Astronomical unit: Difference between revisions
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{{ | {{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 = | | bgcolour = | ||
| name = | | name = astronomical unit | ||
| image= | | image= Astronomical unit svg.svg | ||
| caption=The grey line indicates the Earth–Sun distance, which on average is about 1 astronomical unit. | | caption=The grey line indicates the Earth–Sun distance, which on average is about 1 astronomical unit. | ||
| standard = [[Astronomical system of units]] | | standard = [[Astronomical system of units]] | ||
| quantity = [[length]] | | quantity = [[length]] | ||
| symbol = au | | symbol = au | ||
| symbol2 = {{ | | symbol2 = {{smallcaps|au}} | ||
| symbol3 = AU | | symbol3 = AU | ||
| units1 = [[International System of Units|SI]] units | | units1 = [[International System of Units|SI]] units | ||
| Line 21: | Line 21: | ||
}} | }} | ||
The '''astronomical unit''' (symbol: '''au'''<ref name="IAUresB2">{{cite conference |title=On the re-definition of the astronomical unit of length |id=Resolution B2 |conference=XXVIII 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 | The '''astronomical unit''' (symbol: '''au'''<ref name="IAUresB2">{{cite conference |title=On the re-definition of the astronomical unit of length |id=Resolution B2 |conference=XXVIII 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 as {{val|149597870700|u=metres|fmt=periods}}.<ref>{{cite conference |id=Resolution B2 |title=On the re-definition of the astronomical unit of length |publisher=International Astronomical Union |conference=XXVIII 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 2009 Resolution 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. | 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 == | == 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]] (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 C to [[ISO 80000-3 | A variety of unit symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the [[International Astronomical Union]] (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 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 80000-3:2019, which replaces ISO 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 80000-3:2019(en) |series=Quantities and units |title=Part 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> | 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 80000-3:2019, which replaces ISO 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 80000-3:2019(en) |series=Quantities and units |title=Part 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 == | == 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. | [[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]] | 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 12: Unit distance |series=IAU (1976) System of Astronomical Constants |author=Commission 4: Ephemerides/Ephémérides |id=Commission 4, part III, Recommendation 1, item 12 <!-- Resolution No. 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=§ 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> au<sup>3</sup>/d<sup>2</sup>, when the length is used to describe the positions of objects in the Solar System. | 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 12: Unit distance |series=IAU (1976) System of Astronomical Constants |author=Commission 4: Ephemerides/Ephémérides |id=Commission 4, part III, Recommendation 1, item 12 <!-- Resolution No. 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=§ 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> 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]] (TDB) leads to a value for the speed of light in astronomical units per day (of {{val|86400|u=s}}). | 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]].{{cn|date=January 2026}} Comparison of the ephemeris positions with time measurements expressed in [[Barycentric Dynamical Time]] (TDB) leads to a value for the speed of light in astronomical units per day (of {{val|86400|u=s}}). In 2009, the IAU reported the "light-time for unit distance" as {{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 | In 1983, the BIPM modified the [[International System of Units]] (SI) to make the metre defined as the distance travelled in a vacuum by light in 1 / {{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 minutes 19 seconds. By multiplication, the best IAU 2009 estimate was ''A'' = ''c''<sub>0</sub>''τ''<sub>A</sub> = {{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 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 Brochure, the BIPM recognised the IAU's 2012 redefinition of the astronomical unit as {{val|149597870700|u=m}}.<ref name=SI_Brochure2012/> | 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 Brochure, the BIPM recognised the IAU's 2012 redefinition of the astronomical unit as {{val|149597870700|u=m}}.<ref name=SI_Brochure2012/> | ||
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|= {{val|149597870700}} [[metre]]s (by definition) | |= {{val|149597870700}} [[metre]]s (by definition) | ||
|- | |- | ||
|= {{convert|1|au|km|disp=out|lk=on|abbr=off|sigfig= | |= {{convert|1|au|km|disp=out|lk=on|abbr=off|sigfig=12|comma=5}} (exactly) | ||
|- | |- | ||
|≈ {{convert|1|au|mi|disp=out|lk=on|abbr=off|sigfig=12|comma=5}} | |≈ {{convert|1|au|mi|disp=out|lk=on|abbr=off|sigfig=12|comma=5}} | ||
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|≈ {{convert|1|au|pc|disp=out|lk=on|abbr=off|sigfig=12|comma=gaps}} | |≈ {{convert|1|au|pc|disp=out|lk=on|abbr=off|sigfig=12|comma=gaps}} | ||
|} | |} | ||
== Usage and significance == | == Usage and significance == | ||
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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=§ 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 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=§ 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=§ 6.2.8: Light-year |chapter-url=https://books.google.com/books?id=UC_1_804BXgC&pg=PA82}}</ref> | The astronomical unit is typically used for [[stellar system]] scale distances, such as the size of a protostellar disk or the [[heliocentric distance]] (distance from the Sun's centre) 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=§ 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. | 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 == | == History == | ||
Many early measurements of the Earth-Sun distance are wildly incorrect, primarily because the measurements rely on the ratio of the | Many early measurements of the Earth-Sun distance are wildly incorrect, primarily because the measurements rely on the ratio of the diameter of the Earth to the distance of the Sun. Since this ratio is 1/12000, small errors in the size of the Earth lead to large errors in the Earth-Sun distance.<ref name=Hughes-2001>Hughes, D. W. (2001). [https://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?2001JAHH....4...15H&defaultprint=YES&filetype=.pdf Six stages in the history of the astronomical unit. Journal of Astronomical History and Heritage] (ISSN 1440-2807), Vol. 4, No. 1, p. 15-28 (2001)., 4, 15-28.</ref> | ||
Around 280 BC, [[Aristarchus of Samos|Aristarchus]] carefully measured the Moon-Earth-Sun angle when the Moon is in its first [[Lunar phase|quarter]] and used this to estimate the distance to the Sun. The exact timing and angle measurement are essential.<ref name=Hughes-2001/> He estimated the angle at as {{val|87|u=deg}} (the true value being close to {{val|89.853|u=deg}}) and reported in ''[[On the Sizes and Distances (Aristarchus)|On the Sizes and Distances of the Sun and Moon]]'' 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}}. Depending on the distance that 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 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> | Around 280 BC, [[Aristarchus of Samos|Aristarchus]] carefully measured the Moon-Earth-Sun angle when the Moon is in its first [[Lunar phase|quarter]] and used this to estimate the distance to the Sun. The exact timing and angle measurement are essential.<ref name=Hughes-2001/> He estimated the angle at as {{val|87|u=deg}} (the true value being close to {{val|89.853|u=deg}}) and reported in ''[[On the Sizes and Distances (Aristarchus)|On the Sizes and Distances of the Sun and Moon]]'' 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}}. Depending on the distance that 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 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> | ||
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[[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.]] | [[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, [[ | [[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, [[Rømer's determination of the speed of light|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|url-access=subscription}}</ref> | 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|url-access=subscription}}</ref> | ||
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| {{val|0.000000003}} | | {{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" | 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" was first used in 1848. | ||
<ref>{{cite book | |||
| title = Webster's Third New International Dictionary, Unabridged | |||
| edition = 3rd | |||
| publisher = Merriam-Webster | |||
| year = 1992 | |||
| isbn = 978-0-87779-789-0 | |||
| entry = astronomical unit | |||
}}</ref> | |||
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> | 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> | ||
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The unit distance {{mvar|A}} (the value of the astronomical unit in metres) can be expressed in terms of other astronomical constants: | 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> | : <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"/> | 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> | 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> | ||
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|- | |- | ||
|''[[Voyager 2]]'' | |''[[Voyager 2]]'' | ||
| align=right| {{val| | | align=right| {{val|141}} | ||
| — | | — | ||
| Distance from the Sun in | | Distance from the Sun in September 2025 | ||
| <ref name="distantprobes">[https://voyager.jpl.nasa.gov/mission/status/ Voyager Mission Status].</ref> | | <ref name="distantprobes">[https://voyager.jpl.nasa.gov/mission/status/ Voyager Mission Status].</ref> | ||
|- | |- | ||
| ''[[Voyager 1]]'' | | ''[[Voyager 1]]'' | ||
| align=right| {{val| | | align=right| {{val|168}} | ||
| — | | — | ||
| Distance from the Sun in | | Distance from the Sun in September 2025 | ||
| <ref name="distantprobes"/> | | <ref name="distantprobes"/> | ||
|- style="background-color: #e2e2e2" | |- style="background-color: #e2e2e2" | ||
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== Further reading == | == Further reading == | ||
<!-- Cite templates used in further reading section because it more closely resembles format for reference lists used in most publications. --> | <!-- 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}} | * {{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 == | == External links == | ||
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* [http://www.transitofvenus.org/ Transit of Venus] | * [http://www.transitofvenus.org/ Transit of Venus] | ||
{{ | {{units of length used in Astronomy}} | ||
{{SI units}} | {{SI units}} | ||
{{ | {{portal bar|Astronomy|Stars|Spaceflight|Outer space|Solar System|Science}} | ||
{{ | {{authority control}} | ||
{{DEFAULTSORT:Astronomical Unit}} | {{DEFAULTSORT:Astronomical Unit}} | ||