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An '''astronomical constant''' is a [[physical constant]] used in [[astronomy]]. Formal sets of constants, along with recommended values, have been defined by the [[International Astronomical Union]] (IAU) several times: in 1964<ref name="IAU1964">Resolution No.4 of the [http://www.iau.org/static/resolutions/IAU1964_French.pdf XIIth General Assembly of the International Astronomical Union], Hamburg, 1964.</ref> and in 1976<ref name="IAU76">Resolution No. 1 on the recommendations of Commission 4 on ephemerides in the [http://www.iau.org/static/resolutions/IAU1976_French.pdf XVIth General Assembly of the International Astronomical Union], Grenoble, 1976.</ref> (with an update in 1994<ref name="IAU94">{{citation | author = Standish, E. M. | contribution = Report of the IAU WGAS Sub-group on Numerical Standards | url = http://iau-comm4.jpl.nasa.gov/iausgnsrpt.pdf | title = Highlights of Astronomy | editor = Appenzeller, I. | location = Dordrecht | publisher = Kluwer | year = 1995}}</ref>). In 2009 the IAU adopted a new current set, and recognizing that new observations and techniques continuously provide better values for these constants, they decided
<ref name="IAU2009">
Resolution B2 of the [http://www.iau.org/static/resolutions/IAU2009_English.pdf XXVIIth General Assembly of the International Astronomical Union], Rio de Janeiro, 2009.
</ref>
to not fix these values, but have the Working Group on Numerical Standards continuously maintain a set of Current Best Estimates
<ref name="IAUWG">
IAU Division I Working Group on Numerical Standards for Fundamental Astronomy and Astronomical Constants: Current Best Estimates (CBEs) [http://maia.usno.navy.mil/NSFA/NSFA_cbe.html]
</ref>
.  The set of constants is widely reproduced in publications such as the ''[[Astronomical Almanac]]'' of the [[United States Naval Observatory]] and [[Her Majesty's Nautical Almanac Office]].
 
Besides the IAU list of units and constants, also the [[International Earth Rotation Service]] defines constants relevant to the orientation and rotation of the Earth, in its technical notes
.<ref name=IERS2010>
{{cite web |title=Table 1.1: IERS numerical standards |work=IERS technical note no. 36: General definitions and numerical standards  |author=Gérard Petit and Brian Luzum, eds. |url=ftp://tai.bipm.org/iers/conv2010/chapter1/tn36_c1.pdf |publisher=[[International Earth Rotation and Reference Systems Service]] |year=2010}}
For complete document see {{cite book |title=IERS Conventions (2010): IERS technical note no. 36 |author=Gérard Petit and Brian Luzum, eds. |isbn=978-3-89888-989-6 |url=http://www.iers.org/nn_11216/IERS/EN/Publications/TechnicalNotes/tn36.html |publisher=International Earth Rotation and Reference Systems Service |year=2010}}
</ref>
 
The IAU system of constants defines a system of astronomical units for length, mass and time (in fact, several such systems), and also includes constants such as the [[speed of light]] and the [[constant of gravitation]] which allow transformations between astronomical units and [[SI unit]]s. Slightly different values for the constants are obtained depending on the [[frame of reference]] used. Values quoted in [[barycentric dynamical time]] (TDB) or equivalent time scales such as the [[Ephemeris Time|''T''<sub>eph</sub>]] of the [[Jet Propulsion Laboratory]] [[Ephemeris|ephemerides]] represent the mean values that would be measured by an observer on the Earth's surface (strictly, on the surface of the [[geoid]]) over a long period of time. The IAU also recommends values in SI units, which are the values which would be measured (in [[proper length]] and [[proper time]]) by an observer at the [[barycentre]] of the Solar System: these are obtained by the following transformations:<ref name="IAU94" />
:<math>\tau_A({\rm SI}) = (1+L_{\rm B})^{\frac{1}{3}} \tau_A({\rm TDB})\,</math>
:<math>GE({\rm SI}) = (1+L_{\rm B}) GE({\rm TDB})\,</math>
:<math>GS({\rm SI}) = (1+L_{\rm B}) GS({\rm TDB})\,</math>
 
== Astronomical system of units ==
{{main|Astronomical system of units}}
The astronomical unit of time is a time interval of one day (''D'') of 86400 seconds. The astronomical unit of mass is the mass of the Sun (''S''). The astronomical unit of length is that length (''A'') for which the [[Gaussian gravitational constant]] (''k'') takes the value {{nowrap|0.017&thinsp;202&thinsp;098&thinsp;95}} when the units of measurement are the astronomical units of length, mass and time.<ref name="IAU76" />
 
==Table of astronomical constants==
{| class="wikitable"
|-
! Quantity !! Symbol !! Value !! Relative<br />uncertainty !! Ref.
|-
| colspan=5 | '''''Defining constants'''''
|-
| [[Gaussian gravitational constant]] || align=center | ''k'' || 0.017&thinsp;202&thinsp;098&thinsp;95 ''A''<sup>3/2</sup>&thinsp;''S''<sup>&minus;1/2</sup>&thinsp;''D''<sup>&minus;1</sup> || defined ||<ref name="IAU76" />
|-
| [[Speed of light]] || align=center | ''c'' || 299&thinsp;792&thinsp;458 m&thinsp;s<sup>&minus;1</sup> || defined ||<ref name="SIc">{{SIbrochure8th|pages=112–13}}.</ref>
|-
| Mean ratio of the [[Terrestrial Time|TT second]] to the [[Geocentric Coordinate Time|TCG second]] || align=center | 1 &minus; ''L''<sub>G</sub> || 1 &minus; 6.969&thinsp;290&thinsp;134{{e|&minus;10}} || defined ||<ref name="IAU00">Resolutions Nos. B1.5 and B1.9 of the [http://www.iau.org/static/resolutions/IAU2000_French.pdf XXIVth General Assembly of the International Astronomical Union], Manchester, 2000.</ref>
|-
| Mean ratio of the [[Barycentric Coordinate Time|TCB second]] to the [[Barycentric Dynamical Time|TDB second]] || align=center | 1 &minus; ''L''<sub>B</sub> || 1 &minus; 1.550&thinsp;519&thinsp;767&thinsp;72{{e|&minus;8}} || defined ||<ref name="IAU06_3">[http://www.iau.org/static/resolutions/IAU2006_Resol3.pdf Resolution 3] of the [http://www.iau.org/static/resolutions/IAU2006_French.pdf XXVIth General Assembly of the International Astronomical Union], Prague, 2006.</ref>
|-
| colspan=5 | '''''Primary constants'''''
|-
| Mean ratio of the [[Barycentric Coordinate Time|TCB second]] to the [[Geocentric Coordinate Time|TCG second]] || align=center | 1 &minus; ''L''<sub>C</sub> || 1 &minus; 1.480&thinsp;826&thinsp;867&thinsp;41{{e|&minus;8}} || 1.4{{e|&minus;9}} ||<ref name="IAU00" />
|-
| [[Light-time]] for [[Astronomical unit|unit distance]] || align=center | ''τ''<sub>A</sub> || 499.004&thinsp;786&thinsp;3852 s || 4.0{{e|&minus;11}} ||<ref name="JPL">{{citation | author = Standish, E. M. | year = 1998 | title = JPL Planetary and Lunar Ephemerides, DE405/LE405 | url = http://iau-comm4.jpl.nasa.gov/de405iom/de405iom.pdf | id = JPL IOM 312.F-98-048}}</ref><ref name="IERS">{{citation | editor = McCarthy, Dennis D.; Petit, Gérard | year = 2004 | contribution = IERS Conventions (2003) | url = http://www.iers.org/MainDisp.csl?pid=46-25776 | title = IERS Technical Note No.&nbsp;32 | location = Frankfurt | publisher = Bundesamts für Kartographie und Geodäsie | isbn = 3-89888-884-3}}</ref>
|-
| [[Equatorial radius]] for [[Earth]] || align=center | ''a''<sub>e</sub> || 6.378&thinsp;1366{{e|6}} m || 1.6{{e|&minus;8}} ||<ref name="IERS" />
|-
| [[Potential of the geoid]] || align=center | ''W''<sub>0</sub> || 6.263&thinsp;685&thinsp;60{{e|7}} m<sup>2</sup>&thinsp;s<sup>&minus;2</sup> || 8.0{{e|&minus;9}} ||<ref name="IERS" />
|-
| [[Dynamical form-factor]] for [[Earth]] || align=center | ''J''<sub>2</sub> || 0.001&thinsp;082&thinsp;6359 || 9.2{{e|&minus;8}} ||<ref name="IERS" />
|-
| [[Flattening factor]] for [[Earth]] || align=center | 1/''ƒ'' || 0.003&thinsp;352&thinsp;8197<br />= 1/298.256&thinsp;42 || 3.4{{e|&minus;8}} ||<ref name="IERS" />
|-
| [[Geocentric gravitational constant]] || align=center | ''GE'' || 3.986&thinsp;004&thinsp;391{{e|14}} m<sup>3</sup>&thinsp;s<sup>&minus;2</sup> || 2.0{{e|&minus;9}} ||<ref name="JPL" />
|-
| [[Constant of gravitation]] || align=center | ''G'' || 6.673&thinsp;84{{e|&minus;11}} m<sup>3</sup>&thinsp;kg<sup>&minus;1</sup>&thinsp;s<sup>&minus;2</sup> || 1.2{{e|&minus;4}} ||<ref name="JPL" /><ref name="CODATA">{{CODATA2006|url=http://www.physics.nist.gov/cgi-bin/cuu/Value?bg}}</ref>
|-
| Ratio of [[mass of Moon]] to [[mass of Earth]] || align=center | ''μ'' || 0.012&thinsp;300&thinsp;0383<br />= 1/81.300&thinsp;56 || 4.0{{e|&minus;8}} ||<ref name="JPL" /><ref name="IERS" />
|-
| [[General precession in longitude]], per [[Julian century]], at [[standard epoch 2000]] || align=center | ''ρ'' || 5029.796&thinsp;195″ || * ||<ref name="IAU06_1">[http://www.iau.org/static/resolutions/IAU2006_Resol1.pdf Resolution 1] of the [http://www.iau.org/static/resolutions/IAU2006_French.pdf XXVIth General Assembly of the International Astronomical Union], Prague, 2006.</ref>
|-
| [[Obliquity of the ecliptic]], at [[standard epoch 2000]] || align=center | ''ε'' || 23° 26′ 21.406″ || * ||<ref name="IAU06_1" />
|-
| colspan=5 | '''''Derived constants'''''
|-
| [[Constant of nutation]], at [[standard epoch 2000]] || align=center | ''N'' || 9.205&thinsp;2331″ || * ||<ref>Resolution No. B1.6 of the [http://www.iau.org/static/resolutions/IAU2000_French.pdf XXIVth General Assembly of the International Astronomical Union], Manchester, 2000.</ref>
|-
| [[Astronomical unit|Unit distance]] = ''cτ''<sub>A</sub>|| align=center | ''A'' || 149&thinsp;597&thinsp;870&thinsp;691 m || 4.0{{e|&minus;11}} ||<ref name="JPL" /><ref name="IERS" />
|-
| [[Solar parallax]] = arcsin(''a''<sub>e</sub>/''A'') || align=center | ''π''<sub>☉</sub> || 8.794&thinsp;1433″ || 1.6{{e|&minus;8}} ||<ref name="IAU76" />†
|-
| [[Constant of aberration]], at [[standard epoch 2000]] || align=center | ''κ'' || 20.495&thinsp;52″ || ||<ref name="IAU76" />
|-
| [[Heliocentric gravitational constant]] = ''A''<sup>3</sup>''k''<sup>2</sup>/''D''<sup>2</sup> || align=center | ''GS'' || 1.327&thinsp;2440{{e|20}} m<sup>3</sup>&thinsp;s<sup>&minus;2</sup> ||  3.8{{e|&minus;10}} ||<ref name="IERS" />
|-
| Ratio of [[mass of Sun]] to [[mass of Earth]] = (''GS'')/(''GE'') || align=center | ''S''/''E'' || 332&thinsp;946.050&thinsp;895 || ||<ref name="JPL" />
|-
| Ratio of [[mass of Sun]] to mass of (Earth + Moon) || align=center | (''S''/''E'')<br /><u style="text-decoration:overline">(1 + ''μ'')</u> || 328&thinsp;900.561&thinsp;400 || ||<ref name="JPL" />
|-
| [[Mass of Sun]] = (''GS'')/''G'' || align=center | ''S'' || 1.9818{{e|30}} kg || 1.0{{e|&minus;4}} ||<ref name="IAU76" />†
|-
| colspan=5 | '''''System of planetary masses''''': Ratios of mass of Sun to mass of planet<ref name="JPL" />
|-
| [[Mercury (planet)|Mercury]] || || 6&thinsp;023&thinsp;600 || colspan=2 |
|-
| [[Venus]] || || 408&thinsp;523.71 || colspan=2 |
|-
| [[Earth]] + [[Moon]] || || 328&thinsp;900.561&thinsp;400 || colspan=2 |
|-
| [[Mars]] || || 3&thinsp;098&thinsp;708 || colspan=2 |
|-
| [[Jupiter]] || || 1047.3486 || colspan=2 |
|-
| [[Saturn]] || || 3497.898 || colspan=2 |
|-
| [[Uranus]] || || 22&thinsp;902.98 || colspan=2 |
|-
| [[Neptune]] || || 19&thinsp;412.24 || colspan=2 |
|-
| [[Pluto]] || || 135&thinsp;200&thinsp;000 || colspan=2 |
|-
| colspan=5 | '''''Other constants''''' (outside the formal IAU System)
|-
| [[Parsec]] = ''A''/tan(1") || align=center | pc || 3.085&thinsp;677&thinsp;581&thinsp;28×10<sup>16</sup> m || 4.0{{e|&minus;11}} ||<ref name="IAUgen">{{citation | title = The IAU and astronomical units | url = http://www.iau.org/public_press/themes/measuring/ | publisher = [[International Astronomical Union]]}}</ref>†
|-
| [[Light-year]] = 365.25''cD'' || align=center | ly || 9.460&thinsp;730&thinsp;472&thinsp;5808{{e|15}} m || defined ||<ref name="IAUgen" />†
|-
| [[Hubble constant]] || align=center | ''H''<sub>0</sub> || 70.1&nbsp;km&thinsp;s<sup>&minus;1</sup>&thinsp;Mpc<sup>&minus;1</sup> || 0.019 ||<ref>{{citation | url = http://wmap.gsfc.nasa.gov/universe/uni_expansion.html | title = How Fast is the Universe Expanding? | publisher = [[NASA]] | year = 2008}}</ref>
|-
| [[Solar luminosity]] || align=center | ''L''<sub>☉</sub> || 3.939{{e|26}}&nbsp;W<br />= 2.107{{e|&minus;15}} ''S&thinsp;D''<sup>&minus;1</sup> || variable,<br />±0.1% ||<ref>{{citation | author = Noedlinger, Peter D. | arxiv = 0801.3807 | title = Solar Mass Loss, the Astronomical Unit, and the Scale of the Solar System | journal = Celest. Mech. Dynam. Astron.|bibcode = 2008arXiv0801.3807N }}</ref>
|}
 
;Notes
<span>*</span> The theories of [[precession]] and [[nutation]] have advanced since 1976, and these also affect the definition of the [[ecliptic]]. The values here are appropriate for the older theories, but additional constants are required for current models.
 
† The definitions of these derived constants have been taken from the references cited, but the values have been recalculated to take account of the more precise values of the primary constants cited in the table.
 
== References ==
*"[http://asa.usno.navy.mil/SecK/2009/Astronomical_Constants_2009.pdf 2009 Selected Astronomical Constants]" in {{citation | title = The Astronomical Almanac Online | url = http://asa.usno.navy.mil/ | publisher = [[United States Naval Observatory|USNO]]–[[United Kingdom Hydrographic Office|UKHO]]}}.
{{reflist}}
 
== External links ==
* [http://www.astronomynotes.com/tables/tablesa.htm Tables of constants] &mdash; from Nick Strobel's [http://www.astronomynotes.com/ Astronomy Notes]
* [http://www.jqjacobs.net/astro/astro.html Astronomical constants index] &mdash; James Q. Jacobs
 
{{DEFAULTSORT:Astronomical Constant}}
[[Category:Physical constants]]
[[Category:Astrophysics|Constants]]
[[Category:Units of measurement in astronomy|Constant]]

Latest revision as of 09:02, 9 August 2014

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