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Lesson 1: Relate addition and subtraction

Sal shows the relationship between 2+3=5, 5-2=3, and 5-3=2.

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• 2 green balls and 3 purple balls is 5 balls together
• that is correct mfunk0886. Good job for getting that correct.
• There are 4 types of basic adding, subtracting.( I think ). There is addition+, subtraction-,multiplicationX, and dividing/. Now, if you are willing to add, you need to take the first number and add that to the second number. Then you have your answer. Subtraction is different, I you have a number, and a different number than you have got to take away the how ever many numbers from the first number of the second number. Now, multiplication is a whole new level. The way you work this type is to add the first number however many times the second number is. Dividing is harder. You have the first number and the lower second number. You have got to put in the second number until you have the first. You count however many times you put in the second number until you have the remaining first number. Than you have the answer! Your welcome! (I hope this helps)
• Just by looking at the addition problem we can also understand the subtraction problem without writing the subtraction problem.
• Um what is a reciprocal
• Good question for first grade!

A reciprocal of a number is 1 divided by that number. Taking a reciprocal can also be thought of as switching the numerator (top) and denominator (bottom) of a fraction.

Examples:
Because 1 is 1/1, the reciprocal of 1 is just 1.
Since 3 is 3/1, the reciprocal of 3 is 1/3.
The reciprocal of 4/7 is 7/4, or 1 3/4.
Because 2 4/5 is 14/5, the reciprocal of 2 4/5 is 5/14.
0 is the only number without a reciprocal since 1/0 is undefined.

Note that any number (other than 0) times its reciprocal is always 1. Later on, when you study operations with fractions, you will learn that division by a number is the same as multiplication by that number's reciprocal.
• Math goes on infinitely, does that mean it goes infinitely both positively and negatively? So, if it is limitless in positive numbers (above zero), then would the opposite of infinity be 'negative infinity' or simply, again, infinity?
• this line from the video is veeeeeery sus
"We have two balls. if we split those balls in half, we have one ball." Sal Khan. like what?? :|
• 101010101001010101010100101
• i need help with my math. {PLZ HELP!}
• The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth creates pressure, absorbs most meteoroids and ultraviolet solar radiation, warms the surface through heat retention (greenhouse effect), allowing life and liquid water to exist on the Earth's surface, and reduces temperature extremes between day and night (the diurnal temperature variation).

As of 2023, by mole fraction (i.e., by number of molecules), dry air contains 78.08% nitrogen, 20.95% oxygen, 0.93% argon, 0.04% carbon dioxide, and small amounts of other gases.[8] Air also contains a variable amount of water vapor, on average around 1% at sea level, and 0.4% over the entire atmosphere. Air composition, temperature, and atmospheric pressure vary with altitude. Within the atmosphere, air suitable for use in photosynthesis by terrestrial plants and breathing of terrestrial animals is found only in Earth's troposphere.[citation needed]

Earth's early atmosphere consisted of gases in the solar nebula, primarily hydrogen. The atmosphere changed significantly over time, affected by many factors such as volcanism, life, and weathering. Recently, human activity has also contributed to atmospheric changes, such as global warming, ozone depletion and acid deposition.

The atmosphere has a mass of about 5.15×1018 kg,[9] three quarters of which is within about 11 km (6.8 mi; 36,000 ft) of the surface. The atmosphere becomes thinner with increasing altitude, with no definite boundary between the atmosphere and outer space. The Kármán line, at 100 km (62 mi) or 1.57% of Earth's radius, is often used as the border between the atmosphere and outer space. Atmospheric effects become noticeable during atmospheric reentry of spacecraft at an altitude of around 120 km (75 mi). Several layers can be distinguished in the atmosphere, based on characteristics such as temperature and composition.

The study of Earth's atmosphere and its processes is called atmospheric science (aerology), and includes multiple subfields, such as climatology and atmospheric physics. Early pioneers in the field include Léon Teisserenc de Bort and Richard Assmann.[10] The study of historic atmosphere is called paleoclimatology.

Composition
Main article: Atmospheric chemistry

Composition of Earth's atmosphere by molecular count, excluding water vapor. Lower pie represents trace gases that together compose about 0.0434% of the atmosphere (0.0442% at August 2021 concentrations[4][5]). Numbers are mainly from 2000, with CO2 and methane from 2019, and do not represent any single source.[3]
The three major constituents of Earth's atmosphere are nitrogen, oxygen, and argon. Water vapor accounts for roughly 0.25% of the atmosphere by mass. The concentration of water vapor (a greenhouse gas) varies significantly from around 10 ppm by mole fraction in the coldest portions of the atmosphere to as much as 5% by mole fraction in hot, humid air masses, and concentrations of other atmospheric gases are typically quoted in terms of dry air (without water vapor).[11]: 8  The remaining gases are often referred to as trace gases,[12] among which are other greenhouse gases, principally carbon dioxide, methane, nitrous oxide, and ozone. Besides argon, already mentioned, other noble gases, neon, helium, krypton, and xenon are also present. Filtered air includes trace amounts of many other chemical compounds. Many substances of natural origin may be present in locally and seasonally variable small amounts as aerosols in an unfiltered air sample, including dust of mineral and organic composition, pollen and spores, sea spray, and volcanic ash. Various industrial pollutants also may be present as gases or aerosols, such as chlorine (elemental or in compounds), fluorine compounds and elemental mercury vapor. Sulfur compounds such as hydrogen sulfide and sulfur dioxide (SO2) may be derived from natural sources or from industrial air pollution.

Major constituents of dry air, by mole fraction[8]
Gas Mole fraction(A)
Name Formula in ppm(B) in %
Nitrogen N2 780,840 78.084
Oxygen O2 209,460 20.946
Argon Ar 9,340 0.9340
Carbon dioxide
(April 2022)(C)[13] CO2 417 0.0417
Neon Ne 18.18 0.001818
Helium He 5.24 0.000524
Methane CH4 1.87 0.000187
Krypton Kr 1.14 0.000114
Not included in above dry atmosphere:
Water vapor(D) H2O 0–30,000(D) 0–3%(E)
notes:
(A) Mole fraction is sometimes referred to as volume fraction; these are identical for an ideal gas only.
(B) ppm: parts per million by molecular count
The total ppm above adds up to more than 1 million (currently 83.43 above it) due to experimental error.
(C) The concentration of CO2 has been increasing in recent decades
(D) Water vapor is about 0.25% by mass over full atmosphere
(E) Water vapor varies significantly locally[11]
The average molecular weight of dry air, which can be used to calculate densities or to convert between mole fraction and mass fraction, is about 28.946[14] or 28.96[15][16] g/mol. This is decreased when the air is humid.

The relative concentration of gases remains constant until about 10,000 m (33,000 ft).[17]

Stratification

Earth's atmosphere. Lower four layers of the atmosphere in three dimensions as seen diagonally from above the exobase. Layers drawn to scale, objects within the layers are not to scale. Aurorae shown here at the bottom of the thermosphere can actually form at any altitude in this atmospheric layer.
In general, air pressure and density decrease with altitude in the atmosphere. However, the temperature has a more complicated profile with altitude, and may remain relatively constant or even increase with altitude in some regions (see the temperature section, below). Because the general pattern of the temperature/altitude profile, or lapse rate, is constant and measurable by means of instrumented balloon soundings, the temperature behavior provides a useful metric to distinguish atmospheric layers. In this way, Earth's atmosphere can be divided (called atmospheric stratification) into five main layers: troposphere, stratosphere, mesosphere, thermosphere, and exosphere.[18] The altitudes of the five layers are as follows:

Exosphere: 700 to 10,000 km (440 to 6,200 miles)[19]
Thermosphere: 80 to 700 km (50 to 440 miles)[20]
Mesosphere: 50 to 80 km (31 to 50 miles)
Stratosphere: 12 to 50 km (7 to 31 miles)
Troposphere: 0 to 12 km (0 to 7 miles)[21]
Exosphere
Main article: Exosphere
The exosphere is the outermost layer of Earth's atmosphere (though it is so tenuous that some scientists consider it to be part of interplanetary space rather than part of the atmosphere). It extends from the thermopause (also known as the "exobase") at the top of the thermosphere to a poorly defined boundary with the solar wind and interplanetary medium. The altitude of the exobase varies from about 500 kilometres (310 mi; 1,600,000 ft) to about 1,000 kilometres (620 mi) in times of higher incoming solar radiation.[22]

The upper limit varies depending on the definition. Various authorities consider it to end at about 10,000 kilometres (6,200 mi)[23] or about 190,000 kilometres (120,000 mi)—about halfway to the moon, where the influence of Earth's gravity is about the same as radiation pressure from sunlight.[22] The geocorona visible in the far ultraviolet (caused by neutral hydrogen) extends to at least 100,000 kilometres (62,000 mi).[22]

This layer is mainly composed of extremely low densities of hydrogen, helium and several heavier molecules including nitrogen, oxygen and carbon dioxide closer to the exobase. The atoms and molecules are so far apart that they can travel hundreds of kilometers without colliding with one another. Thus, the exosphere no longer behaves like a gas, and the particles constantly escape into space. These free-moving particles follow ballistic trajectories and may migrate in and out of the magnetosphere or the solar wind. Every second, the Earth loses about 3 kg of hydrogen, 50 g of helium, and much smaller amounts of other constituents.[24]

The exosphere is too far above Earth for meteorological phenomena to be possible. However, Earth's auroras—the aurora borealis (northern lights) and aurora australis (southern lights)—sometimes occur in the lower part of the exosphere, where they overlap into the thermosphere. The exosphere contains many of the artificial satellites that orbit Earth.

Thermosphere
Main article: Thermosphere
The thermosphere is the second-highest layer of Earth's atmosphere. It extends from the mesopause (which separates it from the mesosphere) at an altitude of about 80 km (50 mi; 260,000 ft) up to the thermopause at an altitude range of 500–1000 km (310–620 mi; 1,600,000–3,300,000 ft). The height of the thermopause varies considerably due to changes in solar activity.[20] Because the thermopause lies at the lower boundary of the exosphere, it is also referred to as the exobase. The lower part of the thermosphere, from 80 to 550 kilometres (50 to 342 mi) above Earth's surface, contains the ionosphere.

The temperature of the thermosphere gradually increases with height and can rise as high as 1500 °C (2700 °F), though the gas molecules are so far apart that its temperature in the usual sense is not very meaningful. The air is so rarefied that an individual molecule (of oxygen, for example) travels an average of 1 kilometre (0.62 mi; 3300 ft) between collisions with other molecules.[25] Although the thermosphere has a high proportion of molecules with high energy, it would not feel hot to a human in direct contact, because its density is too low to conduct a significant amount of energy to or from the skin.

This layer is completely cloudless and free of water vapor. However, non-hydrometeorological phenomena such as the aurora borealis and aurora australis are occasionally seen in the thermosphere. The International Space Station orbits in this layer, between 350 and 420 km (220 and 260 mi). It is this layer where many of the satellites orbiting the earth are present.

Mesosphere
Main article: Mesosphere

Afterglow of the troposphere (orange), the stratosphere (blue) and the mesosphere (dark) at which atmospheric entry begins, leaving smoke trails, such as in this case of a spacecraft reentry.
The mesosphere is the third highest layer of Earth's atmosphere, occupying the region above the stratosphere and below the thermosphere. It extends from the stratopause at an altitude of about 50 km (31 mi; 160,000 ft) to the mesopause at 80–85 km (50–53 mi; 260,000–280,000 ft) above sea level.

Temperatures drop with increasing altitude to the mesopause that marks the top of this middle layer of the atmosphere. It is the coldest place on Earth and has an average temperature around −85 °C (−120 °F; 190 K).[26][27]

Just below the mesopause, the air is so cold that even the very scarce water vapor at this altitude can condense into polar-mesospheric noctilucent clouds of ice particles. These are the highest clouds in the atmosphere and may be visible to the naked eye if sunlight reflects off them about an hour or two after sunset or similarly before sunrise. They are most readily visible when the Sun is around 4 to 16 degrees below the horizon. Lightning-induced discharges known as transient luminous events (TLEs) occasionally form in the mesosphere above tropospheric thunderclouds. The mesosphere is also the layer where most meteors burn up upon atmospheric entrance. It is too high above Earth to be accessible to jet-powered aircraft and balloons, and too low to permit orbital spacecraft. The mesosphere is mainly accessed by sounding rockets and rocket-powered aircraft.

Stratosphere
Main article: Stratosphere
The stratosphere is the second-lowest layer of Earth's atmosphere. It lies above the troposphere and is separated from it by the tropopause. This layer extends from the top of the troposphere at roughly 12 km (7.5 mi; 39,000 ft) above Earth's surface to the stratopause at an altitude of about 50 to 55 km (31 to 34 mi; 164,000 to 180,000 ft).

The atmospheric pressure at the top of the stratosphere is roughly 1/1000 the pressure at sea level. It contains the ozone layer, which is the part of Earth's atmosphere that contains relatively high concentrations of that gas. The stratosphere defines a layer in which temperatures rise with increasing altitude. This rise in temperature is caused by the absorption of ultraviolet radiation (UV) radiation from the Sun by the ozone layer, which restricts turbulence and mixing. Although the temperature may be −60 °C (−76 °F; 210 K) at the tropopause, the top of the stratosphere is much warmer, and may be near 0 °C.[28]

The stratospheric temperature profile creates very stable atmospheric conditions, so the stratosphere lacks the weather-producing air turbulence that is so prevalent in the troposphere. Consequently, the stratosphere is almost completely free of clouds and other forms of weather. However, polar stratospheric or nacreous clouds are occasionally seen in the lower part of this layer of the atmosphere where the air is coldest. The stratosphere is the highest layer that can be accessed by jet-powered aircraft.

Troposphere
Main article: Troposphere

A picture of Earth's troposphere with its different cloud types of low to high altitudes casting shadows. Sunlight is reflected off the ocean, after it was filtered into a redish light by passing through much of the troposphere at sunset. The above lying stratosphere can be seen at the horizon as a band of its characteristic glow of blue scattered sunlight.
The troposphere is the lowest layer of Earth's atmosphere. It extends from Earth's surface to an average height of about 12 km (7.5 mi; 39,000 ft), although this altitude varies from about 9 km (5.6 mi; 30,000 ft) at the geographic poles to 17 km (11 mi; 56,000 ft) at the Equator,[21] with some variation due to weather. The troposphere is bounded above by the tropopause, a boundary marked in most places by a temperature inversion (i.e. a layer of relatively warm air above a colder one), and in others by a zone that is isothermal with height.[29][30]

Although variations do occur, the temperature usually declines with increasing altitude in the troposphere because the troposphere is mostly heated through energy transfer from the surface. Thus, the lowest part of the troposphere (i.e. Earth's surface) is typically the warmest section of the troposphere. This promotes vertical mixing (hence, the origin of its name in the Greek word τρόπος, tropos, meaning "turn"). The troposphere contains roughly 80% of the mass of Earth's atmosphere.[31] The troposphere is denser than all its overlying layers because a larger atmospheric weight sits on top of the troposphere and causes it to be most severely compressed. Fifty percent of the total mass of the atmosphere is located in the lower 5.6 km (3.5 mi; 18,000 ft) of the troposphere.

Nearly all atmospheric water vapor or moisture is found in the troposphere, so it is the layer where most of Earth's weather takes place. It has basically all the weather-associated cloud genus types generated by active wind circulation, although very tall cumulonimbus thunder clouds can penetrate the tropopause from below and rise into the lower part of the stratosphere. Most conventional aviation activity takes place in the troposphere, and it is the only layer that can be accessed by propeller-driven aircraft.

Other layers

The volume fraction of the main gases in Earth's atmosphere according to height. The boundary between the homosphere (left) and heterosphere (right) is at about 100 km. The outermost layer of the exosphere (off the chart) is dominated by hydrogen.[32]
Within the five principal layers above, which are largely determined by temperature, several secondary layers may be distinguished by other properties:

The ozone layer is contained within the stratosphere. In this layer ozone concentrations are about 2 to 8 parts per million, which is much higher than in the lower atmosphere but still very small compared to the main components of the atmosphere. It is mainly located in the lower portion of the stratosphere from about 15–35 km (9.3–21.7 mi; 49,000–115,000 ft), though the thickness varies seasonally and geographically. About 90% of the ozone in Earth's atmosphere is contained in the stratosphere.
The ionosphere is a region of the atmosphere that is ionized by solar radiation. It is responsible for auroras. During daytime hours, it stretches from 50 to 1,000 km (31 to 621 mi; 160,000 to 3,280,000 ft) and includes the mesosphere, thermosphere, and parts of the exosphere. However, ionization in the mesosphere largely ceases during the night, so auroras are normally seen only in the thermosphere and lower exosphere. The ionosphere forms the inner edge of the magnetosphere. It has practical importance because it influences, for example, radio propagation on Earth.
The homosphere and heterosphere are defined by whether the atmospheric gases are well mixed. The surface-based homosphere includes the troposphere, stratosphere, mesosphere, and the lowest part of the thermosphere, where the chemical composition of the atmosphere does not depend on molecular weight because the gases are mixed by turbulence.[33] This relatively homogeneous layer ends at the turbopause found at about 100 km (62 mi; 330,000 ft), the very edge of space itself as accepted by the FAI, which places it about 20 km (12 mi; 66,000 ft) above the mesopause.
Above this altitude lies the heterosphere, which includes the exosphere and most of the thermosphere. Here, the chemical composition varies with altitude. This is because the distance that particles can move without colliding with one another is large compared with the size of motions that cause mixing. This allows the gases to stratify by molecular weight, with the heavier ones, such as oxygen and nitrogen, present only near the bottom of the heterosphere. The upper part of the heterosphere is composed almost completely of hydrogen, the lightest element.[32]
The planetary boundary layer is the part of the troposphere that is closest to Earth's surface and is directly affected by it, mainly through turbulent diffusion. During the day the planetary boundary layer usually is well-mixed, whereas at night it becomes stably stratified with weak or intermittent mixing. The depth of the planetary boundary layer ranges from as little as about 100 metres (330 ft) on clear, calm nights to 3,000 m (9,800 ft) or more during the afternoon in dry regions.
The average temperature of the atmosphere at Earth's surface is 14 °C (57 °F; 287 K)[34] or 15 °C (59 °F; 288 K),[35] depending on the reference.[36][37][38]

Physical properties

Comparison of the 1962 US Standard Atmosphere graph of geometric altitude against air density, pressure, the speed of sound and temperature with approximate altitudes of various objects.[39]
Pressure and thickness
Main article: Atmospheric pressure
The average atmospheric pressure at sea level is defined by the International Standard Atmosphere as 101325 pascals (760.00 Torr; 14.6959 psi; 760.00 mmHg). This is sometimes referred to as a unit of standard atmospheres (atm). Total atmospheric mass is 5.1480×1018 kg (1.135×1019 lb),[40] about 2.5% less than would be inferred from the average sea level pressure and Earth's area of 51007.2 megahectares, this portion being displaced by Earth's mountainous terrain. Atmospheric pressure is the total weight of the air above unit area at the point where the pressure is measured. Thus air pressure varies with location and weather.

If the entire mass of the atmosphere had a uniform density equal to sea level density (about 1.2 kg per m3) from sea level upwards, it would terminate abruptly at an altitude of 8.50 km (27,900 ft).

Air pressure actually decreases exponentially with altitude, dropping by half every 5.6 km (18,000 ft) or by a factor of 1/e (0.368) every 7.64 km (25,100 ft), (this is called the scale height) -- for altitudes out to around 70 km (43 mi; 230,000 ft). However, the atmosphere is more accurately modeled with a customized equation for each layer that takes gradients of temperature, molecular composition, solar radiation and gravity into account. At heights over 100 km, an atmosphere may no longer be well mixed. Then each chemical species has its own scale height.

In summary, the mass of Earth's atmosphere is distributed approximately as follows:[41]

50% is below 5.6 km (18,000 ft).
90% is below 16 km (52,000 ft).
99.99997% is below 100 km (62 mi; 330,000 ft), the Kármán line. By international convention, this marks the beginning of space where human travelers are considered astronauts.
By comparison, the summit of Mt. Everest is at 8,848 m (29,029 ft); commercial airliners typically cruise between 10 and 13 km (33,000 and 43,000 ft) where the lower density and temperature of the air improve fuel economy; weather balloons reach 30.4 km (100,000 ft) and above; and the highest X-15 flight in 1963 reached 108.0 km (354,300 ft).

Even above the Kármán line, significant atmospheric effects such as auroras still occur. Meteors begin to glow in this region, though the larger ones may not burn up until they penetrate more deeply. The various layers of Earth's ionosphere, important to HF radio propagation, begin below 100 km and extend beyond 500 km. By comparison, the International Space Station and Space Shuttle typically orbit at 350–400 km, within the F-layer of the ionosphere where they encounter enough atmospheric drag to require reboosts every few months, otherwise, orbital decay will occur resulting in a return to Earth. Depending on solar activity, satellites can experience noticeable atmospheric drag at altitudes as high as 700–800 km.

Temperature
Main article: Atmospheric temperature

Temperature trends in two thick layers of the atmosphere as measured between January 1979 and December 2005 by microwave sounding units and advanced microwave sounding units on NOAA weather satellites. The instruments record microwaves emitted from oxygen molecules in the atmosphere. Source:[42]
The division of the atmosphere into layers mostly by reference to temperature is discussed above. Temperature decreases with altitude starting at sea level, but variations in this trend begin above 11 km, where the temperature stabilizes over a large vertical distance through the rest of the troposphere. In the stratosphere, starting above about 20 km, the temperature increases with height, due to heating within the ozone layer caused by the capture of significant ultraviolet radiation from the Sun by the dioxygen and ozone gas in this region. Still another region of increasing temperature with altitude occurs at very high altitudes, in the aptly-named thermosphere above 90 km.

Speed of sound
Main article: Speed of sound
Because in an ideal gas of constant composition the speed of sound depends only on temperature and not on pressure or density, the speed of sound in the atmosphere with altitude takes on the form of the complicated temperature profile (see illustration to the right), and does not mirror altitudinal changes in density or pressure.

Density and mass

Temperature and mass density against altitude from the NRLMSISE-00 standard atmosphere model (the eight dotted lines in each "decade" are at the eight cubes 8, 27, 64, ..., 729)
Main article: Density of air
The density of air at sea level is about 1.2 kg/m3 (1.2 g/L, 0.0012 g/cm3). Density is not measured directly but is calculated from measurements of temperature, pressure and humidity using the equation of state for air (a form of the ideal gas law). Atmospheric density decreases as the altitude increases. This variation can be approximately modeled using the barometric formula. More sophisticated models are used to predict the orbital decay of satellites.

The average mass of the atmosphere is about 5 quadrillion (5×1015) tonnes or 1/1,200,000 the mass of Earth. According to the American National Center for Atmospheric Research, "The total mean mass of the atmosphere is 5.1480×1018 kg with an annual range due to water vapor of 1.2 or 1.5×1015 kg, depending on whether surface pressure or water vapor data are used; somewhat smaller than the previous estimate. The mean mass of water vapor is estimated as 1.27×1016 kg and the dry air mass as 5.1352 ±0.0003×1018 kg."

Tabulated properties
Table of physical and thermal properties of air at atmospheric pressure:[43][44]

Temperature (K) Density (kg/m^3 ) Specific heat (J/kg °C) Dynamic viscosity (kg/m s) Kinematic viscosity (m^2/s) Thermal conductivity (W/m °C) Thermal diffusivity (m^2/s) Prandtl Number Bulk modulus (K^-1 )
Optical properties

Find sources: "Atmosphere of Earth" – news · newspapers · books · scholar · JSTOR (October 2013) (Learn how and when to remove this template message)
Solar radiation (or sunlight) is the energy Earth receives from the Sun. Earth also emits radiation back into space, but at longer wavelengths that humans cannot see. Part of the incoming and emitted radiation is absorbed or reflected by the atmosphere. In May 2017, glints of light, seen as twinkling from an orbiting satellite a million miles away, were found to be reflected light from ice crystals in the atmosphere.[45][46]

Scattering
Main article: Atmospheric scattering
When light passes through Earth's atmosphere, photons interact with it through scattering. If the light does not interact with the atmosphere, it is called direct radiation and is what you see if you were to look directly at the Sun. Indirect radiation is light that has been scattered in the atmosphere. For example, on an overcast day when you cannot see your shadow, there is no direct radiation reaching you, it has all been scattered. As another example, due to a phenomenon called Rayleigh scattering, shorter (blue) wavelengths scatter more easily than longer (red) wavelengths. This is why the sky looks blue; you are seeing scattered blue light. This is also why sunsets are red. Because the Sun is close to the horizon, the Sun's rays pass through more atmosphere than normal before reaching your eye. Much of the blue light has been scattered out, leaving the red light in a sunset.

Absorption

Rough plot of Earth's atmospheric transmittance (or opacity) to various wavelengths of electromagnetic radiation, including visible light.
Different molecules absorb different wavelengths of radiation. For example, O2 and O3 absorb almost all radiation with wavelengths shorter than 300 nanometers. Water (H2O) absorbs at many wavelengths above 700 nm. When a molecule absorbs a photon, it increases the energy of the molecule. This heats the atmosphere, but the atmosphere also cools by emitting radiation, as discussed below.

The combined absorption spectra of the gases in the atmosphere leave "windows" of low opacity, allowing the transmission of only certain bands of light. The optical window runs from around 300 nm (ultraviolet-C) up into the range humans can see, the visible spectrum (commonly called light), at roughly 400–700 nm and continues to the infrared to around 1100 nm. There are also infrared and radio windows that transmit some infrared and radio waves at longer wavelengths. For example, the radio window runs from about one centimeter to about eleven-meter waves.

Emission
Further information: Emission spectrum
Emission is the opposite of absorption, it is when an object emits radiation. Objects tend to emit amounts and wavelengths of radiation depending on their "black body" emission curves, therefore hotter objects tend to emit more radiation, with shorter wavelengths. Colder objects emit less radiation, with longer wavelengths. For example, the Sun is approximately 6,000 K (5,730 °C; 10,340 °F), its radiation peaks near 500 nm, and is visible to the human eye. Earth is approximately 290 K (17 °C; 62 °F), so its radiation peaks near 10,000 nm, and is much too long to be visible to humans.

Because of its temperature, the atmosphere emits infrared radiation. For example, on clear nights Earth's surface cools down faster than on cloudy nights. This is because clouds (H2O) are strong absorbers and emitters of infrared radiation. This is also why it becomes colder at night at higher elevations.

The greenhouse effect is directly related to this absorption and emission effect. Some gases in the atmosphere absorb and emit infrared radiation, but do not interact with sunlight in the visible spectrum. Common examples of these are CO2 and H2O.

Refractive index

Distortive effect of atmospheric refraction upon the shape of the sun at the horizon.
Main article: Atmospheric refraction
The refractive index of air is close to, but just greater than 1. Systematic variations in the refractive index can lead to the bending of light rays over long optical paths. One example is that, under some circumstances, observers on board ships can see other vessels just over the horizon because light is refracted in the same direction as the curvature of Earth's surface.

The refractive index of air depends on temperature,[47] giving rise to refraction effects when the temperature gradient is large. An example of such effects is the mirage.

Circulation
Main article: Atmospheric circulation

An idealised view of three pairs of large circulation cells.
Atmospheric circulation is the large-scale movement of air through the troposphere, and the means (with ocean circulation) by which heat is distributed around Earth. The large-scale structure