Editing Astronomical unit

{{Short description|Mean distance between Earth and the Sun}}
{{About|the unit of length|constants|astronomical constant|units in astronomy|astronomical system of units|other uses of "AU"|AU (disambiguation){{!}}Au}}
{{Use dmy dates|date=September 2019}}
{{Use British English|date=October 2015}}
{{Infobox unit
| bgcolour =
| name = Astronomical unit
| image= File:Astronomical unit.png
| caption=The grey line indicates the Earth–Sun distance, which on average is about 1&nbsp;astronomical unit.
| standard = [[Astronomical system of units]]<br/>[[Non-SI units mentioned in the SI|(Accepted for use with the SI)]]
| quantity = [[length]]
| symbol = au or {{sc|au}} or AU
| units1 = [[metric system|metric]] ([[International_System_of_Units|SI]]) units
| inunits1 = {{val|1.495978707|e=11|ul=m}}
| units2 = [[Imperial units|imperial]]&nbsp;&&nbsp;[[United States customary units|US]]&nbsp;units
| inunits2 ={{val|9.2956|e=7|ul=mi}}
| units3 = [[Astronomical system of units|astronomical units]]
| inunits3 = {{val|4.8481|e=-6|ul=pc}}<br/>&nbsp;&nbsp;&nbsp;{{val|1.5813|e=-5|ul=ly}}<br/>&nbsp;&nbsp;&nbsp;{{val|215.03|ul=solar radius}}
}}

The '''astronomical unit''' (symbol: '''au'''<ref name="IAUresB2">{{cite conference |title=On the re-definition of the astronomical unit of length |id=Resolution&nbsp;B2 |conference=XXVIII&nbsp;General Assembly of International Astronomical Union |publisher=International Astronomical Union |place=Beijing, China |date=31 August 2012 | url = http://www.iau.org/static/resolutions/IAU2012_English.pdf|url-status=dead |archive-url=https://web.archive.org/web/20250305215811/http://www.iau.org/static/resolutions/IAU2012_English.pdf |archive-date=5 March 2025 |quote=... recommends ... 5. that the unique symbol "au" be used for the astronomical unit.}}</ref><ref name="mnras_style">{{cite web | url=http://www.oxfordjournals.org/our_journals/mnras/for_authors/#6.4%20Miscellaneous%20journal%20style | archive-url=https://web.archive.org/web/20121022064348/http://www.oxfordjournals.org/our_journals/mnras/for_authors/#6.4%20Miscellaneous%20journal%20style | url-status=dead | archive-date=22 October 2012 | title=Monthly Notices of the Royal Astronomical Society: Instructions for Authors | website=Oxford Journals | access-date=20 March 2015 | quote=The units of length/distance are Å, nm, μm, mm, cm, m, km, au, light-year, pc.}}</ref><ref name="AAS_style"/><ref>{{SIbrochure9th |page=145}}</ref> or '''AU''') is a [[unit of length]] defined to be exactly equal to {{val|149597870700|u=metres}}.<ref>{{cite conference |id=Resolution B2 |title=On the re-definition of the astronomical unit of length |publisher=International Astronomical Union |conference=XXVIII&nbsp;General Assembly of International Astronomical Union |place=Beijing |date=31 August 2012 |url=http://www.iau.org/static/resolutions/IAU2012_English.pdf |url-status=dead |archive-url=https://web.archive.org/web/20250305215811/http://www.iau.org/static/resolutions/IAU2012_English.pdf |archive-date=5 March 2025|quote=... recommends [adopted] that the astronomical unit be re-defined to be a conventional unit of length equal to exactly {{val|149,597,870,700}} metres, in agreement with the value adopted in IAU&nbsp;2009 Resolution&nbsp;B2}}</ref> Historically, the astronomical unit was conceived as the average Earth-Sun distance (the average of Earth's [[aphelion]] and [[perihelion]]), before its modern redefinition in 2012.

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]].<ref name=au_parsec>{{cite journal |author1=Luque, B. |author2=Ballesteros, F.J. |year=2019 |title=Title: To the Sun and beyond |journal=[[Nature Physics]] |volume=15 |issue=12 |page=1302 |doi=10.1038/s41567-019-0685-3 |doi-access=free|bibcode=2019NatPh..15.1302L }}</ref> One au is approximately equivalent to 499 [[light-second]]s.

== 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]]&nbsp;(IAU) had used the symbol ''A'' to denote a length equal to the astronomical unit.<ref name="IAU76"/> In the astronomical literature, the symbol AU is common. In 2006, the [[International Bureau of Weights and Measures]] (BIPM) had recommended ua as the symbol for the unit, from the French "unité astronomique".<ref name="Bureau International des Poids et Mesures 2006 126">{{citation |author=Bureau International des Poids et Mesures |author-link=Bureau International des Poids et Mesures |date=2006 |title=The International System of Units (SI) |edition=8th |publisher=Organisation Intergouvernementale de la Convention du Mètre |page=126 |url=http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf |archive-date=2022-10-09 |url-status=dead}}</ref> In the non-normative Annex&nbsp;C to [[ISO 80000-3]]:2006 (later withdrawn), the symbol of the astronomical unit was also ua.

In 2012, the IAU, noting "that various symbols are presently in use for the astronomical unit", recommended the use of the symbol "au".<ref name="IAUresB2"/> The [[scientific journal]]s published by the [[American Astronomical Society]] and the [[Royal Astronomical Society]] subsequently adopted this symbol.<ref name="AAS_style">{{cite web |title=Manuscript Preparation: AJ & ApJ Author Instructions |website=American Astronomical Society |url=http://aas.org/authors/manuscript-preparation-aj-apj-author-instructions#_Toc2.2 |access-date=29 October 2016 |url-status=dead |archive-url=https://web.archive.org/web/20160221121728/http://aas.org/authors/manuscript-preparation-aj-apj-author-instructions#_Toc2.2 |archive-date=21 February 2016 |quote=Use standard abbreviations for ... natural units (e.g., au, pc, cm).}}</ref><ref>{{cite web |title=Instructions to Authors |website=Monthly Notices of the Royal Astronomical Society |publisher=Oxford University Press |url=https://academic.oup.com/mnras/pages/General_Instructions |access-date=5 November 2020 |quote=The units of length/distance are Å, nm, µm, mm, cm, m, km, au, light-year, pc.}}</ref> In the 2014 revision and 2019 edition of the SI Brochure, the BIPM used the unit symbol "au".<ref name=SI_Brochure2012>{{cite web |orig-year=2006 |year=2014 |title=The International System of Units (SI) |edition=8th |publisher=BIPM |series=SI Brochure |url=http://www.bipm.org/en/publications/si-brochure/table6.html |access-date=3 January 2015}}</ref><ref name=SI_Brochure2019>{{cite web |url=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf |archive-date=2022-10-09 |url-status=live |series=SI Brochure |title=The International System of Units (SI) |edition=9th |year=2019 |publisher=BIPM |page = 145 |access-date=1 July 2019}}</ref> ISO&nbsp;80000-3:2019, which replaces ISO&nbsp;80000-3:2006, does not mention the astronomical unit.<ref>{{cite web |title=ISO 80000-3:2019 |date=19 May 2020 |url=https://www.iso.org/standard/64974.html |publisher=[[International Organization for Standardization]] |access-date=2020-07-03}}</ref><ref>{{cite web |id=ISO&nbsp;80000-3:2019(en) |series=Quantities and units |title=Part&nbsp;3: Space and time |url=https://www.iso.org/obp/ui/#iso:std:iso:80000:-3:ed-2:v1:en |publisher=[[International Organization for Standardization]] |access-date=2020-07-03}}</ref>

== Development of unit definition ==
{{See also|Earth's orbit}}

[[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]]. 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 [[Albert Einstein|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]], 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]]. [[NASA]]{{'s}} [[Jet Propulsion Laboratory]] HORIZONS System provides one of several ephemeris computation services.<ref name=Horizons>{{cite web |title=HORIZONS System |url=http://ssd.jpl.nasa.gov/?horizons |work=Solar system dynamics |date=4 January 2005 |access-date=16 January 2012 |publisher=NASA: Jet Propulsion Laboratory}}</ref>

In 1976, to establish a more precise measure for the astronomical unit, the IAU formally [[IAU (1976) System of Astronomical Constants|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]] (''k'') takes the value {{val|0.01720209895}} when the units of measurement are the astronomical units of length, mass and time".<ref name="IAU76">{{cite conference |title=item&nbsp;12: Unit distance |series=IAU (1976) System of Astronomical Constants |author=Commission&nbsp;4: Ephemerides/Ephémérides |id=Commission&nbsp;4, part&nbsp;III, Recommendation&nbsp;1, item&nbsp;12 <!-- Resolution No.&nbsp;10 --> |url=http://www.iau.org/static/resolutions/IAU1976_French.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.iau.org/static/resolutions/IAU1976_French.pdf |archive-date=2022-10-09 |url-status=dead |conference=XVIth General Assembly of the International Astronomical Union |place=Grenoble, FR |year=1976}}</ref><ref name="Trümper">{{cite book |title=Astronomy, astrophysics, and cosmology – Volume VI/4B ''Solar System'' |chapter-url=https://books.google.com/books?id=wgydrPWl6XkC&pg=RA1-PA4 |page=4 |date=2009 |author1=Hussmann, H. |author2=Sohl, F. |author3=Oberst, J. |chapter=§&nbsp;4.2.2.1.3: Astronomical units |editor=Trümper, Joachim E. |isbn=978-3-540-88054-7 |publisher=Springer}}</ref><ref name= Fairbridge>{{cite book |title=Encyclopedia of planetary sciences |author=Williams Gareth V. |editor1=Shirley, James H. |editor2=Fairbridge, Rhodes Whitmore |chapter=Astronomical unit |chapter-url=https://books.google.com/books?id=dw2GadaPkYcC&pg=PA48 |page=48 |isbn=978-0-412-06951-2 |date=1997 |publisher=Springer}}</ref> 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]] of {{val|0.01720209895|u=radians per day}}";<ref name=SIbrochure>{{SIbrochure8th|page=126}}</ref> or alternatively that length for which the [[standard gravitational parameter|heliocentric gravitational constant]] (the product ''G''{{Solar mass}}) is equal to ({{val|0.01720209895}})<sup>2</sup>&nbsp;au<sup>3</sup>/d<sup>2</sup>, when the length is used to describe the positions of objects in the Solar System.

Subsequent explorations of the Solar System by [[space probe]]s made it possible to obtain precise measurements of the relative positions of the [[Solar System#Inner planets|inner planets]] and other objects by means of [[radar]] and [[telemetry]]. As with all radar measurements, these rely on measuring the time taken for [[photons]] 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]]&nbsp;(TDB) leads to a value for the speed of light in astronomical units per day (of {{val|86400|u=s}}). By 2009, the IAU had updated its standard measures to reflect improvements, and calculated the speed of light at {{val|173.1446326847|(69)|u=au/d}} (TDB).<ref>{{cite book |chapter-url=http://asa.usno.navy.mil/static/files/2009/Astronomical_Constants_2009.pdf |chapter=Selected Astronomical Constants |title=The Astronomical Almanac Online |publisher=[[USNO]]–[[UKHO]] |page=K6 |date=2009 |archive-url=https://web.archive.org/web/20140726132053/http://asa.usno.navy.mil/static/files/2009/Astronomical_Constants_2009.pdf|archive-date=26 July 2014}}</ref>

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&nbsp;/&nbsp;{{val|299792458|u=s}}. 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''<sub>0</sub> = {{val|299792458|u=m/s}}, a standard also adopted by the [[IERS]] numerical standards.<ref name="IERS">{{cite report |url=http://tai.bipm.org/iers/conv2010/chapter1/tn36_c1.pdf |title=Table 1.1: IERS numerical standards |date=2010 |publisher=[[International Earth Rotation and Reference Systems Service]] |archive-url=https://ghostarchive.org/archive/20221009/http://tai.bipm.org/iers/conv2010/chapter1/tn36_c1.pdf |archive-date=2022-10-09 |url-status=live |work=IERS technical note no. 36: General definitions and numerical standards |editor=Petit, Gérard |editor2=Luzum, Brian}} For complete document see {{cite report |url=http://www.iers.org/nn_11216/IERS/EN/Publications/TechnicalNotes/tn36.html |title=IERS Conventions (2010): IERS technical note no. 36 |date=2010 |publisher=International Earth Rotation and Reference Systems Service |isbn=978-3-89888-989-6 |access-date=16 January 2012 |archive-url=https://web.archive.org/web/20190630104818/https://www.iers.org/nn_11216/IERS/EN/Publications/TechnicalNotes/tn36.html |archive-date=30 June 2019 |url-status=dead |editor=Gérard Petit |editor2=Brian Luzum}}</ref> From this definition and the 2009 IAU standard, the time for light to traverse an astronomical unit is found to be ''τ''<sub>A</sub> = {{val|499.0047838061|0.00000001|u=s}}, which is slightly more than 8&nbsp;minutes 19&nbsp;seconds. By multiplication, the best IAU 2009 estimate was ''A''&nbsp;= ''c''<sub>0</sub>''τ''<sub>A</sub>&nbsp;= {{val|149597870700|3|u=m}},<ref name=Captaine>{{cite report |last1=Capitaine |first1=Nicole |last2=Klioner |first2=Sergei |last3=McCarthy |first3=Dennis | author3-link = Dennis McCarthy (scientist) |title=IAU Joint Discussion&nbsp;7: Space-time reference systems for future research at IAU General Assembly – The re-definition of the astronomical unit of length: Reasons and consequences |volume=7 |pages=40 |place=Beijing, China |date=2012 |url=http://referencesystems.info/uploads/3/0/3/0/3030024/jd7_5-06.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://referencesystems.info/uploads/3/0/3/0/3030024/jd7_5-06.pdf |archive-date=2022-10-09 |url-status=live |access-date=16 May 2013 |bibcode=2012IAUJD...7E..40C}}</ref> based on a comparison of Jet Propulsion Laboratory and [[Russian Academy of Sciences|IAA–RAS]] ephemerides.<ref name="IAU">{{cite report |title=IAU WG on NSFA current best estimates |url=http://maia.usno.navy.mil/NSFA/CBE.html |access-date=25 September 2009 |url-status=dead |archive-url=https://web.archive.org/web/20091208011235/http://maia.usno.navy.mil/NSFA/CBE.html |archive-date=8 December 2009 }}</ref><ref name="Pitjeva09">{{cite journal |last1=Pitjeva |first1=E.V. |author-link1=Elena V. Pitjeva |last2=Standish |first2=E.M. |author-link2=E. Myles Standish |date=2009 |title=Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the Astronomical Unit |journal=[[Celestial Mechanics and Dynamical Astronomy]] |volume=103 |issue=4 |pages=365–72 |doi=10.1007/s10569-009-9203-8 |bibcode=2009CeMDA.103..365P |s2cid=121374703 |url=https://zenodo.org/record/1000691 }}</ref><ref>{{cite news |url=http://www.astronomy2009.com.br/10.pdf |newspaper=Estrella d'Alva |date=14 August 2009 |page=1 |title=The final session of the [IAU] General Assembly |url-status=dead |archive-url=https://web.archive.org/web/20110706151452/http://www.astronomy2009.com.br/10.pdf |archive-date=6 July 2011 }}</ref>

In 2006, the BIPM reported a value of the astronomical unit as {{val|1.49597870691|(6)|e=11|u=m}}.<ref name="Bureau International des Poids et Mesures 2006 126"/> In the 2014 revision of the SI&nbsp;Brochure, the BIPM recognised the IAU's 2012 redefinition of the astronomical unit as {{val|149597870700|u=m}}.<ref name=SI_Brochure2012/>

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 {{val|149597870700|u=m}}).<ref name=Captaine/><ref name=Nature2012>{{cite news |url=http://www.nature.com/news/the-astronomical-unit-gets-fixed-1.11416 |title=The astronomical unit gets fixed: Earth–Sun distance changes from slippery equation to single number |journal=Nature |first=Geoff |last=Brumfiel |date=14 September 2012 |access-date=14 September 2012|doi=10.1038/nature.2012.11416 |s2cid=123424704 }}</ref> The new definition recognizes as a consequence that the astronomical unit has reduced importance, limited in use to a convenience in some applications.<ref name=Captaine/>

:{| style="border-spacing:0"
|-
|rowspan=7 style="vertical-align:top; padding-right:0"|1 astronomical unit&nbsp;
|= {{val|149597870700}} [[metre]]s (by definition)
|-
|= {{convert|1|au|km|disp=out|lk=on|abbr=off|sigfig=10|comma=5}} (exactly)
|-
|≈ {{convert|1|au|mi|disp=out|lk=on|abbr=off|sigfig=12|comma=5}}
|-
|≈ {{convert|1|au/s|ly/year|disp=number|sigfig=12|comma=gaps}} [[light-second]]s
|-
|≈ {{convert|1|au|ly|disp=out|lk=on|abbr=off|sigfig=12|comma=gaps}}
|-
|≈ {{convert|1|au|pc|disp=out|lk=on|abbr=off|sigfig=12|comma=gaps}}
|}

This definition makes the speed of light, defined as exactly {{val|299792458|u=m/s}}, equal to exactly {{val|299792458}}&nbsp;×&nbsp;{{val|86400}}&nbsp;÷&nbsp;{{val|149597870700}} or about {{val|173.144632674240|u=au/d}}, some 60 parts per [[Orders of magnitude (numbers)#1012|trillion]] 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]], {{Solar mass}}. Neither ''G'' nor {{Solar mass}} 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]] 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 {{val|0.9832898912}} and {{val|1.0167103335|u=au}}) 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]]. Indeed, the [[International Committee for Weights and Measures]] (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".<ref>{{SIbrochure8th|pages=166–67}}</ref> As such, a distance within the Solar System without specifying the [[frame of reference]] for the measurement is problematic. The 1976 definition of the astronomical unit was incomplete because it did not specify the frame of reference in which to apply the measurement, but proved practical for the calculation of ephemerides: a fuller definition that is consistent with general relativity was proposed,<ref name="Huang">{{cite journal |author=Huang, T.-Y. |author2=Han, C.-H. |author3=Yi, Z.-H. |author4=Xu, B.-X. |date=1995 |title=What is the astronomical unit of length? |bibcode=1995A&A...298..629H |journal=[[Astronomy and Astrophysics]] |volume=298 |pages=629–33 }}</ref> and "vigorous debate" ensued<ref name="Dodd">{{cite book |author=Dodd |first=Richard |title=Using SI Units in Astronomy |date=2011 |publisher=Cambridge University Press |isbn=978-0-521-76917-4 |page=76 |chapter=§&nbsp;6.2.3: Astronomical unit: ''Definition of the astronomical unit, future versions'' |chapter-url=https://books.google.com/books?id=UC_1_804BXgC&pg=PA76}} and also p. 91, ''Summary and recommendations''.</ref> until August 2012 when the IAU adopted the current definition of 1 astronomical unit = {{val|149597870700}} [[metre]]s.

The astronomical unit is typically used for [[stellar system]] scale distances, such as the size of a protostellar disk or the [[heliocentric distance]] of an asteroid, whereas other units are used for [[cosmic distance ladder|other distances in astronomy]]. The astronomical unit is too small to be convenient for interstellar distances, where the [[parsec]] and [[light-year]] are widely used. The parsec (parallax [[Minute and second of arc|arcsecond]]) is defined in terms of the astronomical unit, being the distance of an object with a parallax of {{val|1|u=arcsecond}}. The light-year is often used in popular works, but is not an approved non-SI unit and is rarely used by professional astronomers.<ref name="Dodd1">{{cite book |author=Dodd |first=Richard |title=Using SI Units in Astronomy |date=2011 |publisher=Cambridge University Press |isbn=978-0-521-76917-4 |page=82 |chapter=§&nbsp;6.2.8: Light-year |chapter-url=https://books.google.com/books?id=UC_1_804BXgC&pg=PA82}}</ref>

When simulating a [[numerical model of the Solar System]], the astronomical unit provides an appropriate scale that minimizes ([[arithmetic overflow|overflow]], [[arithmetic underflow|underflow]] and [[truncation]]) errors in [[floating point]] calculations.

== History ==
The book ''[[On the Sizes and Distances (Aristarchus)|On the Sizes and Distances of the Sun and Moon]]'', which is ascribed to [[Aristarchus of Samos|Aristarchus]], says the distance to the Sun is 18 to 20 times the [[Lunar distance (astronomy)|distance to the Moon]], whereas the true ratio is about {{val|389.174}}. The latter estimate was based on the angle between the [[Lunar phase|half-moon]] and the Sun, which he estimated as {{val|87|u=deg}} (the true value being close to {{val|89.853|u=deg}}). Depending on the distance that Albert van Helden assumes Aristarchus used for the distance to the Moon, his calculated distance to the Sun would fall between {{val|380}} and {{val|1520}} Earth radii.<ref>{{cite book |last=van&nbsp;Helden |first=Albert |title=Measuring the Universe: Cosmic dimensions from Aristarchus to Halley |place=Chicago |publisher=University of Chicago Press |date=1985 |pages=5–9 |isbn=978-0-226-84882-2}}</ref>

[[Hipparchus]] gave an estimate of the distance of Earth from the Sun, quoted by [[Pappus of Alexandria|Pappus]] as equal to 490 Earth radii. According to the conjectural reconstructions of [[Noel Swerdlow]] and [[G. J. Toomer]], this was derived from his assumption of a "least perceptible" solar parallax of {{val|7|ul=arcminute}}.<ref>{{cite journal |doi=10.1007/BF00329826 |title=Hipparchus on the distances of the sun and moon |journal=Archive for History of Exact Sciences |volume=14 |issue=2 |pages=126–42 |last=Toomer |first=G.J. |date=1974|bibcode=1974AHES...14..126T |s2cid=122093782 }}</ref>

A Chinese mathematical treatise, the ''[[Zhoubi Suanjing]]'' ({{circa|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 {{val|1000}} [[Li (unit)|''li'']] apart and the assumption that Earth is flat.<ref>{{cite book |first=G. E. R. |last=Lloyd |author-link=G. E. R. Lloyd |title=Adversaries and Authorities: Investigations into Ancient Greek and Chinese Science |publisher=Cambridge University Press |date=1996 |pages=59–60 |isbn=978-0-521-55695-8}}</ref>

According to [[Eusebius]] in the ''[[Praeparatio evangelica]]'' (Book XV, Chapter 53), [[Eratosthenes]] found the distance to the Sun to be "σταδιων μυριαδας τετρακοσιας και οκτωκισμυριας" (literally ''myriads ten hundreds and eighty thousands of stadia'', where in the Greek text the numerals ''[[myriad]]s'', ''ten hundreds'' and ''eighty thousands'' are all [[accusative]] plural, while ''stadia'' is the [[genitive]] plural of ''[[stadion (unit of length)|stadion]]''.) This has been translated either as {{val|4080000}} ({{nowrap|1== ({{val|10000}} × 400) + {{val|80000}}}}) stadia (1903 translation by [[Edwin Hamilton Gifford]]), or as {{val|804000000}} ({{nowrap|1== {{val|10000}} × (400 + {{val|80000}})}}) stadia (edition of [[Édouard des Places]], dated 1974–1991). Using the Greek stadium of 185 to 190 metres,<ref name="Engels1985">{{cite journal |title=The Length of Eratosthenes' Stade |journal=The American Journal of Philology |last=Engels |first=Donald |volume=106 |issue=3 |pages=298–311 |date=1985 |doi=10.2307/295030 |jstor=295030}}</ref><ref name="Gulbekian1987">{{cite journal |url=https://link.springer.com/article/10.1007/BF00417008 |title=The origin and value of the stadion unit used by Eratosthenes in the third century B.C. |journal=Archive for History of Exact Sciences |first=Edward |last=Gulbekian |volume=37 |issue=4 |pages=359–63 |date=1987 |doi=10.1007/BF00417008|s2cid=115314003 }}</ref> the former translation comes to {{val|754800|u=km}} to {{val|775200|u=km}}<!--Depends on if 185 m or 190 m is used-->, which is far too low, whereas the second translation comes to 148.7 to 152.8&nbsp;billion metres (accurate within 2%).<ref>{{cite journal |url=http://www.dioi.org/vols/we0.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.dioi.org/vols/we0.pdf |archive-date=2022-10-09 |url-status=live |title=Eratosthenes' Too-Big Earth & Too-Tiny Universe |journal=DIO |first=D. |last=Rawlins |date=March 2008 |volume=14 |pages=3–12|bibcode=2008DIO....14....3R }}</ref> 

{|class="wikitable"
! rowspan=2 | Distance to the Sun<br/>estimated by
! colspan=2 | Estimate
! rowspan=2 | In au
! rowspan=2 |Percentage error
|-
! [[Solar parallax|Solar<br/>parallax]]
! [[Earth radii|Earth<br/>radii]]
|-
| [[Aristarchus of Samos|Aristarchus]] {{small|(3rd century BCE)}} {{small|''(in [[On the Sizes and Distances of the Sun and Moon|On Sizes]])''}}&nbsp;&nbsp;
| align=left | {{val|13|u=arcmin}} {{val|24|u=arcsec}}–{{val|7|u=arcmin}} {{val|12|u=arcsec}}
| align=right | {{val|256.5}}–{{val|477.8}}
| align=center | {{val|0.011}}–{{val|0.020}}
| −98.9% to −98%
|-
| [[Archimedes]] {{small|(3rd century BCE)}} {{small|''(in [[The Sand Reckoner]])''}}
| align=left | {{val|21|u=arcsec}}
| align=right | {{val|10000}}
| align=center | {{val|0.426}}
| −57.4%
|-
| [[Hipparchus]] {{small|(2nd century BCE)}}
| align=left | {{val|7|u=arcmin}}
| align=right | {{val|490}}
| align=center | {{val|0.021}}
| −97.9%
|-
| [[Posidonius]] {{small|(1st century BCE)}} {{small|''(quoted by coeval [[Cleomedes]])''}}
| align=left | {{val|21|u=arcsec}}
| align=right | {{val|10000}}
| align=center | {{val|0.426}}
| −57.4%
|-
| [[Ptolemy]] {{small|(2nd century)}}
| align=left | 2′ 50″
| align=right | {{val|1210}}
| align=center | {{val|0.052}}
| −94.8%
|-
| [[Godefroy Wendelin]] {{small|(1635)}}
| align=left | {{val|15|u=arcsec}}
| align=right | {{val|14000}}
| align=center | {{val|0.597}}
| −40.3%
|-
| [[Jeremiah Horrocks]] {{small|(1639)}}
| align=left | {{val|15|u=arcsec}}
| align=right | {{val|14000}}
| align=center | {{val|0.597}}
| −40.3%
|-
| [[Christiaan Huygens]] {{small|(1659)}}
| align=left | {{val|8.2|u=arcsec}}
| align=right | {{val|25086}}<ref name="Goldstein1">{{cite journal |bibcode = 1985Obs...105...32G|title = Christiaan Huygens' measurement of the distance to the Sun|journal = The Observatory|volume = 105|pages = 32|last1 = Goldstein|first1 = S. J.|year = 1985}}</ref>
| align=center | {{val|1.068}}
| +6.8%
|-
| [[Giovanni Domenico Cassini|Cassini]] & [[Jean Richer|Richer]] {{small|(1672)}}
| align=left | {{val|9.5|u=arcsec}}
| align=right | {{val|21700}}
| align=center | {{val|0.925}}
| −7.5%
|-
| [[John Flamsteed|Flamsteed]] {{small|(1672)}}
| align=left | {{val|9.5|u=arcsec}}
| align=right | {{val|21700}}
| align=center | {{val|0.925}}
| −7.5%
|-
| [[Jérôme Lalande]] {{small|(1771)}}
| align=left | {{val|8.6|u=arcsec}}
| align=right | {{val|24000}}
| align=center | {{val|1.023}}
| +2.3%
|-
| [[Simon Newcomb]] {{small|(1895)}}
| align=left | {{val|8.80|u=arcsec}}
| align=right | {{val|23440}}
| align=center | {{val|0.9994}}
| −0.06%
|-
| [[Arthur Robert Hinks|Arthur Hinks]] {{small|(1909)}}
| align=left | {{val|8.807|u=arcsec}}
| align=right | {{val|23420}}
| align=center | {{val|0.9985}}
| −0.15%
|-
| [[Harold Spencer Jones|H. Spencer Jones]] {{small|(1941)}}
| align=left | {{val|8.790|u=arcsec}}
| align=right | {{val|23466}}
| align=center | {{val|1.0005}}
| +0.05%
|-
| Modern [[astronomy]]
| align=left| {{val|8.794143|u=arcsec}}
| align=right | {{val|23455}}
| align=center | {{val|1.0000}}
|}

In the 2nd century CE, [[Ptolemy]] estimated the mean distance of the Sun as {{val|1210}} times [[Earth's radius]].<ref>{{cite journal |first=Bernard R. |last=Goldstein |title=The Arabic version of Ptolemy's ''planetary hypotheses'' |journal=Trans. Am. Philos. Soc. |volume=57 |issue=4 |date=1967 |pages=9–12 |doi=10.2307/1006040 |jstor=1006040}}</ref><ref>{{cite book |last=van Helden |first=Albert |title=Measuring the Universe: Cosmic Dimensions from Aristarchus to Halley |place=Chicago |publisher=University of Chicago Press |date=1985 |pages=15–27 |isbn=978-0-226-84882-2}}</ref> To determine this value, Ptolemy started by measuring the Moon's parallax, finding what amounted to a horizontal lunar parallax of 1°&nbsp;26′, which was much too large. He then derived a maximum lunar distance of {{sfrac|64|1|6}} 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.<ref name=vh1619>van Helden 1985, pp. 16–19.</ref><ref>''Ptolemy's Almagest'', translated and annotated by G.&nbsp;J. Toomer, London: Duckworth, 1984, p.&nbsp;251. {{ISBN|0-7156-1588-2}}.</ref> 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 {{val|1210}} 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.<ref name=vh1619/>

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, [[Ahmad ibn Muhammad ibn Kathir al-Farghani|al-Farghānī]] gave a mean solar distance of {{val|1170}} Earth radii, whereas in his ''[[zij]]'', [[Al-Battani|al-Battānī]] used a mean solar distance of {{val|1108}} Earth radii. Subsequent astronomers, such as [[Al-Biruni|al-Bīrūnī]], used similar values.<ref>van Helden 1985, pp. 29–33.</ref> Later in Europe, [[Nicolaus Copernicus|Copernicus]] and [[Tycho Brahe]] also used comparable figures ({{val|1142}} and {{val|1150}} Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century.<ref>van Helden 1985, pp. 41–53.</ref>

[[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]] 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]] allowed far more accurate measurements of angles than is possible with the naked eye. Flemish astronomer [[Godefroy Wendelin]] 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]].<ref name=Bell>
{{cite magazine
 |first=Trudy E. |last=Bell
 |date=Summer 2004
 |title=Quest for the astronomical unit
 |magazine=The Bent of Tau Beta Pi
 |page=20
 |url=http://www.tbp.org/pages/publications/bent/features/su04bell.pdf
 |access-date=16 January 2012 |url-status=dead
 |archive-url=https://web.archive.org/web/20120324164801/http://www.tbp.org/pages/publications/bent/features/su04bell.pdf
 |archive-date=24 March 2012
 |postscript=none
}} – provides an extended historical discussion of the [[transit of Venus]] method.</ref> 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 [[Parallax#Solar parallax|solar parallax]] {{mvar|α}} (which cannot be measured directly due to the brightness of the Sun<ref name="Weaver">{{cite report |last=Weaver |first=Harold F. |title=The Solar Parallax |bibcode=1943ASPL....4..144W |date=March 1943 |journal=Astronomical Society of the Pacific Leaflets |volume=4 |issue=169 |pages=144–51}}</ref>). [[Jeremiah Horrocks]] had attempted to produce an estimate based on his observation of the [[1639 transit of Venus|1639 transit]] (published in 1662), giving a solar parallax of {{val|15|ul=arcsecond}}, similar to Wendelin's figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by
: <math>A = \cot\alpha \approx 1\,\textrm{radian}/\alpha.</math>

The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of {{val|15|u=arcsecond}} is equivalent to an Earth–Sun distance of {{val|13750}} Earth radii.

[[Christiaan Huygens]] believed that the distance was even greater: by comparing the apparent sizes of Venus and [[Mars]], he estimated a value of about {{val|24000}} Earth radii,<ref name="Goldstein1"/> equivalent to a solar parallax of {{val|8.6|u=arcsecond}}. 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.

[[File:Venustransit 2004-06-08 07-44.jpg|thumb|right|Transits of Venus across the face of the Sun were, for a long time, the best method of measuring the astronomical unit, despite the difficulties (here, the so-called "[[black drop effect]]") and the rarity of observations.]]
[[Jean Richer]] and [[Giovanni Domenico Cassini]] measured the parallax of Mars between [[Paris]] and [[Cayenne]] in [[French Guiana]] when Mars was at its closest to Earth in 1672. They arrived at a figure for the solar parallax of {{val|9.5|u=arcsecond}}, equivalent to an Earth–Sun distance of about {{val|22000}} 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]] in 1669 as {{val|3269000}} ''[[toise]]s''. This same year saw another estimate for the astronomical unit by [[John Flamsteed]], which accomplished it alone by measuring the [[Mars|martian]] [[diurnal parallax]].<ref>Van Helden, A. (2010). Measuring the universe: cosmic dimensions from Aristarchus to Halley. University of Chicago Press. Ch. 12.</ref> 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 (astronomer and mathematician)|James Gregory]] and published in his ''[[Optica Promata]]'' (1663). It was strongly advocated by [[Edmond Halley]]<ref>{{cite journal |last=Halley |first=E. |author-link=Edmond Halley |date=1716 |title=A new method of determining the parallax of the Sun, or his distance from the Earth |journal=Philosophical Transactions of the Royal Society |volume=29 |issue=338–350 |pages=454–64 |doi=10.1098/rstl.1714.0056 |s2cid=186214749 |doi-access=free }}</ref> 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.<ref>{{cite web |last=Pogge |first=Richard |title=How far to the Sun? The Venus transits of 1761 & 1769 |url=http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit4/venussun.html |date=May 2004 |publisher=Ohio State University |department=Astronomy |access-date=15 November 2009}}</ref> The various results were collated by [[Jérôme Lalande]] to give a figure for the solar parallax of {{val|8.6|u=arcsecond}}. [[Karl Rudolph Powalky]] had made an estimate of {{val|8.83|u=arcsecond}} in 1864.<ref>{{cite journal|last=Newcomb|first=Simon|date=1871|title=The Solar Parallax|url=http://www.nature.com/articles/005060a0|journal=Nature|language=en|volume=5|issue=108|pages=60–61|doi=10.1038/005060a0|bibcode=1871Natur...5...60N|s2cid=4001378|issn=0028-0836}}</ref>

{| class="wikitable" style="float:right; margin:0 0 0 0.5em;"
|-
! Date
! Method
! ''A''/Gm
! Uncertainty
|-
| 1895
| aberration
| {{val|149.25}}
| {{val|0.12}}
|-
| 1941
| parallax
| {{val|149.674}}
| {{val|0.016}}
|-
| 1964
| radar
| {{val|149.5981}}
| {{val|0.001}}
|-
| 1976
| telemetry
| {{val|149.597870}}
| {{val|0.000001}}
|-
| 2009
| telemetry
| {{val|149.597870700}}
| {{val|0.000000003}}
|}
Another method involved determining the constant of [[aberration of light|aberration]]. [[Simon Newcomb]] gave great weight to this method when deriving his widely accepted value of {{val|8.80|u=arcsecond}} for the solar parallax (close to the modern value of {{val|8.794143|u=arcsec}}), 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 metres. 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]]s in 1896,<ref>Conférence internationale des étoiles fondamentales, Paris, 18–21 May 1896</ref> which remained in place for the calculation of ephemerides until 1964.<ref>{{cite conference |title=On the system of astronomical constants |conference= XIIth General Assembly of the International Astronomical Union |publisher=International Astronomical Union |place=Hamburg, Germany |date=1964 | url =http://www.iau.org/static/resolutions/IAU1964_French.pdf|url-status=dead |archive-url=https://web.archive.org/web/20250311181040/https://www.iau.org/static/resolutions/IAU1964_French.pdf |archive-date=11 March 2025}}</ref> The name "astronomical unit" appears first to have been used in 1903.<ref>[http://www.merriam-webster.com/dictionary/astronomical%20unit "astronomical unit"], ''Merriam-Webster's Online Dictionary''</ref>{{failed verification|date=June 2019}}

The discovery of the [[near-Earth asteroid]] [[433 Eros]] and its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement.<ref>{{cite journal |last=Hinks |first=Arthur R. |author-link=Arthur Robert Hinks |title=Solar parallax papers No. 7: The general solution from the photographic right ascensions of Eros, at the opposition of 1900 |journal=Monthly Notices of the Royal Astronomical Society |volume=69 |issue=7 |pages=544–67 |date=1909 |bibcode=1909MNRAS..69..544H |doi=10.1093/mnras/69.7.544|url=https://zenodo.org/record/1431881 |doi-access=free }}</ref> Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931.<ref name="Weaver"/><ref>{{cite journal |last=Spencer Jones |first=H. |author-link=Harold Spencer Jones |title=The solar parallax and the mass of the Moon from observations of Eros at the opposition of 1931 |journal=Mem. R. Astron. Soc. |volume=66 |date=1941 |pages=11–66 |issn=0369-1829 }}</ref>

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.<ref>{{cite journal |last=Mikhailov |first=A. A. |date=1964 |title=The Constant of Aberration and the Solar Parallax |bibcode=1964SvA.....7..737M |journal=Sov. Astron. |volume=7 |issue=6 |pages=737–39 }}</ref>

== Developments ==

[[File:Stellarparallax parsec1.svg|thumb|The ''astronomical unit'' is used as the baseline of the triangle to measure [[stellar parallax]]es (distances in the image are not to scale)]]

The unit distance {{mvar|A}} (the value of the astronomical unit in metres) can be expressed in terms of other astronomical constants:
:<math>A^3 = \frac{G M_\odot D^2}{k^2},</math>
where {{mvar|G}} is the [[Newtonian constant of gravitation]], {{Solar mass}} is the solar mass, {{mvar|k}} is the numerical value of Gaussian gravitational constant and {{mvar|D}} is the time period of one day.<ref name="IAUresB2"/>
The Sun is constantly losing mass by radiating away energy,<ref>{{cite journal |author=Noerdlinger, Peter D. |arxiv=0801.3807 |title=Solar Mass Loss, the Astronomical Unit, and the Scale of the Solar System |journal=[[Celestial Mechanics and Dynamical Astronomy]] |bibcode=2008arXiv0801.3807N |volume=0801 |date=2008 |pages=3807}}</ref> 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.<ref>{{cite magazine |url=https://www.newscientist.com/article/dn13286-astronomical-unit-may-need-to-be-redefined.html |title=AU may need to be redefined |magazine=[[New Scientist]] |date=6 February 2008}}</ref>

As the speed of light has an exact defined value in SI units and the Gaussian gravitational constant {{mvar|k}} is fixed in the [[astronomical system of units]], measuring the light time per unit distance is exactly equivalent to measuring the product {{mvar|G}}×{{Solar mass}} 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 variation|secular increase]] in the unit distance was much larger than can be accounted for by solar radiation, +{{val|15|4}} metres per century.<ref>{{cite journal |author1=Krasinsky, G.A. |author2=Brumberg, V.A. |title=Secular increase of astronomical unit from analysis of the major planet motions, and its interpretation |journal=[[Celestial Mechanics and Dynamical Astronomy]] |volume=90 |issue=3–4 |date=2004 |doi=10.1007/s10569-004-0633-z |pages=267–88|bibcode = 2004CeMDA..90..267K |s2cid=120785056 }}</ref><ref name="Anderson">{{cite journal |last1=Anderson |first1=John D. |last2=Nieto |first2=Michael Martin |name-list-style=amp |date=2009 |title=Astrometric Solar-System Anomalies; §2: Increase in the astronomical unit |journal= Proceedings of the International Astronomical Union |volume=5 |issue=S261 |pages=189–97 |arxiv=0907.2469 |bibcode=2009IAU...261.0702A |doi=10.1017/s1743921309990378 |s2cid=8852372}}</ref>

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.<ref>{{cite journal |display-authors=1 |first1=A. |last1=Fienga |last2=Kuchynka |first2=P. |last3=Manche |first3=H. |last4=Desvignes |first4=G. |last5=Gastineau |first5=M. |last6=Cognard |first6=I. |last7=Theureau |first7=G. |title=The INPOP10a planetary ephemeris and its applications in fundamental physics |journal=[[Celestial Mechanics and Dynamical Astronomy]] |volume=111 |issue=3 |date=2011 |doi=10.1007/s10569-011-9377-8 |page=363 |bibcode=2011CeMDA.111..363F |arxiv=1108.5546|s2cid=122573801 }}</ref>

== 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.

{| class="wikitable sortable"
! width= 100 | Object or length
! Length or{{br}}distance{{br}}in au
! width= 50 class="unsortable"| Range
! class="unsortable" | Comment and reference point
! width= 25 class="unsortable" | Refs
|- style="background-color: #e2e2e2"
| [[Light-second]]
| align=right| {{val|0.002}}
| —
| Distance light travels in one second
| —
|-
| [[Lunar distance (astronomy)|Lunar distance]]
| align=right| {{val|0.0026}}
| —
| Average distance from Earth (which the [[Apollo program|Apollo missions]] took about 3 days to travel)
| —
|- style="background-color: #e2e2e2"
|[[Solar radius]]
| align=right| {{val|0.005}}
| —
| Radius of the [[Sun]] ({{val|695500|u=km}}, {{val|432450|u=mi}}, a hundred times the radius of Earth or ten times the average radius of Jupiter)
| —
|- style="background-color: #e2e2e2"
| [[Light-minute]]
| align=right| {{val|0.12}}
| —
| Distance light travels in one minute
| —
|-
| [[Mercury (planet)|Mercury]]
| align=right| {{val|0.39}}
| —
| Average distance from the Sun
| —
|-
| [[Venus]]
| align=right| {{val|0.72}}
| —
| Average distance from the Sun
| —
|-
|[[Earth]]
| align=right| {{val|1.00}}
| —
|Average distance of [[Earth's orbit]] from the Sun ([[sunlight]] travels for 8 minutes and 19 seconds before reaching Earth)
| —
|-
| [[Mars]]
| align=right| {{val|1.52}}
| —
| Average distance from the Sun
| —
|-
| [[Jupiter]]
| align=right| {{val|5.2}}
| —
| Average distance from the Sun
| —
|- style="background-color: #e2e2e2"
| [[Light-second#Use in astronomy|Light-hour]]
| align=right| {{val|7.2}}
| —
| Distance light travels in one hour
| —
|-
| [[Saturn]]
| align=right| {{val|9.5}}
| —
| Average distance from the Sun
| —
|-
| [[Uranus]]
| align=right| {{val|19.2}}
| —
| Average distance from the Sun
| —
|-
| [[Kuiper belt]]
| align=right| {{val|30}}
| —
| align=left | Inner edge begins at approximately 30&nbsp;au
|<ref>{{cite journal |author=Stern |first1=Alan |last2=Colwell |first2=Joshua E. |date=1997 |title=Collisional erosion in the primordial Edgeworth-Kuiper belt and the generation of the 30–50&nbsp;au Kuiper gap |journal=The Astrophysical Journal |volume=490 |issue=2 |pages=879–82 |bibcode=1997ApJ...490..879S |doi=10.1086/304912 |s2cid=123177461 |doi-access=free}}</ref>
|-
| [[Neptune]]
| align=right| {{val|30.1}}
| —
| Average distance from the Sun
| —
|-
| [[Eris (dwarf planet)|Eris]]
| align=right| {{val|67.8}}
| —
| Average distance from the Sun
| —
|-
|''[[Voyager 2]]''
| align=right| {{val|137}}
| —
| Distance from the Sun in October 2024
| <ref name="distantprobes">[https://voyager.jpl.nasa.gov/mission/status/ Voyager Mission Status].</ref>
|-
| ''[[Voyager 1]]''
| align=right| {{val|165}}
| —
| Distance from the Sun in October 2024
| <ref name="distantprobes"/>
|- style="background-color: #e2e2e2"
| [[Light-day]]
| align=right| {{val|173}}
| —
|Distance light travels in one day
| —
|- style="background-color: #e2e2e2"
| [[Light-year]]
| align=right| {{val|63241}}
| —
| Distance light travels in one [[Julian year (astronomy)|Julian year]] (365.25 days)
| —
|-
| [[Oort cloud]]
| align=right| {{val|75000}}
| ± {{val|25000}}
|Distance of the outer limit of Oort cloud from the Sun (estimated, corresponds to 1.2 light-years)
| —
|- style="background-color: #e2e2e2"
| [[Parsec]]
| align=right| {{val|206265}}
| —
| One [[parsec]]. The parsec is defined in terms of the astronomical unit, is used to measure distances beyond the scope of the Solar System and is about 3.26 light-years: 1 pc = 1&nbsp;au/tan(1″)
|<ref name=au_parsec/><ref>{{cite web |url=http://www.iau.org/public/themes/measuring/ |url-status=dead |archive-url=https://web.archive.org/web/20250310001225/http://www.iau.org/public/themes/measuring/ |archive-date=10 March 2025 |title=Measuring the Universe – The IAU and astronomical units |publisher=International Astronomical Union |access-date=20 April 2025 }}</ref>
|-
| [[Proxima Centauri]]
| align=right| {{val|268000}}
| ± 126
| Distance to the nearest star to the Solar System
| —
|-
| [[Galactic Centre]] of the [[Milky Way]]
| align=right| {{val|1700000000}}
| —
| Distance from the Sun to the centre of the Milky Way
| —
|-
! colspan=5 style="font-weight: normal; font-size: 0.9em; text-align: left; padding: 6px 2px 4px 4px" | Note: Figures in this table are generally rounded estimates, often rough estimates, and may considerably differ from other sources. Table also includes other units of length for comparison.
|}

== See also ==
* [[Orders of magnitude (length)]]

== References ==
{{Reflist}}

== Further reading ==
<!-- Cite templates used in further reading section because it more closely resembles format for reference lists used in most publications. -->
* {{cite journal |last1=Williams |first1=D. |last2=Davies |first2=R. D. |date=1968 |title=A radio method for determining the astronomical unit |journal=[[Monthly Notices of the Royal Astronomical Society]] |volume=140 |issue=4 |page=537 |bibcode=1968MNRAS.140..537W |doi=10.1093/mnras/140.4.537 |ref=none|doi-access= free}}

== External links ==
* [https://web.archive.org/web/20250310001225/http://www.iau.org/public/themes/measuring/ The IAU and astronomical units], archived 10 Mar 2025
* [https://web.archive.org/web/20070216041250/http://www.iau.org/Units.234.0.html Recommendations concerning Units] (HTML version of the IAU Style Manual), archived 16 Feb 2007
* [http://www.sil.si.edu/exhibitions/chasing-venus/intro.htm Chasing Venus, Observing the Transits of Venus]
* [http://www.transitofvenus.org/ Transit of Venus]

{{Units of length used in Astronomy}}
{{SI units}}
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{{DEFAULTSORT:Astronomical Unit}}
[[Category:Celestial mechanics]]
[[Category:Units of measurement in astronomy|Unit]]
[[Category:Units of length]]