the rain becomes intermittent. By 36 hours after the center's passage, the high overcast breaks and the pressure begins to level off. Flight is the process by which an object moves through or beyond the sky (as in the case of spaceflight), whether by generating aerodynamic lift , propulsive thrust , aerostatically using buoyancy, or by ballistic movement, without any direct mechanical support from
28380-452: The two constituent linearly polarized states of unpolarized light cannot form an interference pattern , even if rotated into alignment ( Fresnel–Arago 3rd law ). A so-called depolarizer acts on a polarized beam to create one in which the polarization varies so rapidly across the beam that it may be ignored in the intended applications. Conversely, a polarizer acts on an unpolarized beam or arbitrarily polarized beam to create one which
28552-425: The wave's state of polarization is only dependent on the (complex) ratio of e y to e x . So let us just consider waves whose | e x | + | e y | = 1 ; this happens to correspond to an intensity of about 0.001 33 W /m in free space (where η = η 0 ). And because the absolute phase of a wave is unimportant in discussing its polarization state, let us stipulate that
28724-503: The wave. DOP can be used to map the strain field in materials when considering the DOP of the photoluminescence . The polarization of the photoluminescence is related to the strain in a material by way of the given material's photoelasticity tensor . DOP is also visualized using the Poincaré sphere representation of a polarized beam. In this representation, DOP is equal to
28896-400: The weather, the sky refers to only the lower, denser layers of the atmosphere. The daytime sky appears blue because air molecules scatter shorter wavelengths of sunlight more than longer ones (redder light). The night sky appears to be a mostly dark surface or region spangled with stars. The Sun and sometimes the Moon are visible in the daytime sky unless obscured by clouds . At night,
29068-669: The wind, as a method of propagating their species. Many mythologies have deities especially associated with the sky. In Egyptian religion , the sky was deified as the goddess Nut and as the god Horus . Dyeus is reconstructed as the god of the sky, or the sky personified, in Proto-Indo-European religion , whence Zeus , the god of the sky and thunder in Greek mythology and the Roman god of sky and thunder Jupiter . In Australian Aboriginal mythology , Altjira (or Arrernte)
29240-461: The word eorðe was used to translate the many senses of Latin terra and Greek γῆ gē : the ground, its soil , dry land, the human world, the surface of the world (including the sea), and the globe itself. As with Roman Terra /Tellūs and Greek Gaia , Earth may have been a personified goddess in Germanic paganism : late Norse mythology included Jörð ("Earth"), a giantess often given as
29412-620: The year. This causes the seasonal change in climate, with summer in the Northern Hemisphere occurring when the Tropic of Cancer is facing the Sun, and in the Southern Hemisphere when the Tropic of Capricorn faces the Sun. In each instance, winter occurs simultaneously in the opposite hemisphere. During the summer, the day lasts longer, and the Sun climbs higher in the sky. In winter, the climate becomes cooler and
29584-570: Was used above to show how different states of polarization are possible. The amplitude and phase information can be conveniently represented as a two-dimensional complex vector (the Jones vector ): e = [ a 1 e i θ 1 a 2 e i θ 2 ] . {\displaystyle \mathbf {e} ={\begin{bmatrix}a_{1}e^{i\theta _{1}}\\a_{2}e^{i\theta _{2}}\end{bmatrix}}.} Here
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