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Astrophysics

Astrophysics

] Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties (luminosity, density, temperature and chemical composition) of astronomical objects such as stars, galaxies, and the interstellar medium, as well as their interactions. The study of cosmology is theoretical astrophysics at the largest scales. Because it is a very broad subject, astrophysicists typically apply many disciplines of physics including, but not limited to, mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and molecular physics. In practice, modern astronomical research involves a substantial amount of physics. The name of a university's department ("astrophysics" or "astronomy") often has to do more with the department's history than with the contents of the programs.

History

Although astronomy is as old as recorded history, it was long separated from the study of physics. In the Aristotelian worldview, the celestial pertained to perfection—bodies in the sky being perfect spheres moving in perfectly circular orbits—while the earthly pertained to imperfection; these two realms were seen as unrelated. For centuries, the apparently common-sense view that the Sun and other planets went round the Earth went basically unquestioned, until Nicolaus Copernicus suggested in the 16th century that the Earth and all the other planets in the Solar System orbited the Sun. This idea had been around, though, for nearly 2000 years when Aristarchus first suggested it, but not in such a nice mathematical model. Galileo Galilei made quantitative measurements central to physics, but in astronomy his observation did not have astrophysical significance. The availability of accurate observational data led to research into theoretical explanations for the observed behavior. At first, only ad-hoc rules were discovered, such as Kepler's laws of planetary motion, discovered at the start of the 17th century. Later that century, Isaac Newton, bridged the gap between Kepler's laws and Galileo's dynamics, discovering that the same laws that rule the dynamics of objects on earth rules the motion of planets and the moon. Celestial mechanics, the application of Newtonian gravity and Newton's laws to explain Kepler's laws of planetary motion, was the first unification of astronomy and physics. After Isaac Newton published his Principia, maritime navigation was transformed. Starting around 1670, the entire world was measured using essentially modern latitude instruments and the best available clocks. The needs of navigation provided a drive for progressively more accurate astronomical observations and instruments, providing a background for ever more available data for scientists. At the end of the 19th century it was discovered that, when decomposing the light from the Sun, a multitude of spectral lines were observed (regions where there was less or no light). Experiments with hot gases showed that the same lines could be observed in the spectra of gases, specific lines corresponding to unique chemical elements. In this way it was proved that the chemical elements found in the Sun (chiefly hydrogen) were also found on Earth. Indeed, the element helium was first discovered in the spectrum of the sun and only later on earth, hence its name. During the 20th century, spectroscopy (the study of these spectral lines) advanced, particularly as a result of the advent of quantum physics that was necessary to understand the astronomical and experimental observations. See also:
- Timeline of knowledge about galaxies, clusters of galaxies, and large-scale structure
- Timeline of white dwarfs, neutron stars, and supernovae
- Timeline of black hole physics
- Timeline of gravitational physics and relativity

Observational astrophysics

Most astrophysical processes cannot be reproduced in laboratories on Earth. However, there is a huge variety of astronomical objects visible all over the electromagnetic spectrum. The study of these objects through passive collection of data is the goal of observational astrophysics. The equipment and techniques required to study an astrophysical phenomenon can vary widely. Many astrophysical phenomena that are of current interest can only be studied by using very advanced technology and were simply not known until very recently. The majority of astrophysical observations are made using the electromagnetic spectrum.
- Radio astronomy studies radiation with a wavelength greater than a few millimeters. Radio waves are usually emitted by cold objects, including interstellar gas and dust clouds. The cosmic microwave background radiation is the redshifted light from the Big Bang. Pulsars were first detected at microwave frequencies. The study of these waves requires very large radio telescopes.
- Infrared astronomy studies radiation with a wavelength that is too long to be visible but shorter than radio waves. Infrared observations are usually made with telescopes similar to the usual optical telescopes. Objects colder than stars (such as planets) are normally studied at infrared frequencies.
- Optical astronomy is the oldest kind of astronomy. Telescopes paired with a charge-coupled device or a spectroscope are the most common instruments used. The Earth's atmosphere interferes somewhat with optical observations, so adaptive optics and space telescopes are used to obtain the highest possible image quality. In this range, stars are highly visible, and many chemical spectra can be observed to study the chemical composition of stars, galaxies and nebulae.
- Ultraviolet, X-ray and gamma ray astronomy study very energetic processes such as binary pulsars, black holes, magnetars, and many others. These kinds of radiation do not penetrate the Earth's atmosphere well, so they are studied with space-based telescopes such as RXTE, the Chandra X-ray Observatory and the Compton Gamma Ray Observatory. Other than electromagnetic radiation, few things may be observed from the Earth that originate from great distances. A few gravitational wave observatories have been constructed, but gravitational waves are extremely difficult to detect. Neutrino observatories have also been built, primarily to study our Sun. Cosmic rays consisting of very high energy particles can be observed hitting the Earth's atmosphere. Observations can also vary in their time scale. Most optical observations take minutes to hours, so phenomena that change faster than this cannot readily be observed. However, historical data on some objects is available spanning centuries or millennia. On the other hand, radio observations may look at events on a millisecond timescale (millisecond pulsars) or combine years of data (pulsar deceleration studies). The information obtained from these different timescales is very different. The study of our own Sun has a special place in observational astrophysics. Due to the tremendous distance of all other stars, the Sun can be observed in a kind of detail unparalleled by any other star. Our understanding of our own sun serves as a guide to our understanding of other stars. The topic of how stars change, or stellar evolution, is often modelled by placing the varieties of star types in their respective positions on the Hertzsprung-Russell diagram, which can be viewed as representing the state of a stellar object, from birth to destruction. The material composition of the astronomical objects can often be examined using:
- Spectroscopy
- Radio astronomy

Theoretical astrophysics

Theoretical astrophysicists create and evaluate models to reproduce and properly predict observations. They use a wide variety of tools which include analytical models (for example, polytropes to approximate the behaviors of a star) and computational numerical simulations. A few examples of this process: Dark matter and dark energy are the current leading topics in astrophysics, as their discovery and controversy originated during the study of the galaxies.

Astrodynamics

Main article: Astrodynamics Astrodynamics is the branch of celestial mechanics concerned with the motion of rockets, satellites and missiles. It is based upon Newton's laws of motion, and law of universal gravitation. The formula for escape velocity is defined in astrodynamics as:

v\geq\sqrt

Astrodynamics is also used to compute the position of a satellite at a given time, a problem first solved by Johannes Kepler, who computed the formula:

MT = E - e \sin E \;

This formula is commonly referred to as Kepler's equation, and can compute the time required for a satellite to travel from periapsis P to a given point S. Modern techniques for computing time-of-flight include the patched conic approximation, where one must choose the one dominant gravitating body in each region of space through which the trajectory will pass, and to model only that body's effects in that region, or the universal variable formulation.

Astrophysicists

Main article: List of astrophysicists

References

Herman Roth, "A Slowly Contracting or Expanding Fluid Sphere and its Stability" Phys. Rev. 39, 525–529 (1932) [Issue 3 – 1 February 1932 ]

External links

- [http://home.slac.stanford.edu/ppap.html Stanford Linear Accelerator Center, Stanford, California] Category:Astronomy Category:Applied and interdisciplinary physics ms:Astrofizik ja:天体物理学 simple:Astrophysics

Luminosity

Luminosity has different meanings in several different fields of science.

In general physics

In general physics, luminosity (more properly called luminance) is the density of luminous intensity in a given direction. The SI unit for luminosity is candela per square meter.

In astronomy

In astronomy, luminosity is the amount of energy a body radiates per unit time. It is typically expressed in the SI units watts, in the cgs units ergs per second, or in terms of solar luminosities, L_s; that is, how many times more energy the object radiates than the Sun, whose luminosity is 3.827×10²⁶ W. Luminosity is an intrinsic constant independent of distance, while in contrast apparent brightness observed is related to distance with an inverse square relationship. Brightness is usually measured by apparent magnitude, which is a logarithmic scale. In measuring star brightnesses, luminosity, apparent magnitude (brightness), and distance are interrelated parameters. If you know two, you can determine the third. Since the sun's luminosity is the standard, comparing these parameters with the sun's apparent magnitude and distance is the easiest way to remember how to convert between them.

Computing between brightness and luminosity

Imagine a point source of light of luminosity

L

that radiates equally in all directions. A hollow sphere centered on the point would have its entire interior surface illuminated. As the radius increases, the surface area will also increase, and the constant luminosity has more surface area to illuminate, leading to a decrease in observed brightess.

b = \frac

where

A

is the area of the illuminated surface. For stars and other point sources of light,

A = 4\pi r^2

b = \frac \,

where

r

is the distance from the observer to the light source. It has been shown that the luminosity of a star

L

is also related to temperature

T

and radius

R

of the star by the equation

L = 4\pi\R^2\sigma T^4

Dividing by the luminosity of the sun

L_s

and cancelling constants, we obtain the relationship

\frac = ^2 ^4

. For stars on the main sequence, luminosity is also related to mass:

\frac \sim ^

It is easy to see that a star's luminosity, temperature, radius, and mass are all related. The magnitude of a star is a logarithmic scale of observed brightness. The apparent magnitude is the observed brightness from Earth, and the absolute magnitude is the apparent magnitude at a distance of 10 parsecs. Given a luminosity, one can calculate the apparent magnitude of a star from a given distance: :

m_=m_-2.5\log_\left( \cdot \left(\right)^2\right)

where m_star is the apparent magnitude of the star (a pure number) m_sun is the apparent magnitude of the reference sun (also a pure number) L_star is solar luminosity of the star, measured in multiples of the Sun's luminosity L_sun is solar luminosity of the reference sun, which can be taken as 1 Dist_star is the distance to the star, measured in any units Dist_sun is the distance to the reference sun, measured in the same units Or simplified, given m_sun = −26.73, dist_sun = 1.58 × 10⁻⁵ lyr: : m_star = − 2.72 − 2.5 · log(L_star/dist_star²) Example: :How bright would a star like the sun be from 4.3 light years away? (The distance to the next closest star Alpha Centauri) ::m_sun (@4.3lyr) = −2.72 − 5 · log(1/4.3) = 0.45 :0.45 magnitude would be a very bright star, but not quite as bright as Alpha Centauri. Also you can calculate the luminosity given a distance and apparent magnitude: :L_star/L_sun = (dist_star/dist_sun)² · 10 :L_star = 0.0813 · dist_star² · 10^{(−0.4 · m_star)} · L_sun Example: :What is the luminosity of the star Sirius? ::Sirius is 8.6 lyr distant, and magnitude −1.47. ::Lum(Sirius) = 0.0813 · 8.6² · 10^{−0.4·(−1.47)} = 23.3 × Lum_sun :You can say that Sirius is 23 times brighter than the sun, or it radiates 23 suns. A bright star with bolometric magnitude −10 has a luminosity of 10⁶ L_s, whereas a dim star with bolometric magnitude +17 has luminosity of 10⁻⁵ L_s. Note that absolute magnitude is directly related to luminosity, but apparent magnitude is also a function of distance. Since only apparent magnitude can be measured observationally, an estimate of distance is required to determine the luminosity of an object.

Hertzsprung-Russell diagram

The Hertzsprung-Russell diagram relates luminosity to color, stellar classification or surface temperature.

In scattering theory and accelerator physics

In scattering theory and accelerator physics, luminosity is the number of particles per unit area per unit time times the opacity of the target, usally expressed in either the cgs units cm^{-2 s^-1 or b^{-1 s^-1. The integrated luminosity is the integral of the luminosity with respect to time. The luminosity is an important value to characterize the performance of an accelerator.

Elementary relations for luminosity

- $L$ is the Luminosity.

- $N$ is the number of interactions.

- $\rho$ is the number density of a particle beam, e.g. within a bunch.

- $\sigma$ is the total cross section.

- $d\Omega$ is the differential solid angle.

- $\left(\frac\right)$ is the differential cross section.

Then the following relation holds:

: $L = \rho v$ (if the target is perfectly opaque)
: $\frac = L \sigma$
: $\left(\frac\right) = \frac \frac$

For a intersecting storage ring collider:

- $f$ is the revolution frequency

- $n$ is the number of bunches in one beam in the storage ring.

- $N_$ is the number of particles in each beam

- $A$ is the cross section of the beam.

: $L = f n \frac$

Category:Astrophysics
Category:Physical quantity
Category:Photometry
Category:Particle accelerators
Category:Scattering theory

ja:光度 (天文学)

Temperature

Temperature is the physical property of a system which underlies the common notions of "hot" and "cold"; the material with the higher temperature is said to be hotter.

Physically, temperature is a measure of the random agitation of matter and ambiant photons, under the effect of thermal fluctuations. It is a fundamental parameter in thermodynamics and it is conjugate to entropy.

More quantitatively, the order of magnitude of the fluctuations of the energy associated with an atom, molecule or another elementary constituant of a physical system is $k_B T$ , where $k_B$ is Boltzmann's constant, and T is temperature, expressed in Kelvins.

Overview
The formal properties of temperature are studied in thermodynamics and statistical mechanics. The temperature of a system at thermodynamic equilibrium is defined by a relation between the amount of heat $\delta Q$ incident on the system during an infinitesimal quasistatic transformation, and the variation $\delta S$ of its entropy during this transformation.
: $\delta S = \frac$

Contrarly to entropy and heat, whose microscopic definitions are valid even far away from thermodynamic equilibrium temperature can only be defined at thermodynamic equilibrium, or local thermodynamic equilibrium (see below).

As a system receives heat its temperature rises, similarly a loss of heat from the system tends to decrease its temperature (at the - uncommon - exception of negative temperature, see below).

When two systems are at the same temperature, no heat transfer occurs between them. When a temperature difference does exist, heat will tend to move from the higher-temperature system to the lower-temperature system, until they are at thermal equilibrium. This heat transfer may occur via conduction, convection or radiation (see heat for additional discussion of the various mechanisms of heat transfer).

Temperature is also related to the amount of internal energy and enthalpy of a system. The higher the temperature of a system, the higher its internal energy and enthalpy are.

Temperature is an intensive property of a system, meaning that it does not depend on the system size or the amount of material in the system. Other intensive properties include pressure and density. By contrast, mass and volume are extensive properties, and depend on the amount of material in the system.

Role of temperature in nature
Temperature plays an important role in almost all fields of science, including physics, chemistry, and biology.

Many physical properties of materials including the phase (solid, liquid, gaseous or plasma), density, solubility, vapor pressure, and electrical conductivity depend on the temperature. Temperature also plays an important role in determining the rate and extent to which chemical reactions occur. This is one reason why the human body has several elaborate mechanisms for maintaining the temperature at 37 °C, since temperatures only a few degrees higher can result in harmful reactions with serious consequences. Temperature also controls the type and quantity of thermal radiation emitted from a surface. One application of this effect is the incandescent light bulb, in which a tungsten filament is electrically heated to a temperature at which significant quantities of visible light are emitted.

Temperature-dependence of the speed of sound in air c, density of air ρ and acoustic impedance Z vs. temperature °C

Temperature measurement
Main article: Temperature measurement

Temperature measurement using modern scientific thermometers and temperature scales goes back at least as far as the early 18th century, when Gabriel Fahrenheit adapted a thermometer (switching to mercury) and a scale both developed by Ole Christensen Rømer. Fahrenheit's scale is still in use, alongside the Celsius scale and the Kelvin scale.

Units of temperature
The basic unit of temperature (symbol: T) in the International System of Units (SI) is the kelvin (K). One kelvin is formally defined as 1/273.16 of the temperature of the triple point of water (the point at which water, ice and water vapor exist in equilibrium). The temperature 0 K is called absolute zero and corresponds to the point at which the molecules and atoms have the least possible thermal energy. An important unit of temperature in theoretical physics is the Planck temperature (1.4 × 10³² K).

In the field of plasma physics, because of the high temperatures encountered and the electromagnetic nature of the phenomena involved, it is customary to express temperature in electronvolts (eV) or kiloelectronvolts (keV), where 1 eV = 11,605 K. In the study of QCD matter one routinely meets temperatures of the order of a few hundred MeV, equivalent to about 10¹² K.

For everyday applications, it is often convenient to use the Celsius scale, in which 0 °C corresponds to the temperature at which water freezes and 100 °C corresponds to the boiling point of water at sea level. In this scale a temperature difference of 1 degree is the same as a 1 K temperature difference, so the scale is essentially the same as the kelvin scale, but offset by the temperature at which water freezes (273.15 K). Thus the following equation can be used to convert from degrees Celsius to kelvins.
: $\mathrm$

In the United States, the Fahrenheit scale is widely used. On this scale the freezing point of water corresponds to 32 °F and the boiling point to 212 °F. The following formula can be used to convert from Fahrenheit to Celsius:
: $\mathrm$

See temperature conversion formulas for conversions between most temperature scales.

¹ Only the kelvin, Celsius, Fahrenheit, and Rankine scales are in use today.

² Some numbers in this table have been rounded off.

³ Normal human body temperature is 36.8 °C ±0.7 °C, or 98.2 °F ±1.3 °F.

Negative temperatures

:See main article: Negative temperature.

For some systems and specific definitions of temperature, it is possible to obtain a negative temperature. A system with a negative temperature is not colder than absolute zero, but rather it is, in a sense, hotter than infinite temperature (sic).

Articles about temperature ranges:

- 10⁻¹² K = 1 picokelvin (pK)

- 10⁻⁹ K = 1 nanokelvin (nK)

- 10⁻⁶ K = 1 microkelvin (µK)

- 10⁻³ K = 1 millikelvin (mK)

- 10⁰ K = 1 kelvin

- 10¹ K = 10 kelvins

- 10² K = 100 kelvins

- 10³ K = 1,000 kelvin = 1 kilokelvin (kK)

- 10⁴ K = 10,000 kelvins = 10 kK

- 10⁵ K = 100,000 kelvins = 100 kK

- 10⁶ K = 1 megakelvin (MK)

- 10⁹ K = 1 gigakelvin (GK)

- 10¹² K = 1 terakelvin (TK)

See Orders of magnitude (temperature).

Theoretical foundation of temperature

Zeroth-law definition of temperature

While most people have a basic understanding of the concept of temperature, its formal definition is rather complicated. Before jumping to a formal definition, let us consider the concept of thermal equilibrium. If two closed systems with fixed volumes are brought together, so that they are in thermal contact, changes may take place in the properties of both systems. These changes are due to the transfer of heat between the systems. When a state is reached in which no further changes occur, the systems are in thermal equilibrium.

Now a basis for the definition of temperature can be obtained from the so-called zeroth law of thermodynamics which states that if two systems, A and B, are in thermal equilibrium and a third system C is in thermal equilibrium with system A then systems B and C will also be in thermal equilibrium (being in thermal equilibrium is a transitive relation; moreover, it is an equivalence relation). This is an empirical fact, based on observation rather than theory. Since A, B, and C are all in thermal equilibrium, it is reasonable to say each of these systems shares a common value of some property. We call this property temperature.

Generally, it is not convenient to place any two arbitrary systems in thermal contact to see if they are in thermal equilibrium and thus have the same temperature. Also, it would only provide an ordinal scale.

Therefore, it is useful to establish a temperature scale based on the properties of some reference system. Then, a measuring device can be calibrated based on the properties of the reference system and used to measure the temperature of other systems. One such reference system is a fixed quantity of gas. The ideal gas law indicates that the product of the pressure and volume (P · V) of a gas is directly proportional to the temperature:
: $P \cdot V = n \cdot R \cdot T$ (1)

where 'T is temperature, n is the number of moles of gas and R is the gas constant. Thus, one can define a scale for temperature based on the corresponding pressure and volume of the gas: the temperature in kelvins is the pressure in pascals of one mole of gas in a container of one cubic metre, divided by 8.31... In practice, such a gas thermometer is not very convenient, but other measuring instruments can be calibrated to this scale.

Equation 1 indicates that for a fixed volume of gas, the pressure increases with increasing temperature. Pressure is just a measure of the force applied by the gas on the walls of the container and is related to the energy of the system. Thus, we can see that an increase in temperature corresponds to an increase in the thermal energy of the system. When two systems of differing temperature are placed in thermal contact, the temperature of the hotter system decreases, indicating that heat is leaving that system, while the cooler system is gaining heat and increasing in temperature. Thus heat always moves from a region of high temperature to a region of lower temperature and it is the temperature difference that drives the heat transfer between the two systems.

Temperature in gases

As mentioned previously for a monatomic ideal gas the temperature is related to the translational motion or average speed of the atoms. The kinetic theory of gases uses statistical mechanics to relate this motion to the average kinetic energy of atoms and molecules in the system. For this case 7736 K = 7463 degrees Celsius corresponds to an average kinetic energy of one electronvolt; to take room temperature (300 K) as an example, the average energy of air molecules is 300/7736 eV, or 0.0388 electronvolt. This average energy is independent of particle mass, which seems counterintuitive to many people. Although the temperature is related to the average kinetic energy of the particles in a gas, each particle has its own energy which may or may not correspond to the average. However, after an examination of some basic physics equations it makes perfect sense. The second law of thermodynamics states that any two given systems when interacting with each other will later reach the same average energy. Temperature is a measure of the average kinetic energy of a system. The formula for the kinetic energy of an atom is:

: $K_t = \begin \frac \end mv^2$
(Note that a calculation of the kinetic energy of a more complicated object, such as a molecule, is slightly more involved. Additional degrees of freedom are available, so molecular rotation or vibration must be included.)

Thus, particles of greater mass (say a neon atom relative to a hydrogen molecule) will move slower than lighter counterparts, but will have the same average energy. This average energy is independent of the mass because of the nature of a gas, all particles are in random motion with collisions with other gas molecules, solid objects that may be in the area and the container itself (if there is one). A visual illustration of this [http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm from Oklahoma State University] makes the point more clear. Not all the particles in the container have different velocities, regardless of whether there are particles of more than one mass in the container, but the average kinetic energy is the same because of the ideal gas law. In a gas the distribution of energy (and thus speeds) of the particles corresponds to the Boltzmann distribution.

An electronvolt is a very small unit of energy, approximately 1.602×10^-19 joule.

Temperature of the vacuum
When a satellite in empty space is heated by sunshine and cooled by radiating energy away it is not in thermodynamic equilibrium and has no well-defined temperature.

A system in a vacuum will radiate its thermal energy, i.e. convert heat into electromagnetic waves. If vacuum is filled with electromagnetic waves (say, radiation from walls of vacuum chamber, or relic microwave radiation in space) then the system will exchange by energy with these waves and thermally equilibrates at some finite (non zero) temperature.

Cosmic microwave background radiation being remnant of radiation of hot early universe when radiation was in thermal equilibrium with matter has Planck spectrum (black body spectrum) with the temperature (at present) of about 2.7 K.

Second-law definition of temperature

In the previous section temperature was defined in terms of the Zeroth Law of thermodynamics. It is also possible to define temperature in terms of the second law of thermodynamics, which deals with entropy. Entropy is a measure of the disorder in a system. The second law states that any process will result in either no change or a net increase in the entropy of the universe. This can be understood in terms of probability. Consider a series of coin tosses. A perfectly ordered system would be one in which every coin toss would come up either heads or tails. For any number of coin tosses, there is only one combination of outcomes corresponding to this situation. On the other hand, there are multiple combinations that can result in disordered or mixed systems, where some fraction are heads and the rest tails. As the number of coin tosses increases, the number of combinations corresponding to imperfectly ordered systems increases. For a very large number of coin tosses, the number of combinations corresponding to ~50% heads and ~50% tails dominates and obtaining an outcome significantly different from 50/50 becomes extremely unlikely. Thus the system naturally progresses to a state of maximum disorder or entropy.

Now, we have stated previously that temperature controls the flow of heat between two systems and we have just shown that the universe, and we would expect any natural system, tends to progress so as to maximize entropy. Thus, we would expect there to be some relationship between temperature and entropy. In order to find this relationship let's first consider the relationship between heat, work and temperature. A heat engine is a device for converting heat into mechanical work and analysis of the Carnot heat engine provides the necessary relationships we seek. The work from a heat engine corresponds to the difference between the heat put into the system at the high temperature, q_H and the heat ejected at the low temperature, q_C. The efficiency is the work divided by the heat put into the system or:
: $\textrm = \frac = \frac = 1 - \frac$ (2)

where w_cy is the work done per cycle. We see that the efficiency depends only on q_C/q_H. Because q_C and q_H correspond to heat transfer at the temperatures T_C and T_H, respectively, q_C/q_H should be some function of these temperatures:
: $\frac = f(T_H,T_C)$ (3)

Carnot's theorem states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, a heat engine operating between T₁ and T₃ must have the same efficiency as one consisting of two cycles, one between T₁ and T₂, and the second between T₂ and T₃. This can only be the case if:
: $q_ = \frac$

which implies:
: $q_13 = f(T_1,T_3) = f(T_1,T_2)f(T_2,T_3)$

Since the first function is independent of T₂, this temperature must cancel on the right side, meaning f(T₁,T₃) is of the form g(T₁)/g(T₃) (i.e. f(T₁,T₃) = f(T₁,T₂)f(T₂,T₃) = g(T₁)/g(T₂)· g(T₂)/g(T₃) = g(T₁)/g(T₃)), where g is a function of a single temperature. We can now choose a temperature scale with the property that:

: $\frac = \frac$ (4)

Substituting Equation 4 back into Equation 2 gives a relationship for the efficiency in terms of temperature:
: $\textrm = 1 - \frac = 1 - \frac$ (5)

Notice that for T_C = 0 K the efficiency is 100% and that efficiency becomes greater than 100% below 0 K. Since an efficiency greater than 100% violates the first law of thermodynamics, this implies that 0 K is the minimum possible temperature. In fact the lowest temperature ever obtained in a macroscopic system was 20 nK, which was achieved in 1995 at NIST. Subtracting the right hand side of Equation 5 from the middle portion and rearranging gives:
: $\frac - \frac = 0$

where the negative sign indicates heat ejected from the system. This relationship suggests the existence of a state function, S, defined by:
: $dS = \frac$ (6)

where the subscript indicates a reversible process. The change of this state function around any cycle is zero, as is necessary for any state function. This function corresponds to the entropy of the system, which we described previously. We can rearranging Equation 6 to get a new definition for temperature in terms of entropy and heat:
: $T = \frac$ (7)

For a system, where entropy S may be a function S(E) of its energy E, the temperature T is given by:
: $\frac = \frac$ (8)

The reciprocal of the temperature is the rate of increase of entropy with energy.

See also

- Entropy

- Maxwell's demon

- Heat conduction

- ITS-90 International Temperature Scale

References

-

External links

- [http://www.unitconversion.org/unit_converter/temperature.html Online Temperature Converter] - convert between various units of temperature, such as kelvin, Celsius, Fahrenheit, Rankine, Reaumur, and even Triple point of water

- [http://www.unitconversion.org/unit_converter/temperature-v.html Interactive Temperature Conversion Table] - convert selected unit to all other units of temperature

- [http://www.indiana.edu/~animal/fun/conversions/temperature.html Temperature Conversions: Celsius, Fahrenheit, Kelvin, Réaumur and Rankine]

- [http://www.unidata.ucar.edu/staff/blynds/tmp.html An elementary introduction to temperature aimed at a middle school audience]

- [http://www.straightdope.com/mailbag/mtempscales.html Why do we have so many temperature scales?]

- [http://thermodynamics-information.net A Brief History of Temperature Measurement]

Category:Meteorology
Category:Physical quantity
Category:Thermodynamics
Category:Heat

ko:온도

ja:温度

th:อุณหภูมิ

Chemistry
Chemistry (derived from the Arabic word kimia, alchemy, where al is Arabic for the) is the science of matter that deals with the composition, structure, and properties of substances and with the transformations that they undergo. In the study of matter, chemistry also investigates its interactions with energy and itself (see physics, biology). Because of the diversity of matter, which is mostly composed of different combinations of atoms, chemists often study how atoms of different chemical elements interact to form molecules and how molecules interact with each other.
molecules

Introduction
Chemistry is a large field encompassing many subdisciplines that often overlap with significant portions of other sciences. The fundamental component of chemistry is that it involves matter in some way (this explains its broad reach). It may involve the interaction of matter with non-material phenomena such as energy. More central to chemistry is the interaction of matter with other matter such as in the classic chemical reaction where chemical bonds are broken and made, forming new molecules.

Matter, such as the chair you are sitting on or the air you breathe, is known today to consist of molecules. Each molecule consists of small bits of matter known as atoms that are connected together through chemical bonds. Each atom consists of smaller bits of matter known as subatomic particles. The structure of the world we commonly experience and the properties of the matter we commonly interact with are determined by the nature of this matter on the chemical level. Steel is hard because of how the atoms are bound together. Wood will burn because it can react with oxygen in a chemical reaction. Water is a liquid at room temperature because of how each molecule of water interacts with its neighbors. In fact, you are a thinking, sentient being because of an on-going series of chemical reactions and other chemical interactions. You can see this text because of how light interacts with molecules called proteins in the back of your eye.

Chemistry is often called the central science because it is what connects most of the other sciences together. Chemistry is in some ways physics on a larger scale and in some ways is biology or geology on a smaller scale. Chemistry is used to understand and make better materials for engineering. It is used to understand the chemical mechanisms of disease as well as to create pharmaceuticals to treat disease. Chemistry is somehow involved in almost every science, every technology and every "thing".

With such a large area of study, it is impossible to know everything about chemistry and very difficult to summarize the field concisely. Even the most knowledgable, experienced chemist only knows a very narrow area of chemistry better than others. Of course, most chemists have a broad general knowledge of many areas of chemistry as well. Chemistry is divided into many areas of study called subdisciplines in which chemists specialize. The chemistry taught at the high school or early college level is often called "general chemistry" and is intended to be an introduction to a wide variety of fundamental concepts and to give the student the tools to continue on to more advanced subjects. Many concepts presented at this level are often incomplete and technically inaccurate yet of extraordinary utility. Chemists regularly use these simple, elegant tools and explanations in their work when they suffice because the best solution possible is often so overwhelmingly difficult and the true solution is usually unobtainable.

The science of chemistry is historically a recent development but has its roots in alchemy which has been practiced for millennia throughout the world. The word chemistry is directly derived from the word alchemy, however the etymology of alchemy is unclear (see alchemy).

Subdisciplines of chemistry

Chemistry typically is divided into several major sub-disciplines. There are also several main cross-disciplinary and more specialized fields of chemistry.

; Analytical chemistry : Analytical chemistry is the analysis of material samples to gain an understanding of their chemical composition and structure. Analytical chemistry incorporates standardized experimental methods in chemistry. These methods may be used in all subdiciplines of chemistry, exluding purely theoretical chemistry.

; Biochemistry : Biochemistry is the study of the chemicals, chemical reactions and chemical interactions that take place in living organisms. Biochemistry and organic chemistry are closely related f.e. in medicinal chemistry.

; Inorganic chemistry : Inorganic chemistry is the study of the properties and reactions of inorganic compounds. The distinction between organic and inorganic disciplines is not absolute and there is much overlap, most importantly in the sub-discipline of organometallic chemistry.

; Organic chemistry : Organic chemistry is the study of the structure, properties, composition, mechanisms, and reactions of organic compounds.

; Physical chemistry : Physical chemistry or physicochemistry is the study of the physical basis of chemical systems and processes. In particular, the energetics and dynamics of such systems and processes are of interest to physical chemists. Important areas of study include chemical thermodynamics, chemical kinetics, electrochemistry, statistical mechanics, and spectroscopy. Physical chemistry has large overlap with molecular physics.

; Theoretical chemistry : Theoretical chemistry is the study of chemistry via theoretical reasoning (usually within mathematics or physics). In particular the application of quantum mechanics to chemistry is called quantum chemistry. Since the end of the second world war, the development of computers has allowed a systematic development of computational chemistry, which is the art of developing and applying computer programs for solving chemical problems. Theoretical chemistry has large overlap with molecular physics.

; Other fields : Astrochemistry, Atmospheric chemistry, Chemical Engineering, Electrochemistry, Environmental chemistry, Geochemistry, History of chemistry, Materials science, Medicinal chemistry, Molecular Biology, Molecular genetics, Nuclear chemistry, Organometallic chemistry, Petrochemistry, Pharmacology, Photochemistry, Phytochemistry, Polymer chemistry, Supramolecular chemistry, Surface chemistry, and Thermochemistry.

Fundamental concepts

Nomenclature

Nomenclature refers to the system for naming chemical compounds. There are well-defined systems in place for naming chemical species. Organic compounds are named according to the organic nomenclature system. Inorganic compounds are named according to the inorganic nomenclature system.

See also: IUPAC nomenclature

Atoms

Main article: Atom.

An atom is a collection of matter consisting of a positively charged core (the nucleus) which contains protons and neutrons, and which maintains a number of electrons to balance the positive charge in the nucleus.

Elements

Main article: Chemical element.

An element is a class of atoms which have the same number of protons in the nucleus. This number is known as the atomic number of the element. For example, all atoms with 6 protons in their nuclei are atoms of the chemical element carbon, and all atoms with 92 protons in their nuclei are atoms of the element uranium.

The most convenient presentation of the elements is in the periodic table, which groups elements with similar chemical properties together. Lists of the elements by name, by symbol, and by atomic number are also available.

See also: isotope

Compounds

Main article: Chemical compound

A compound is a substance with a fixed ratio of chemical elements which determines the composition, and a particular organisation which determines chemical properties. For example, water is a compound containing hydrogen and oxygen in the ratio of two to one, with the Oxygen between the hydrogens, and an angle of 104.5° between them. Compounds are formed and interconverted by chemical reactions.

Molecules

Main article: Molecule.

A molecule is the smallest indivisible portion of a pure compound that retains a set of unique chemical properties. A molecule consists of two or more atoms covalently bonded together.

Ions

Main article: Ion.

An ion is a charged species, or an atom or a molecule that has lost or gained an electron. Positively charged cations (e.g. sodium cation Na⁺) and negatively charged anions (e.g. chloride Cl^-) can form neutral salts (e.g. sodium chloride NaCl). Examples of polyatomic ions that do not split up during acid-base reactions are hydroxide (OH^-), or phosphate (PO₄^3-).

Bonding

Main article: Chemical bond.

A chemical bond is an interaction which holds together atoms in molecules or crystals. In many simple compounds, valence bond theory and the concept of oxidation number can be used to predict molecular structure and composition. Similarly, theories from classical physics can be used to predict many ionic structures. With more complicated compounds, such as metal complexes, valence bond theory fails and alternative approaches which are based on quantum chemistry, such as molecular orbital theory, are necessary.

States of matter

Main article: Phase (matter).

A phase is a set of states of a chemical system that have similar bulk structural properties, over a range of conditions, such as pressure or temperature. Physical properties, such as density and refractive index tend to fall within values characteristic of the phase. The phase of matter is defined by the phase transition, which is when energy put into or taken out of the system goes into rearranging the structure of the system, instead of changing the bulk conditions.

Sometimes the distinction between phases can be continuous instead of having a discrete boundary, in this case the matter is considered to be in a supercritical state. When three states meet based on the conditions, it is known as a triple point and since this is invariant, it is a convenient way to define a set of conditions.

The most familiar examples of phases are solids, liquids, and gases. Less familiar phases include plasmas, Bose-Einstein condensates and fermionic condensates and the paramagnetic and ferromagnetic phases of magnetic materials. Even the familiar ice has many different phases, depending on the pressure and temperature of the system. While most familiar phases deal with three-dimensional systems, it is also possible to define analogs in two-dimensional systems, which is getting a lot of attention because of its relevance to biology.

Chemical reactions

Main article: Chemical reaction.

Chemical reactions are transformations in the fine structure of molecules. Such reactions can result in molecules attaching to each other to form larger molecules, molecules breaking apart to form two or more smaller molecules, or rearrangement of atoms within or across molecules. Chemical reactions usually involve the making or breaking of chemical bonds.

Quantum chemistry

Main article: Quantum chemistry.

Quantum chemistry describes the behavior of matter at the molecular scale. It is, in principle, possible to describe all chemical systems using this theory. In practice, only the simplest chemical systems may realistically be investigated in purely quantum mechanical terms, and approximations must be made for most practical purposes (e.g., Hartree-Fock, post Hartree-Fock or Density functional theory, see computational chemistry for more details). Hence a detailed understanding of quantum mechanics is not necessary for most chemistry, as the important implications of the theory (principally the orbital approximation) can be understood and applied in simpler terms.

Laws

The most fundamental concept in chemistry is the law of conservation of mass, which states that there is no detectable change in the quantity of matter during an ordinary chemical reaction. Modern physics shows that it is actually energy that is conserved, and that energy and mass are related; a concept which becomes important in nuclear chemistry. Conservation of energy leads to the important concepts of equilibrium, thermodynamics, and kinetics.

Further laws of chemistry elaborate on the law of conservation of mass. Joseph Proust's law of definite composition says that pure chemicals are composed of elements in a definite formulation; we now know that the structural arrangement of these elements is also important.

Dalton's law of multiple proportions says that these chemicals will present themselves in proportions that are small whole numbers (i.e. 1:2 O:H in water); although in many systems (notably biomacromolecules and minerals) the ratios tend to require large numbers, and are frequently represented as a fraction. Such compounds are known as Non-Stoichiometric Compounds

More modern laws of chemistry define the relationship between energy and transformations.

- In equilibrium, molecules exist in mixture defined by the transformations possible on the timescale of the equilibrium, and are in a ratio defined by the intrinsic energy of the molecules—the lower the intrinsic energy, the more abundant the molecule.

- Transforming one structure to another requires the input of energy to cross an energy barrier; this can come from the intrinsic energy of the molecules themselves, or from an external source which will generally accelerate transformations. The higher the energy barrier, the slower the transformation occurs.

- There is a hypothetical intermediate, or transition structure, that corresponds to the structure at the top of the energy barrier. The Hammond-Leffler Postulate states that this structure looks most similar to the product or starting material which has intrinsic energy closest to that of the energy barrier. Stabilizing this hypothetical intermediate through chemical interaction is one way to achieve catalysis.

- All chemical processes are reversible (law of microscopic reversibility) although some processes have such an energy bias, they are essentially irreversible.

History of chemistry

- Alchemy

- Discovery of the chemical elements

- History of chemistry

- Nobel Prize in chemistry

- Timeline of chemical element discovery

Etymology

Old French: alkemie; Arab al-kimia: the art of transformation. See also: alchemy

See also

- American Chemical Society

- Chemical engineering

- Chemist and list of chemists

- International Union of Pure and Applied Chemistry

- List of chemistry topics

- List of compounds

- List of important publications in chemistry

- Periodic table

- Chemistry resources

- Valency number

External links

- [http://www.allchemicals.info/ Chemical Glossary]

- [http://chem.sis.nlm.nih.gov/chemidplus/ Chemistry Information Database includes basic information and some toxicity]

- [http://www.chem.qmw.ac.uk/iupac/ IUPAC Nomenclature Home Page], see especially the "Gold Book" containing definitions of standard chemical terms

- [http://www.cci.ethz.ch/index.html Experiments] videos and photos of the techniques and results

- [http://physchem.ox.ac.uk/MSDS/ Material safety data sheets for a variety of chemicals]

- [http://www.flinnsci.com/search_MSDS.asp Material Safety Data Sheets]

Further reading

- Chang, Raymond. Chemistry 6th ed. Boston: James M. Smith, 1998. ISBN 0071152210.

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Star
:This article is about celestial bodies.

A star is a massive body of plasma in outer space that is currently producing or has produced energy through nuclear fusion. Unlike a planet, from which most light is reflected, a star emits light because of its intense heat. Scientifically, stars are defined as self-gravitating spheres of plasma in hydrostatic equilibrium, which generate their own energy through the process of nuclear fusion. Small (dwarf) stars such as the Sun generally have essentially featureless disks with only small starspots. Larger (giant) stars have much bigger, much more obvious starspots, and also exhibit strong stellar limb-darkening (the brightness decreases towards the edge of the stellar disk). Stellar astronomy is the study of stars.

Star formation and evolution

Star formation occurs in molecular clouds, large regions of high density in the interstellar medium (though still less dense than the inside of an earthly vacuum chamber). Star formation begins with gravitational instability inside those clouds, often triggered by shockwaves from supernovae or collision of two galaxies (as in a starburst galaxy). High mass stars powerfully illuminate the clouds from which they formed. One example of such a nebula is the Orion Nebula.

Stars spend about 90% of their lifetime fusing hydrogen to produce helium in high-temperature and high-pressure reactions near the core. Such stars are said to be on the main sequence.

Small stars (called red dwarfs) burn their fuel very slowly and last tens to hundreds of billions of years. At the end of their lives, they simply become dimmer and dimmer, fading into black dwarfs. However, since the lifespan of such stars is greater than the current age of the universe (13.6 billion years), no black dwarfs exist yet.

As most stars exhaust their supply of hydrogen, their outer layers expand and cool to form a red giant. In about 5 billion years, when the Sun is a red giant, it will be so large that it will consume both Mercury and Venus. Eventually the core is compressed enough to start helium fusion, and the star heats up and contracts. Larger stars will also fuse heavier elements, all the way to iron, which is the end point of the process. Since iron nuclei are more tightly bound than any heavier nuclei, they cannot be fused to release energy. Likewise, since they are more tightly bound than all lighter nuclei, energy cannot be released by fission. In old, very massive stars, a large core of inert iron will accumulate in the center of the star.

An average-size star will then shed its outer layers as a planetary nebula. The core that remains will be a tiny ball of degenerate matter not massive enough for further fusion to take place, supported only by degeneracy pressure, called a white dwarf. These too will fade into black dwarfs over very long stretches of time.

white dwarf

In larger stars, fusion continues until an iron core accumulates that is too large to be supported by electron degeneracy pressure. This core will suddenly collapse as its electrons are driven into its protons, forming neutrons and neutrinos in a burst of inverse beta decay. The shockwave formed by this sudden collapse causes the rest of the star to explode in a supernova. Supernovae are so bright that they may briefly outshine the star's entire home galaxy. When they occur within the Milky Way, supernovae have historically been observed by naked-eye observers as "new stars" where none existed before. Eventually, most of the matter in a star is blown away by the explosion (forming nebulae such as the Crab Nebula) and what remains will be a neutron star (sometimes a pulsar or X-ray burster) or, in the case of the largest stars, a black hole.

The blown-off outer layers of dying stars include heavy elements which may be recycled during new star formation. These heavy elements allow the formation of rocky planets. The outflow from supernovae and the stellar wind of large stars play an important part in shaping the interstellar medium.

Appearance and distribution of stars
All stars except the Sun appear to the human eye as shining points in the nighttime sky that twinkle because of the effect of the Earth's atmosphere. Interferometer telescopes are required in order to produce images of these objects. The Sun is also a star, but it is close enough to Earth to appear as a disk instead, and to provide daylight.

Stars are not spread uniformly across the universe, but are typically grouped into galaxies. A typical galaxy contains hundreds of billions of stars. The majority of stars are gravitationally bound to other stars, forming binary stars. Larger groups called star clusters also exist.

Astronomers estimate that there are at least 70 sextillion (7×10²²) stars in the known universe [http://news.bbc.co.uk/2/hi/science/nature/3085885.stm]. That is 70 000 000 000 000 000 000 000, or 230 billion times as many as the 300 billion in our own Milky Way.

The nearest star to the Earth, apart from the Sun, is Proxima Centauri, which is 39.9 trillion kilometers, or 4.2 light years away (light from Proxima Centauri takes 4.2 years to reach Earth). Travelling at the orbit speed of the Space Shuttle (5 miles per second -- almost 30,000 kilometers per hour), it would take about 150,000 years to get there. Distances like this are typical inside galactic discs, where the Sun and Earth are located. Stars can be much closer to each other in the centres of galaxies and globular clusters, or much further apart in galactic halos.

Age and size of stars
galactic halo
Many stars are between 1 billion and 10 billion years old. Some stars may even be close to 13.7 billion years old, which is the observed age of the universe. (See Big Bang theory and stellar evolution.) They range in size from the tiny neutron stars (which are actually dead stars) no bigger than a city, to supergiants like the North Star (Polaris) and Betelgeuse, in the Orion constellation, which have a diameter about 1,000 times larger than the Sun—about 1.6 billion kilometers. However, these have a much lower density than the Sun.

One of the most massive stars known is η Carinae, with 100–150 times as much mass as the Sun. Recent work by Donald Figer, an astronomer at the Space Telescope Science Institute in Baltimore, Maryland, suggests that 150 solar masses is the upper limit of stars in the current era of the universe. He used the Hubble Space Telescope to observe about a thousand stars in the Arches cluster, a massive young star cluster near the core of the Milky Way, and found no stars over that limit despite a statistical expectation that there should be several. The reason for this limit is not precisely known, but the Eddington limit is part of the answer. The very first stars to form after the Big Bang may have been larger, up to 300 solar masses or more, due to the complete absence of elements heavier than lithium in their composition. This generation of supermassive star is long extinct, however, and currently only theoretical.

With a mass only 93 times that of Jupiter, AB Doradus C, a companion to AB Doradus A, is the smallest known star undergoing nuclear fusion in its core. Smaller bodies are brown dwarfs, which occupy a poorly-defined grey area between stars and gas giants. The minimum mass a star can have is estimated to be in the vicinity of 75 Jupiters.

Star classification

There are different classifications of stars ranging from type W, which are very large and bright, to M, which is often just large enough to start ignition of the hydrogen. Some of the more common classifications are O, B, A, F, G, K, M, and can perhaps be more easily remembered using the mnemonic "Oh, Be A Fine Girl, Kiss Me" (variant: change "girl" to "guy"), invented by Annie Jump Cannon (1863-1941). There are many other mnemonics for star classification; the most frequent addition tacks "Right Now, Sweetheart" for the red dwarf sub-types R, N and S. The new types L and T have also been recently appended to the end of the OBAFGKM sequence to classify the coldest low-mass stars and brown dwarfs, prompting such additions as "Lovingly Tonight" to the mnemonic.

Each letter has 10 subclassifications. Our Sun is a G2, which is very near the middle in terms of quantities observed. Most stars fall into the main sequence which is a description of stars based on their absolute magnitude and spectral type. The Sun is taken as the prototypical star (not because it is special in any way, but because it is the closest and most studied star we have), and most characteristics of other stars are usually given in solar units.

For example, the mass of the Sun is

:M_Sun = 1.9891×10³⁰ kg

The masses of other stars can be given in terms of M_Sun.

Naming of stars

Most stars are identified only by catalogue numbers; only a few have names as such.
The names are either traditional names (mostly from Arabic), Flamsteed designations, or Bayer designations. The only body which has been recognized by the scientific community as having competence to name stars or other celestial bodies is the International Astronomical Union (IAU). A number of private companies (e.g. the "International Star Registry") purport to sell names to stars; however, these names are not recognized by the scientific community, nor used by them, and many in the astronomy community view these organizations as frauds preying on people ignorant of how stars are in fact named.

See star designations for more information on how stars are named. For a list of traditional names, see the list of stars by constellation.

Energy production

The energy produced by stars radiates into space as electromagnetic radiation, as a stream of neutrinos from the star's core, and as a stream of particles from the star's outer layers (its stellar wind). The peak frequency of the light depends on the temperature of the outer layers of the star. Besides the emitted visible light, the ultraviolet and infrared components are typically significant. The apparent brightness of a star is measured by its apparent magnitude.

Nuclear fusion reaction pathways

A variety of different nuclear fusion reactions take place inside the cores of stars, depending upon their mass and composition (see Stellar nucleosynthesis).

Stars begin as a cloud of mostly hydrogen with about 25% helium and heavier elements in smaller quantities. In the Sun, with a 10⁷ K core, hydrogen fuses to form helium in the proton-proton chain:

:4¹H → 2²H + 2e⁺ + 2ν_e (4.0 MeV + 1.0 MeV)
:2¹H + 2²H → 2³He + 2γ (5.5 MeV)
:2³He → ⁴He + 2¹H (12.9 MeV)

These reactions result in the overall reaction:

:4¹H → ⁴He + 2e⁺ + 2γ + 2ν_e (26.7 MeV)

In more massive stars, helium is produced in a cycle of reactions catalyzed by carbon, the carbon-nitrogen-oxygen cycle.

In stars with cores at 10⁸ K and masses between 0.5 and 10 solar masses, helium can be transformed into carbon in the triple-alpha process:

:⁴He + ⁴He + 92 keV → ^{8
-}Be
:⁴He + ^{8
-}Be + 67 keV → ^{12
-}C
:^{12
-}C → ¹²C + γ + 7.4 MeV

For an overall reaction of:

:3⁴He → ¹²C + γ + 7.2 MeV

Star mythology

As well as certain constellations and the Sun itself, stars as a whole have their own mythology. They were thought to be the souls of the dead, or gods/goddesses.

References

- Cliff Pickover (2001) "The Stars of Heaven", Oxford University Press

- John Gribbin, Mary Gribbin (2001) "Stardust: Supernovae and Life — The Cosmic Connection", Yale University Press.

See also

- Black hole

- Blue straggler

- Overview of star constellations

- Nursery rhyme Twinkle twinkle little star

- sidereal clock

- Star count

- Star clocks

- Stars with articles in Wikipedia

- Stellar navigation

- Stellar evolution

- Timeline of stellar astronomy

- Variable star

Related lists

- List of brightest stars (apparent & absolute magnitude)
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