Editing Astronomical unit (section)

== 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.