The apparent magnitude of an astronomical object is a number, a measure of its brightness as seen by an observer on Earth. The magnitude scale is logarithmic. A difference of 1 in magnitude corresponds to a change in brightness by a factor of 5√100, or about 2.512. The brighter an object appears, the lower its magnitude value, with the brightest astronomical objects having negative apparent magnitudes: for example Sirius at −1.46. The measurement of apparent magnitudes or brightnesses of celestial objects is known as photometry. Apparent magnitudes are used to quantify the brightness of sources at ultraviolet and infrared wavelengths. An apparent magnitude is measured in a specific passband corresponding to some photometric system such as the UBV system. In standard astronomical notation, an apparent magnitude in the V filter band would be denoted either as mV or simply as V, as in "mV = 15" or "V = 15" to describe a 15th-magnitude object; the scale used to indicate magnitude originates in the Hellenistic practice of dividing stars visible to the naked eye into six magnitudes.
The brightest stars in the night sky were said to be of first magnitude, whereas the faintest were of sixth magnitude, the limit of human visual perception. Each grade of magnitude was considered twice the brightness of the following grade, although that ratio was subjective as no photodetectors existed; this rather crude scale for the brightness of stars was popularized by Ptolemy in his Almagest and is believed to have originated with Hipparchus. In 1856, Norman Robert Pogson formalized the system by defining a first magnitude star as a star, 100 times as bright as a sixth-magnitude star, thereby establishing the logarithmic scale still in use today; this implies that a star of magnitude m is about 2.512 times as bright as a star of magnitude m + 1. This figure, the fifth root of 100, became known as Pogson's Ratio; the zero point of Pogson's scale was defined by assigning Polaris a magnitude of 2. Astronomers discovered that Polaris is variable, so they switched to Vega as the standard reference star, assigning the brightness of Vega as the definition of zero magnitude at any specified wavelength.
Apart from small corrections, the brightness of Vega still serves as the definition of zero magnitude for visible and near infrared wavelengths, where its spectral energy distribution approximates that of a black body for a temperature of 11000 K. However, with the advent of infrared astronomy it was revealed that Vega's radiation includes an Infrared excess due to a circumstellar disk consisting of dust at warm temperatures. At shorter wavelengths, there is negligible emission from dust at these temperatures. However, in order to properly extend the magnitude scale further into the infrared, this peculiarity of Vega should not affect the definition of the magnitude scale. Therefore, the magnitude scale was extrapolated to all wavelengths on the basis of the black-body radiation curve for an ideal stellar surface at 11000 K uncontaminated by circumstellar radiation. On this basis the spectral irradiance for the zero magnitude point, as a function of wavelength, can be computed. Small deviations are specified between systems using measurement apparatuses developed independently so that data obtained by different astronomers can be properly compared, but of greater practical importance is the definition of magnitude not at a single wavelength but applying to the response of standard spectral filters used in photometry over various wavelength bands.
With the modern magnitude systems, brightness over a wide range is specified according to the logarithmic definition detailed below, using this zero reference. In practice such apparent magnitudes do not exceed 30; the brightness of Vega is exceeded by four stars in the night sky at visible wavelengths as well as the bright planets Venus and Jupiter, these must be described by negative magnitudes. For example, the brightest star of the celestial sphere, has an apparent magnitude of −1.4 in the visible. Negative magnitudes for other bright astronomical objects can be found in the table below. Astronomers have developed other photometric zeropoint systems as alternatives to the Vega system; the most used is the AB magnitude system, in which photometric zeropoints are based on a hypothetical reference spectrum having constant flux per unit frequency interval, rather than using a stellar spectrum or blackbody curve as the reference. The AB magnitude zeropoint is defined such that an object's AB and Vega-based magnitudes will be equal in the V filter band.
As the amount of light received by a telescope is reduced by transmission through the Earth's atmosphere, any measurement of apparent magnitude is corrected for what it would have been as seen from above the atmosphere. The dimmer an object appears, the higher the numerical value given to its apparent magnitude, with a difference of 5 magnitudes corresponding to a brightness factor of 100. Therefore, the apparent magnitude m, in the spectral band x, would be given by m x = − 5 log 100 , more expressed in terms of common logarithms as m x
A star is type of astronomical object consisting of a luminous spheroid of plasma held together by its own gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye from Earth during the night, appearing as a multitude of fixed luminous points in the sky due to their immense distance from Earth; the most prominent stars were grouped into constellations and asterisms, the brightest of which gained proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. However, most of the estimated 300 sextillion stars in the Universe are invisible to the naked eye from Earth, including all stars outside our galaxy, the Milky Way. For at least a portion of its life, a star shines due to thermonuclear fusion of hydrogen into helium in its core, releasing energy that traverses the star's interior and radiates into outer space. All occurring elements heavier than helium are created by stellar nucleosynthesis during the star's lifetime, for some stars by supernova nucleosynthesis when it explodes.
Near the end of its life, a star can contain degenerate matter. Astronomers can determine the mass, age and many other properties of a star by observing its motion through space, its luminosity, spectrum respectively; the total mass of a star is the main factor. Other characteristics of a star, including diameter and temperature, change over its life, while the star's environment affects its rotation and movement. A plot of the temperature of many stars against their luminosities produces a plot known as a Hertzsprung–Russell diagram. Plotting a particular star on that diagram allows the age and evolutionary state of that star to be determined. A star's life begins with the gravitational collapse of a gaseous nebula of material composed of hydrogen, along with helium and trace amounts of heavier elements; when the stellar core is sufficiently dense, hydrogen becomes converted into helium through nuclear fusion, releasing energy in the process. The remainder of the star's interior carries energy away from the core through a combination of radiative and convective heat transfer processes.
The star's internal pressure prevents it from collapsing further under its own gravity. A star with mass greater than 0.4 times the Sun's will expand to become a red giant when the hydrogen fuel in its core is exhausted. In some cases, it will fuse heavier elements in shells around the core; as the star expands it throws a part of its mass, enriched with those heavier elements, into the interstellar environment, to be recycled as new stars. Meanwhile, the core becomes a stellar remnant: a white dwarf, a neutron star, or if it is sufficiently massive a black hole. Binary and multi-star systems consist of two or more stars that are gravitationally bound and move around each other in stable orbits; when two such stars have a close orbit, their gravitational interaction can have a significant impact on their evolution. Stars can form part of a much larger gravitationally bound structure, such as a star cluster or a galaxy. Stars have been important to civilizations throughout the world, they have used for celestial navigation and orientation.
Many ancient astronomers believed that stars were permanently affixed to a heavenly sphere and that they were immutable. By convention, astronomers grouped stars into constellations and used them to track the motions of the planets and the inferred position of the Sun; the motion of the Sun against the background stars was used to create calendars, which could be used to regulate agricultural practices. The Gregorian calendar used nearly everywhere in the world, is a solar calendar based on the angle of the Earth's rotational axis relative to its local star, the Sun; the oldest dated star chart was the result of ancient Egyptian astronomy in 1534 BC. The earliest known star catalogues were compiled by the ancient Babylonian astronomers of Mesopotamia in the late 2nd millennium BC, during the Kassite Period; the first star catalogue in Greek astronomy was created by Aristillus in 300 BC, with the help of Timocharis. The star catalog of Hipparchus included 1020 stars, was used to assemble Ptolemy's star catalogue.
Hipparchus is known for the discovery of the first recorded nova. Many of the constellations and star names in use today derive from Greek astronomy. In spite of the apparent immutability of the heavens, Chinese astronomers were aware that new stars could appear. In 185 AD, they were the first to observe and write about a supernova, now known as the SN 185; the brightest stellar event in recorded history was the SN 1006 supernova, observed in 1006 and written about by the Egyptian astronomer Ali ibn Ridwan and several Chinese astronomers. The SN 1054 supernova, which gave birth to the Crab Nebula, was observed by Chinese and Islamic astronomers. Medieval Islamic astronomers gave Arabic names to many stars that are still used today and they invented numerous astronomical instruments that could compute the positions of the stars, they built the first large observatory research institutes for the purpose of producing Zij star catalogues. Among these, the Book of Fixed Stars was written by the Persian astronomer Abd al-Rahman al-Sufi, who observed a number of stars, star clusters and galaxies.
According to A. Zahoor, in the 11th century, the Persian polymath scholar Abu Rayhan Biruni described the Milky
In astronomy, stellar classification is the classification of stars based on their spectral characteristics. Electromagnetic radiation from the star is analyzed by splitting it with a prism or diffraction grating into a spectrum exhibiting the rainbow of colors interspersed with spectral lines; each line indicates a particular chemical element or molecule, with the line strength indicating the abundance of that element. The strengths of the different spectral lines vary due to the temperature of the photosphere, although in some cases there are true abundance differences; the spectral class of a star is a short code summarizing the ionization state, giving an objective measure of the photosphere's temperature. Most stars are classified under the Morgan-Keenan system using the letters O, B, A, F, G, K, M, a sequence from the hottest to the coolest; each letter class is subdivided using a numeric digit with 0 being hottest and 9 being coolest. The sequence has been expanded with classes for other stars and star-like objects that do not fit in the classical system, such as class D for white dwarfs and classes S and C for carbon stars.
In the MK system, a luminosity class is added to the spectral class using Roman numerals. This is based on the width of certain absorption lines in the star's spectrum, which vary with the density of the atmosphere and so distinguish giant stars from dwarfs. Luminosity class 0 or Ia+ is used for hypergiants, class I for supergiants, class II for bright giants, class III for regular giants, class IV for sub-giants, class V for main-sequence stars, class sd for sub-dwarfs, class D for white dwarfs; the full spectral class for the Sun is G2V, indicating a main-sequence star with a temperature around 5,800 K. The conventional color description takes into account only the peak of the stellar spectrum. In actuality, stars radiate in all parts of the spectrum; because all spectral colors combined appear white, the actual apparent colors the human eye would observe are far lighter than the conventional color descriptions would suggest. This characteristic of'lightness' indicates that the simplified assignment of colors within the spectrum can be misleading.
Excluding color-contrast illusions in dim light, there are indigo, or violet stars. Red dwarfs are a deep shade of orange, brown dwarfs do not appear brown, but hypothetically would appear dim grey to a nearby observer; the modern classification system is known as the Morgan–Keenan classification. Each star is assigned a spectral class from the older Harvard spectral classification and a luminosity class using Roman numerals as explained below, forming the star's spectral type. Other modern stellar classification systems, such as the UBV system, are based on color indexes—the measured differences in three or more color magnitudes; those numbers are given labels such as "U-V" or "B-V", which represent the colors passed by two standard filters. The Harvard system is a one-dimensional classification scheme by astronomer Annie Jump Cannon, who re-ordered and simplified a prior alphabetical system. Stars are grouped according to their spectral characteristics by single letters of the alphabet, optionally with numeric subdivisions.
Main-sequence stars vary in surface temperature from 2,000 to 50,000 K, whereas more-evolved stars can have temperatures above 100,000 K. Physically, the classes indicate the temperature of the star's atmosphere and are listed from hottest to coldest; the spectral classes O through M, as well as other more specialized classes discussed are subdivided by Arabic numerals, where 0 denotes the hottest stars of a given class. For example, A0 denotes A9 denotes the coolest ones. Fractional numbers are allowed; the Sun is classified as G2. Conventional color descriptions are traditional in astronomy, represent colors relative to the mean color of an A class star, considered to be white; the apparent color descriptions are what the observer would see if trying to describe the stars under a dark sky without aid to the eye, or with binoculars. However, most stars in the sky, except the brightest ones, appear white or bluish white to the unaided eye because they are too dim for color vision to work. Red supergiants are cooler and redder than dwarfs of the same spectral type, stars with particular spectral features such as carbon stars may be far redder than any black body.
The fact that the Harvard classification of a star indicated its surface or photospheric temperature was not understood until after its development, though by the time the first Hertzsprung–Russell diagram was formulated, this was suspected to be true. In the 1920s, the Indian physicist Meghnad Saha derived a theory of ionization by extending well-known ideas in physical chemistry pertaining to the dissociation of molecules to the ionization of atoms. First he applied it to the solar chromosphere to stellar spectra. Harvard astronomer Cecilia Payne demonstrated that the O-B-A-F-G-K-M spectral sequence is a sequence in temperature; because the classification sequence predates our understanding that it is a temperature sequence, the placement of a spectrum into a given subtype, such as B3 or A7, depends upon estimates of the strengths of absorption features in stellar spectra. As a result, these subtypes are not evenly divided into any sort of mathematically representable intervals; the Yerkes spectral classification called the MKK system from the authors' initial
In astronomy, luminosity is the total amount of energy emitted per unit of time by a star, galaxy, or other astronomical object. As a term for energy emitted per unit time, luminosity is synonymous with power. In SI units luminosity is measured in joules per second or watts. Values for luminosity are given in the terms of the luminosity of the Sun, L⊙. Luminosity can be given in terms of the astronomical magnitude system: the absolute bolometric magnitude of an object is a logarithmic measure of its total energy emission rate, while absolute magnitude is a logarithmic measure of the luminosity within some specific wavelength range or filter band. In contrast, the term brightness in astronomy is used to refer to an object's apparent brightness: that is, how bright an object appears to an observer. Apparent brightness depends on both the luminosity of the object and the distance between the object and observer, on any absorption of light along the path from object to observer. Apparent magnitude is a logarithmic measure of apparent brightness.
The distance determined by luminosity measures can be somewhat ambiguous, is thus sometimes called the luminosity distance. In astronomy, luminosity is the amount of electromagnetic energy; when not qualified, the term "luminosity" means bolometric luminosity, measured either in the SI units, watts, or in terms of solar luminosities. A bolometer is the instrument used to measure radiant energy over a wide band by absorption and measurement of heating. A star radiates neutrinos, which carry off some energy, contributing to the star's total luminosity; the IAU has defined a nominal solar luminosity of 3.828×1026 W to promote publication of consistent and comparable values in units of the solar luminosity. While bolometers do exist, they cannot be used to measure the apparent brightness of a star because they are insufficiently sensitive across the electromagnetic spectrum and because most wavelengths do not reach the surface of the Earth. In practice bolometric magnitudes are measured by taking measurements at certain wavelengths and constructing a model of the total spectrum, most to match those measurements.
In some cases, the process of estimation is extreme, with luminosities being calculated when less than 1% of the energy output is observed, for example with a hot Wolf-Rayet star observed only in the infra-red. Bolometric luminosities can be calculated using a bolometric correction to a luminosity in a particular passband; the term luminosity is used in relation to particular passbands such as a visual luminosity of K-band luminosity. These are not luminosities in the strict sense of an absolute measure of radiated power, but absolute magnitudes defined for a given filter in a photometric system. Several different photometric systems exist; some such as the UBV or Johnson system are defined against photometric standard stars, while others such as the AB system are defined in terms of a spectral flux density. A star's luminosity can be determined from two stellar characteristics: size and effective temperature; the former is represented in terms of solar radii, R⊙, while the latter is represented in kelvins, but in most cases neither can be measured directly.
To determine a star's radius, two other metrics are needed: the star's angular diameter and its distance from Earth. Both can be measured with great accuracy in certain cases, with cool supergiants having large angular diameters, some cool evolved stars having masers in their atmospheres that can be used to measure the parallax using VLBI. However, for most stars the angular diameter or parallax, or both, are far below our ability to measure with any certainty. Since the effective temperature is a number that represents the temperature of a black body that would reproduce the luminosity, it cannot be measured directly, but it can be estimated from the spectrum. An alternative way to measure stellar luminosity is to measure the star's apparent brightness and distance. A third component needed to derive the luminosity is the degree of interstellar extinction, present, a condition that arises because of gas and dust present in the interstellar medium, the Earth's atmosphere, circumstellar matter.
One of astronomy's central challenges in determining a star's luminosity is to derive accurate measurements for each of these components, without which an accurate luminosity figure remains elusive. Extinction can only be measured directly if the actual and observed luminosities are both known, but it can be estimated from the observed colour of a star, using models of the expected level of reddening from the interstellar medium. In the current system of stellar classification, stars are grouped according to temperature, with the massive young and energetic Class O stars boasting temperatures in excess of 30,000 K while the less massive older Class M stars exhibit temperatures less than 3,500 K; because luminosity is proportional to temperature to the fourth power, the large variation in stellar temperatures produces an vaster variation in stellar luminosity. Because the luminosity depends on a high power of the stellar mass, high mass luminous stars have much shorter lifetimes; the most luminous stars are always young stars, no more than a few million years for the most extreme.
In the Hertzsprung–Russell diagram, the x-axis represents temperature or spectral type while the y-axis represents luminosity or magnitude. The vast majority of stars are found along the main sequence with blue Class O stars found at the top left of the chart while red Class M stars fall to the bottom right. Certain stars like Deneb and Betelgeuse are
The Kelvin scale is an absolute thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The kelvin is the base unit of temperature in the International System of Units; until 2018, the kelvin was defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. In other words, it was defined such that the triple point of water is 273.16 K. On 16 November 2018, a new definition was adopted, in terms of a fixed value of the Boltzmann constant. For legal metrology purposes, the new definition will come into force on 20 May 2019; the Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Thomson, 1st Baron Kelvin, who wrote of the need for an "absolute thermometric scale". Unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or written as a degree; the kelvin is the primary unit of temperature measurement in the physical sciences, but is used in conjunction with the degree Celsius, which has the same magnitude.
The definition implies that absolute zero is equivalent to −273.15 °C. In 1848, William Thomson, made Lord Kelvin, wrote in his paper, On an Absolute Thermometric Scale, of the need for a scale whereby "infinite cold" was the scale's null point, which used the degree Celsius for its unit increment. Kelvin calculated; this absolute scale is known today as the Kelvin thermodynamic temperature scale. Kelvin's value of "−273" was the negative reciprocal of 0.00366—the accepted expansion coefficient of gas per degree Celsius relative to the ice point, giving a remarkable consistency to the accepted value. In 1954, Resolution 3 of the 10th General Conference on Weights and Measures gave the Kelvin scale its modern definition by designating the triple point of water as its second defining point and assigned its temperature to 273.16 kelvins. In 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol °K. Furthermore, feeling it useful to more explicitly define the magnitude of the unit increment, the 13th CGPM held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction 1/273.16 of the thermodynamic temperature of the triple point of water."In 2005, the Comité International des Poids et Mesures, a committee of the CGPM, affirmed that for the purposes of delineating the temperature of the triple point of water, the definition of the Kelvin thermodynamic temperature scale would refer to water having an isotopic composition specified as Vienna Standard Mean Ocean Water.
In 2018, Resolution A of the 26th CGPM adopted a significant redefinition of SI base units which included redefining the Kelvin in terms of a fixed value for the Boltzmann constant of 1.380649×10−23 J/K. When spelled out or spoken, the unit is pluralised using the same grammatical rules as for other SI units such as the volt or ohm; when reference is made to the "Kelvin scale", the word "kelvin"—which is a noun—functions adjectivally to modify the noun "scale" and is capitalized. As with most other SI unit symbols there is a space between the kelvin symbol. Before the 13th CGPM in 1967–1968, the unit kelvin was called a "degree", the same as with the other temperature scales at the time, it was distinguished from the other scales with either the adjective suffix "Kelvin" or with "absolute" and its symbol was °K. The latter term, the unit's official name from 1948 until 1954, was ambiguous since it could be interpreted as referring to the Rankine scale. Before the 13th CGPM, the plural form was "degrees absolute".
The 13th CGPM changed the unit name to "kelvin". The omission of "degree" indicates that it is not relative to an arbitrary reference point like the Celsius and Fahrenheit scales, but rather an absolute unit of measure which can be manipulated algebraically. In science and engineering, degrees Celsius and kelvins are used in the same article, where absolute temperatures are given in degrees Celsius, but temperature intervals are given in kelvins. E.g. "its measured value was 0.01028 °C with an uncertainty of 60 µK." This practice is permissible because the degree Celsius is a special name for the kelvin for use in expressing relative temperatures, the magnitude of the degree Celsius is equal to that of the kelvin. Notwithstanding that the official endorsement provided by Resolution 3 of the 13th CGPM states "a temperature interval may be expressed in degrees Celsius", the practice of using both °C and K is widespread throughout the scientific world; the use of SI prefixed forms of the degree Celsius to express a temperature interval has not been adopted.
In 2005 the CIPM embarked on a programme to redefine the kelvin using a more experimentally rigorous methodology. In particular, the committee proposed redefining the kelvin such that Boltzmann's constant takes the exact value 1.3806505×10−23 J/K. The committee had hoped tha
A variable star is a star whose brightness as seen from Earth fluctuates. This variation may be caused by a change in emitted light or by something blocking the light, so variable stars are classified as either: Intrinsic variables, whose luminosity changes. Extrinsic variables, whose apparent changes in brightness are due to changes in the amount of their light that can reach Earth. Many most, stars have at least some variation in luminosity: the energy output of our Sun, for example, varies by about 0.1% over an 11-year solar cycle. An ancient Egyptian calendar of lucky and unlucky days composed some 3,200 years ago may be the oldest preserved historical document of the discovery of a variable star, the eclipsing binary Algol. Of the modern astronomers, the first variable star was identified in 1638 when Johannes Holwarda noticed that Omicron Ceti pulsated in a cycle taking 11 months; this discovery, combined with supernovae observed in 1572 and 1604, proved that the starry sky was not eternally invariable as Aristotle and other ancient philosophers had taught.
In this way, the discovery of variable stars contributed to the astronomical revolution of the sixteenth and early seventeenth centuries. The second variable star to be described was the eclipsing variable Algol, by Geminiano Montanari in 1669. Chi Cygni was identified in 1686 by G. Kirch R Hydrae in 1704 by G. D. Maraldi. By 1786 ten variable stars were known. John Goodricke himself discovered Beta Lyrae. Since 1850 the number of known variable stars has increased especially after 1890 when it became possible to identify variable stars by means of photography; the latest edition of the General Catalogue of Variable Stars lists more than 46,000 variable stars in the Milky Way, as well as 10,000 in other galaxies, over 10,000'suspected' variables. The most common kinds of variability involve changes in brightness, but other types of variability occur, in particular changes in the spectrum. By combining light curve data with observed spectral changes, astronomers are able to explain why a particular star is variable.
Variable stars are analysed using photometry, spectrophotometry and spectroscopy. Measurements of their changes in brightness can be plotted to produce light curves. For regular variables, the period of variation and its amplitude can be well established. Peak brightnesses in the light curve are known as maxima. Amateur astronomers can do useful scientific study of variable stars by visually comparing the star with other stars within the same telescopic field of view of which the magnitudes are known and constant. By estimating the variable's magnitude and noting the time of observation a visual lightcurve can be constructed; the American Association of Variable Star Observers collects such observations from participants around the world and shares the data with the scientific community. From the light curve the following data are derived: are the brightness variations periodical, irregular, or unique? What is the period of the brightness fluctuations? What is the shape of the light curve? From the spectrum the following data are derived: what kind of star is it: what is its temperature, its luminosity class? is it a single star, or a binary? does the spectrum change with time?
Changes in brightness may depend on the part of the spectrum, observed if the wavelengths of spectral lines are shifted this points to movements strong magnetic fields on the star betray themselves in the spectrum abnormal emission or absorption lines may be indication of a hot stellar atmosphere, or gas clouds surrounding the star. In few cases it is possible to make pictures of a stellar disk; these may show darker spots on its surface. Combining light curves with spectral data gives a clue as to the changes that occur in a variable star. For example, evidence for a pulsating star is found in its shifting spectrum because its surface periodically moves toward and away from us, with the same frequency as its changing brightness. About two-thirds of all variable stars appear to be pulsating. In the 1930s astronomer Arthur Stanley Eddington showed that the mathematical equations that describe the interior of a star may lead to instabilities that cause a star to pulsate; the most common type of instability is related to oscillations in the degree of ionization in outer, convective layers of the star.
Suppose the star is in the swelling phase. Its outer layers expand; because of the decreasing temperature the degree of ionization decreases. This makes the gas more transparent, thus makes it easier for the star to radiate its energy; this in turn will make the star start to contract. As the gas is thereby compressed, it is heated and the degree of ionization again increases. Thi
Minute and second of arc
A minute of arc, arc minute, or minute arc is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn, one minute of arc is 1/21600 of a turn – it is for this reason that the Earth's circumference is exactly 21,600 nautical miles. A minute of arc is π/10800 of a radian. A second of arc, arcsecond, or arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn, π/648000 of a radian; these units originated in Babylonian astronomy as sexagesimal subdivisions of the degree. To express smaller angles, standard SI prefixes can be employed; the number of square arcminutes in a complete sphere is 4 π 2 = 466 560 000 π ≈ 148510660 square arcminutes. The names "minute" and "second" have nothing to do with the identically named units of time "minute" or "second"; the identical names reflect the ancient Babylonian number system, based on the number 60. The standard symbol for marking the arcminute is the prime, though a single quote is used where only ASCII characters are permitted.
One arcminute is thus written 1′. It is abbreviated as arcmin or amin or, less the prime with a circumflex over it; the standard symbol for the arcsecond is the double prime, though a double quote is used where only ASCII characters are permitted. One arcsecond is thus written 1″, it is abbreviated as arcsec or asec. In celestial navigation, seconds of arc are used in calculations, the preference being for degrees and decimals of a minute, for example, written as 42° 25.32′ or 42° 25.322′. This notation has been carried over into marine GPS receivers, which display latitude and longitude in the latter format by default; the full moon's average apparent size is about 31 arcminutes. An arcminute is the resolution of the human eye. An arcsecond is the angle subtended by a U. S. dime coin at a distance of 4 kilometres. An arcsecond is the angle subtended by an object of diameter 725.27 km at a distance of one astronomical unit, an object of diameter 45866916 km at one light-year, an object of diameter one astronomical unit at a distance of one parsec, by definition.
A milliarcsecond is about the size of a dime atop the Eiffel Tower. A microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth. A nanoarcsecond is about the size of a penny on Neptune's moon Triton as observed from Earth. Notable examples of size in arcseconds are: Hubble Space Telescope has calculational resolution of 0.05 arcseconds and actual resolution of 0.1 arcseconds, close to the diffraction limit. Crescent Venus measures between 66 seconds of arc. Since antiquity the arcminute and arcsecond have been used in astronomy. In the ecliptic coordinate system and longitude; the principal exception is right ascension in equatorial coordinates, measured in time units of hours and seconds. The arcsecond is often used to describe small astronomical angles such as the angular diameters of planets, the proper motion of stars, the separation of components of binary star systems, parallax, the small change of position of a star in the course of a year or of a solar system body as the Earth rotates.
These small angles may be written in milliarcseconds, or thousandths of an arcsecond. The unit of distance, the parsec, named from the parallax of one arc second, was developed for such parallax measurements, it is the distance at which the mean radius of the Earth's orbit would subtend an angle of one arcsecond. The ESA astrometric space probe Gaia, launched in 2013, can approximate star positions to 7 microarcseconds. Apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red giant with a diameter of 0.05 arcsecond. Because of the effects of atmospheric seeing, ground-based telescopes will smear the image of a star to an angular diameter of about 0.5 arcsecond. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1 arcsecond. Space telescopes are diffraction limited. For example, the Hubble Space Telescope can reach an angular size of stars down to about 0.1″. Techniques exist for improving seeing on the ground. Adaptive optics, for example, can produce images around 0.05 arcsecond on a 10 m class telescope.
Minutes and seconds of arc are used in cartography and navigation. At sea level one minute of arc