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The astronomical unit (symbol: au, or or AU) is a
unit of length A unit of length refers to any arbitrarily chosen and accepted reference standard for measurement of length. The most common units in modern use are the metric units, used in every country globally. In the United States the U.S. customary units ...
, roughly the
distance Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
from Earth to the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits the Sun, from a maximum (
aphelion An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any ellip ...
) to a minimum ( perihelion) and back again once each year. The astronomical unit was originally conceived as the average of Earth's aphelion and perihelion; however, since 2012 it has been defined as exactly (see below for several conversions). The astronomical unit is used primarily for measuring distances within the Solar System or around other stars. It is also a fundamental component in the definition of another unit of astronomical length, the
parsec The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, a ...
.


History of symbol usage

A variety of unit symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the
International Astronomical Union The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) is a nongovernmental organisation with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach ...
 (IAU) had used the symbol ''A'' to denote a length equal to the astronomical unit. In the astronomical literature, the symbol AU was (and remains) common. In 2006, the
International Bureau of Weights and Measures The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation, through which its 59 member-states act together on measurement standards in four areas: chemistry, ...
(BIPM) had recommended ua as the symbol for the unit. In the non-normative Annex C to
ISO 80000-3 ISO 80000 or IEC 80000 is an international standard introducing the International System of Quantities (ISQ). It was developed and promulgated jointly by the International Organization for Standardization (ISO) and the International Electrotech ...
:2006 (now withdrawn), the symbol of the astronomical unit was "ua". In 2012, the IAU, noting "that various symbols are presently in use for the astronomical unit", recommended the use of the symbol "au". The
scientific journal In academic publishing, a scientific journal is a periodical publication intended to further the progress of science, usually by reporting new research. Content Articles in scientific journals are mostly written by active scientists such as ...
s published by the
American Astronomical Society The American Astronomical Society (AAS, sometimes spoken as "double-A-S") is an American society of professional astronomers and other interested individuals, headquartered in Washington, DC. The primary objective of the AAS is to promote the adv ...
and the
Royal Astronomical Society (Whatever shines should be observed) , predecessor = , successor = , formation = , founder = , extinction = , merger = , merged = , type = NGO ...
subsequently adopted this symbol. In the 2014 revision and 2019 edition of the SI Brochure, the BIPM used the unit symbol "au". ISO 80000-3:2019, which replaces ISO 80000-3:2006, does not mention the astronomical unit.


Development of unit definition

Earth's orbit around the Sun is an ellipse. The semi-major axis of this elliptic orbit is defined to be half of the straight line segment that joins the
perihelion and aphelion An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any ellip ...
. The centre of the Sun lies on this straight line segment, but not at its midpoint. Because ellipses are well-understood shapes, measuring the points of its extremes defined the exact shape mathematically, and made possible calculations for the entire orbit as well as predictions based on observation. In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, defining times and places for observing the largest parallax (apparent shifts of position) in nearby stars. Knowing Earth's shift and a star's shift enabled the star's distance to be calculated. But all measurements are subject to some degree of error or uncertainty, and the uncertainties in the length of the astronomical unit only increased uncertainties in the stellar distances. Improvements in precision have always been a key to improving astronomical understanding. Throughout the twentieth century, measurements became increasingly precise and sophisticated, and ever more dependent on accurate observation of the effects described by Einstein's theory of relativity and upon the mathematical tools it used. Improving measurements were continually checked and cross-checked by means of improved understanding of the laws of
celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...
, which govern the motions of objects in space. The expected positions and distances of objects at an established time are calculated (in au) from these laws, and assembled into a collection of data called an
ephemeris In astronomy and celestial navigation, an ephemeris (pl. ephemerides; ) is a book with tables that gives the trajectory of naturally occurring astronomical objects as well as artificial satellites in the sky, i.e., the position (and possibly ve ...
. NASA Jet Propulsion Laboratory HORIZONS System provides one of several ephemeris computation services. In 1976, to establish an even precise measure for the astronomical unit, the IAU formally adopted a new definition. Although directly based on the then-best available observational measurements, the definition was recast in terms of the then-best mathematical derivations from celestial mechanics and planetary ephemerides. It stated that "the astronomical unit of length is that length (''A'') for which the
Gaussian gravitational constant The Gaussian gravitational constant (symbol ) is a parameter used in the orbital mechanics of the Solar System. It relates the orbital period to the orbit's semi-major axis and the mass of the orbiting body in Solar masses. The value of histori ...
(''k'') takes the value when the units of measurement are the astronomical units of length, mass and time". Equivalently, by this definition, one au is "the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass, moving with an
angular frequency In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
of "; or alternatively that length for which the heliocentric gravitational constant (the product ''G'') is equal to ()2 au3/d2, when the length is used to describe the positions of objects in the Solar System. Subsequent explorations of the Solar System by space probes made it possible to obtain precise measurements of the relative positions of the
inner planets The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
and other objects by means of radar and telemetry. As with all radar measurements, these rely on measuring the time taken for
photons A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are Massless particle, massless ...
to be reflected from an object. Because all photons move at the speed of light in vacuum, a fundamental constant of the universe, the distance of an object from the probe is calculated as the product of the speed of light and the measured time. However, for precision the calculations require adjustment for things such as the motions of the probe and object while the photons are transiting. In addition, the measurement of the time itself must be translated to a standard scale that accounts for relativistic time dilation. Comparison of the ephemeris positions with time measurements expressed in
Barycentric Dynamical Time Barycentric Dynamical Time (TDB, from the French ) is a relativistic coordinate time scale, intended for astronomical use as a time standard to take account of time dilation when calculating orbits and astronomical ephemerides of planets, asteroi ...
 (TDB) leads to a value for the speed of light in astronomical units per day (of ). By 2009, the IAU had updated its standard measures to reflect improvements, and calculated the speed of light at (TDB). In 1983, the CIPM modified the International System of Units (SI) to make the metre defined as the distance travelled in a vacuum by light in 1 /  second. This replaced the previous definition, valid between 1960 and 1983, which was that the metre equalled a certain number of wavelengths of a certain emission line of krypton-86. (The reason for the change was an improved method of measuring the speed of light.) The speed of light could then be expressed exactly as ''c''0 = , a standard also adopted by the
IERS The International Earth Rotation and Reference Systems Service (IERS), formerly the International Earth Rotation Service, is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation Pa ...
numerical standards. For complete document see From this definition and the 2009 IAU standard, the time for light to traverse an astronomical unit is found to be ''τ''A = , which is slightly more than 8 minutes 19 seconds. By multiplication, the best IAU 2009 estimate was ''A'' = ''c''0''τ''A = , based on a comparison of Jet Propulsion Laboratory and IAA–RAS ephemerides. In 2006, the BIPM reported a value of the astronomical unit as . In the 2014 revision of the SI Brochure, the BIPM recognised the IAU's 2012 redefinition of the astronomical unit as . This estimate was still derived from observation and measurements subject to error, and based on techniques that did not yet standardize all relativistic effects, and thus were not constant for all observers. In 2012, finding that the equalization of relativity alone would make the definition overly complex, the IAU simply used the 2009 estimate to redefine the astronomical unit as a conventional unit of length directly tied to the metre (exactly ). The new definition also recognizes as a consequence that the astronomical unit is now to play a role of reduced importance, limited in its use to that of a convenience in some applications. : This definition makes the speed of light, defined as exactly , equal to exactly  ×  ÷  or about  au/d, some 60 parts per
trillion ''Trillion'' is a number with two distinct definitions: *1,000,000,000,000, i.e. one million million, or (ten to the twelfth power), as defined on the short scale. This is now the meaning in both American and British English. * 1,000,000,000,00 ...
less than the 2009 estimate.


Usage and significance

With the definitions used before 2012, the astronomical unit was dependent on the heliocentric gravitational constant, that is the product of the gravitational constant, ''G'', and the solar mass, . Neither ''G'' nor can be measured to high accuracy separately, but the value of their product is known very precisely from observing the relative positions of planets (
Kepler's Third Law In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbits ...
expressed in terms of Newtonian gravitation). Only the product is required to calculate planetary positions for an ephemeris, so ephemerides are calculated in astronomical units and not in SI units. The calculation of ephemerides also requires a consideration of the effects of general relativity. In particular, time intervals measured on Earth's surface ( Terrestrial Time, TT) are not constant when compared with the motions of the planets: the terrestrial second (TT) appears to be longer near January and shorter near July when compared with the "planetary second" (conventionally measured in TDB). This is because the distance between Earth and the Sun is not fixed (it varies between and ) and, when Earth is closer to the Sun ( perihelion), the Sun's gravitational field is stronger and Earth is moving faster along its orbital path. As the metre is defined in terms of the second and the speed of light is constant for all observers, the terrestrial metre appears to change in length compared with the "planetary metre" on a periodic basis. The metre is defined to be a unit of proper length, but the SI definition does not specify the
metric tensor In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows ...
to be used in determining it. Indeed, the
International Committee for Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established ...
(CIPM) notes that "its definition applies only within a spatial extent sufficiently small that the effects of the non-uniformity of the gravitational field can be ignored". As such, the metre is undefined for the purposes of measuring distances within the Solar System. The 1976 definition of the astronomical unit was incomplete because it did not specify the frame of reference in which time is to be measured, but proved practical for the calculation of ephemerides: a fuller definition that is consistent with general relativity was proposed, and "vigorous debate" ensued and also p. 91, ''Summary and recommendations''. until August 2012 when the IAU adopted the current definition of 1 astronomical unit = metres. The astronomical unit is typically used for
stellar system A star system or stellar system is a small number of stars that orbit each other, bound by gravitational attraction. A large group of stars bound by gravitation is generally called a ''star cluster'' or ''galaxy'', although, broadly speaking ...
scale distances, such as the size of a protostellar disk or the heliocentric distance of an asteroid, whereas other units are used for other distances in astronomy. The astronomical unit is too small to be convenient for interstellar distances, where the
parsec The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, a ...
and light-year are widely used. The parsec (parallax
arcsecond A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The n ...
) is defined in terms of the astronomical unit, being the distance of an object with a parallax of . The light-year is often used in popular works, but is not an approved non-SI unit and is rarely used by professional astronomers. When simulating a numerical model of the Solar System, the astronomical unit provides an appropriate scale that minimizes ( overflow, underflow and truncation) errors in
floating point In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be r ...
calculations.


History

The book '' On the Sizes and Distances of the Sun and Moon'', which is ascribed to Aristarchus, says the distance to the Sun is 18 to 20 times the distance to the Moon, whereas the true ratio is about . The latter estimate was based on the angle between the half-moon and the Sun, which he estimated as (the true value being close to ). Depending on the distance that van Helden assumes Aristarchus used for the distance to the Moon, his calculated distance to the Sun would fall between and Earth radii. According to Eusebius in the '' Praeparatio evangelica'' (Book XV, Chapter 53),
Eratosthenes Eratosthenes of Cyrene (; grc-gre, Ἐρατοσθένης ;  – ) was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandr ...
found the distance to the Sun to be "σταδιων μυριαδας τετρακοσιας και οκτωκισμυριας" (literally "of ''stadia'' myriads 400 and ) but with the additional note that in the Greek text the
grammatical agreement In linguistics, agreement or concord ( abbreviated ) occurs when a word changes form depending on the other words to which it relates. It is an instance of inflection, and usually involves making the value of some grammatical category (such as gende ...
is between ''myriads'' (not ''stadia'') on the one hand and both ''400'' and ' on the other, as in Greek, unlike English, all three (or all four if one were to include ''stadia'') words are
inflected In linguistic morphology, inflection (or inflexion) is a process of word formation in which a word is modified to express different grammatical categories such as tense, case, voice, aspect, person, number, gender, mood, animacy, and de ...
. This has been translated either as ''
stadia Stadia may refer to: * One of the plurals of stadium, along with "stadiums" * The plural of stadion, an ancient Greek unit of distance, which equals to 600 Greek feet (''podes''). * Stadia (Caria), a town of ancient Caria, now in Turkey * Stadia ...
'' (1903 translation by Edwin Hamilton Gifford), or as ''stadia'' (edition of , dated 1974–1991). Using the Greek stadium of 185 to 190 metres, the former translation comes to to , which is far too low, whereas the second translation comes to 148.7 to 152.8 million kilometres (accurate within 2%). Hipparchus also gave an estimate of the distance of Earth from the Sun, quoted by Pappus as equal to 490 Earth radii. According to the conjectural reconstructions of
Noel Swerdlow Noel Mark Swerdlow (9 September 1941 – 24 July 2021) was a professor emeritus of history, astronomy and astrophysics at the University of Chicago. He was a visiting professor at the California Institute of Technology. Career Swerdlow specia ...
and
G. J. Toomer Gerald James Toomer (born 23 November 1934) is a historian of astronomy and mathematics who has written numerous books and papers on ancient Greek and medieval Islamic astronomy. In particular, he translated Ptolemy's ''Almagest'' into English ...
, this was derived from his assumption of a "least perceptible" solar parallax of . A Chinese mathematical treatise, the '' Zhoubi Suanjing'' (c. 1st century BCE), shows how the distance to the Sun can be computed geometrically, using the different lengths of the noontime shadows observed at three places li apart and the assumption that Earth is flat. In the 2nd century CE, Ptolemy estimated the mean distance of the Sun as times
Earth's radius Earth radius (denoted as ''R''🜨 or R_E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly (equatorial radius, denot ...
. To determine this value, Ptolemy started by measuring the Moon's parallax, finding what amounted to a horizontal lunar parallax of 1° 26′, which was much too large. He then derived a maximum lunar distance of Earth radii. Because of cancelling errors in his parallax figure, his theory of the Moon's orbit, and other factors, this figure was approximately correct.van Helden 1985, pp. 16–19. He then measured the apparent sizes of the Sun and the Moon and concluded that the apparent diameter of the Sun was equal to the apparent diameter of the Moon at the Moon's greatest distance, and from records of lunar eclipses, he estimated this apparent diameter, as well as the apparent diameter of the shadow cone of Earth traversed by the Moon during a lunar eclipse. Given these data, the distance of the Sun from Earth can be trigonometrically computed to be Earth radii. This gives a ratio of solar to lunar distance of approximately 19, matching Aristarchus's figure. Although Ptolemy's procedure is theoretically workable, it is very sensitive to small changes in the data, so much so that changing a measurement by a few per cent can make the solar distance infinite. After Greek astronomy was transmitted to the medieval Islamic world, astronomers made some changes to Ptolemy's cosmological model, but did not greatly change his estimate of the Earth–Sun distance. For example, in his introduction to Ptolemaic astronomy, al-Farghānī gave a mean solar distance of Earth radii, whereas in his ''
zij A zij ( fa, زيج, zīj) is an Islamic astronomical book that tabulates parameters used for astronomical calculations of the positions of the Sun, Moon, stars, and planets. Etymology The name ''zij'' is derived from the Middle Persian term '' ...
'',
al-Battānī Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābiʾ al-Battānī ( ar, محمد بن جابر بن سنان البتاني) ( Latinized as Albategnius, Albategni or Albatenius) (c. 858 – 929) was an astron ...
used a mean solar distance of Earth radii. Subsequent astronomers, such as
al-Bīrūnī Abu Rayhan Muhammad ibn Ahmad al-Biruni (973 – after 1050) commonly known as al-Biruni, was a Khwarazmian Iranian in scholar and polymath during the Islamic Golden Age. He has been called variously the "founder of Indology", "Father of Co ...
, used similar values. Later in Europe,
Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulate ...
and Tycho Brahe also used comparable figures ( and Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century. Johannes Kepler was the first to realize that Ptolemy's estimate must be significantly too low (according to Kepler, at least by a factor of three) in his '' Rudolphine Tables'' (1627).
Kepler's laws of planetary motion In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbit ...
allowed astronomers to calculate the relative distances of the planets from the Sun, and rekindled interest in measuring the absolute value for Earth (which could then be applied to the other planets). The invention of the
telescope A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to observ ...
allowed far more accurate measurements of angles than is possible with the naked eye. Flemish astronomer
Godefroy Wendelin Godfried Wendelen or Govaert Wendelen, Latinized Godefridus Wendelinus, or sometimes Vendelinus and in French-language sources referred to as Godefroy Wendelin (6 June 1580 – 24 October 1667) was an astronomer and Catholic priest from Lièg ...
repeated Aristarchus’ measurements in 1635, and found that Ptolemy's value was too low by a factor of at least eleven. A somewhat more accurate estimate can be obtained by observing the transit of Venus. – provides an extended historical discussion of the transit of Venus method. By measuring the transit in two different locations, one can accurately calculate the parallax of Venus and from the relative distance of Earth and Venus from the Sun, the
solar parallax Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight and is measured by the angle or semi-angle of inclination between those two lines. Due to foreshortening, nearby object ...
(which cannot be measured directly due to the brightness of the Sun).
Jeremiah Horrocks Jeremiah Horrocks (16183 January 1641), sometimes given as Jeremiah Horrox (the Latinised version that he used on the Emmanuel College register and in his Latin manuscripts), – See footnote 1 was an English astronomer. He was the first person ...
had attempted to produce an estimate based on his observation of the 1639 transit (published in 1662), giving a solar parallax of , similar to Wendelin's figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by :A = \cot\alpha \approx 1\,\textrm/\alpha. The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of is equivalent to an Earth–Sun distance of Earth radii.
Christiaan Huygens Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor, who is regarded as one of the greatest scientists ...
believed that the distance was even greater: by comparing the apparent sizes of Venus and Mars, he estimated a value of about Earth radii, equivalent to a solar parallax of . Although Huygens' estimate is remarkably close to modern values, it is often discounted by historians of astronomy because of the many unproven (and incorrect) assumptions he had to make for his method to work; the accuracy of his value seems to be based more on luck than good measurement, with his various errors cancelling each other out.
Jean Richer Jean Richer (1630–1696) was a French astronomer and assistant (''élève astronome'') at the French Academy of Sciences, under the direction of Giovanni Domenico Cassini. Between 1671 and 1673 he performed experiments and carried out celestia ...
and Giovanni Domenico Cassini measured the parallax of Mars between Paris and
Cayenne Cayenne (; ; gcr, Kayenn) is the capital city of French Guiana, an overseas region and department of France located in South America. The city stands on a former island at the mouth of the Cayenne River on the Atlantic coast. The city's mot ...
in French Guiana when Mars was at its closest to Earth in 1672. They arrived at a figure for the solar parallax of , equivalent to an Earth–Sun distance of about Earth radii. They were also the first astronomers to have access to an accurate and reliable value for the radius of Earth, which had been measured by their colleague
Jean Picard Jean Picard (21 July 1620 – 12 July 1682) was a French astronomer and priest born in La Flèche, where he studied at the Jesuit Collège Royal Henry-Le-Grand. He is principally notable for his accurate measure of the size of the Earth, bas ...
in 1669 as ''
toise A toise (; symbol: T) is a unit of measure for length, area and volume originating in pre-revolutionary France. In North America, it was used in colonial French establishments in early New France, French Louisiana (''Louisiane''), Acadia (''Acad ...
s''. This same year saw another estimate for the astronomical unit by John Flamsteed, which accomplished it alone by measuring the martian
diurnal parallax Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight and is measured by the angle or semi-angle of inclination between those two lines. Due to foreshortening, nearby objects ...
. Another colleague, Ole Rømer, discovered the finite speed of light in 1676: the speed was so great that it was usually quoted as the time required for light to travel from the Sun to the Earth, or "light time per unit distance", a convention that is still followed by astronomers today. A better method for observing Venus transits was devised by James Gregory and published in his '' Optica Promata'' (1663). It was strongly advocated by
Edmond Halley Edmond (or Edmund) Halley (; – ) was an English astronomer, mathematician and physicist. He was the second Astronomer Royal in Britain, succeeding John Flamsteed in 1720. From an observatory he constructed on Saint Helena in 1676–77, Hal ...
and was applied to the transits of Venus observed in 1761 and 1769, and then again in 1874 and 1882. Transits of Venus occur in pairs, but less than one pair every century, and observing the transits in 1761 and 1769 was an unprecedented international scientific operation including observations by James Cook and Charles Green from Tahiti. Despite the Seven Years' War, dozens of astronomers were dispatched to observing points around the world at great expense and personal danger: several of them died in the endeavour. The various results were collated by
Jérôme Lalande Joseph Jérôme Lefrançois de Lalande (; 11 July 1732 – 4 April 1807) was a French astronomer, freemason and writer. Biography Lalande was born at Bourg-en-Bresse (now in the département of Ain) to Pierre Lefrançois and Marie‐Anne‐Gab ...
to give a figure for the solar parallax of . Karl Rudolph Powalky had made an estimate of in 1864. Another method involved determining the constant of aberration.
Simon Newcomb Simon Newcomb (March 12, 1835 – July 11, 1909) was a Canadian– American astronomer, applied mathematician, and autodidactic polymath. He served as Professor of Mathematics in the United States Navy and at Johns Hopkins University. Born in ...
gave great weight to this method when deriving his widely accepted value of for the solar parallax (close to the modern value of ), although Newcomb also used data from the transits of Venus. Newcomb also collaborated with A. A. Michelson to measure the speed of light with Earth-based equipment; combined with the constant of aberration (which is related to the light time per unit distance), this gave the first direct measurement of the Earth–Sun distance in kilometres. Newcomb's value for the solar parallax (and for the constant of aberration and the Gaussian gravitational constant) were incorporated into the first international system of
astronomical constant An astronomical constant is any of several physical constants used in astronomy. Formal sets of constants, along with recommended values, have been defined by the International Astronomical Union (IAU) several times: in 1964Resolution No.4 of thXIIt ...
s in 1896, which remained in place for the calculation of ephemerides until 1964. The name "astronomical unit" appears first to have been used in 1903. The discovery of the near-Earth asteroid
433 Eros Eros (minor planet designation: (433) Eros), provisional designation is a stony asteroid of the Amor group and the first discovered and second-largest near-Earth object with an elongated shape and a mean diameter of approximately . Vis ...
and its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement. Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931. Direct radar measurements of the distances to Venus and Mars became available in the early 1960s. Along with improved measurements of the speed of light, these showed that Newcomb's values for the solar parallax and the constant of aberration were inconsistent with one another.


Developments

The unit distance (the value of the astronomical unit in metres) can be expressed in terms of other astronomical constants: :A^3 = \frac, where is the
Newtonian constant of gravitation The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in th ...
, is the solar mass, is the numerical value of Gaussian gravitational constant and is the time period of one day. The Sun is constantly losing mass by radiating away energy, so the orbits of the planets are steadily expanding outward from the Sun. This has led to calls to abandon the astronomical unit as a unit of measurement. As the speed of light has an exact defined value in SI units and the Gaussian gravitational constant is fixed in the
astronomical system of units The astronomical system of units, formerly called the IAU (1976) System of Astronomical Constants, is a system of measurement developed for use in astronomy. It was adopted by the International Astronomical Union (IAU) in 1976 via Resolution No. ...
, measuring the light time per unit distance is exactly equivalent to measuring the product × in SI units. Hence, it is possible to construct ephemerides entirely in SI units, which is increasingly becoming the norm. A 2004 analysis of radiometric measurements in the inner Solar System suggested that the secular increase in the unit distance was much larger than can be accounted for by solar radiation, + metres per century. The measurements of the secular variations of the astronomical unit are not confirmed by other authors and are quite controversial. Furthermore, since 2010, the astronomical unit has not been estimated by the planetary ephemerides.


Examples

The following table contains some distances given in astronomical units. It includes some examples with distances that are normally not given in astronomical units, because they are either too short or far too long. Distances normally change over time. Examples are listed by increasing distance.


See also

*
Orders of magnitude (length) The following are examples of orders of magnitude for different lengths. __TOC__ Overview Detailed list To help compare different orders of magnitude, the following list describes various lengths between 1.6 \times 10^ metres and 10^ ...


References


Further reading

*


External links


The IAU and astronomical units


(HTML version of the IAU Style Manual)


Transit of Venus
{{DEFAULTSORT:Astronomical Unit Celestial mechanics Unit Units of length