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Astronomical unit

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This article is about the unit of length. For constants, seeastronomical constant.For units in astronomy, seeastronomical system of units.For other uses of "AU", seeAu.

Astronomical unit
The grey line indicates the Earth–Sun distance, which on average is about 1 astronomical unit.
General information
Unit systemAstronomical system of units
(Accepted for use with the SI)
Unit oflength
Symbolau orAUor AU
Conversions
1 au orAUor AUin...... is equal to...
metric(SI) units1.495978707×1011m
imperial&USunits9.2956×107mi
astronomical units4.8481×10−6pc
1.5813×10−5ly
215.03R☉

Theastronomical unit(symbol:au,[1][2][3][4]orAU) is aunit of lengthdefined to be exactly equal to149,597,870,700 m.[5]Historically, the astronomical unit was conceived as the average Earth-Sun distance (the average of Earth'saphelionandperihelion), before its modern redefinition in 2012.

The astronomical unit is used primarily for measuring distances within theSolar Systemor around other stars. It is also a fundamental component in the definition of another unit of astronomical length, theparsec.[6]One au is equivalent to 499light-secondsto within 10parts per million.

History of symbol usage

[edit]

A variety of unit symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, theInternational Astronomical Union(IAU) had used the symbolAto denote a length equal to the astronomical unit.[7]In the astronomical literature, the symbol AU is common. In 2006, theInternational Bureau of Weights and Measures(BIPM) had recommended ua as the symbol for the unit, from the French "unité astronomique".[8]In the non-normative Annex C toISO 80000-3:2006 (later withdrawn), the symbol of the astronomical unit was also ua.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".[1]Thescientific journalspublished by theAmerican Astronomical Societyand theRoyal Astronomical Societysubsequently adopted this symbol.[3][9]In the 2014 revision and 2019 edition of the SI Brochure, the BIPM used the unit symbol "au".[10][11]ISO 80000-3:2019, which replaces ISO 80000-3:2006, does not mention the astronomical unit.[12][13]

Development of unit definition

[edit]
See also:Earth's orbit

Earth's orbitaround the Sun is anellipse.Thesemi-major axisof thiselliptic orbitis defined to be half of the straightline segmentthat joins theperihelion 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 largestparallax(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 byEinstein'stheory of relativityand upon the mathematical tools it used.

Improving measurements were continually checked and cross-checked by means of improved understanding of the laws ofcelestial 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 anephemeris.NASA'sJet Propulsion LaboratoryHORIZONS System provides one of several ephemeris computation services.[14]

In 1976, to establish an even precise measure for the astronomical unit, the IAU formallyadopted 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 theGaussian gravitational constant(k) takes the value0.01720209895when the units of measurement are the astronomical units of length, mass and time ".[7][15][16]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 anangular frequencyof0.01720209895radians per day";[17]or alternatively that length for which theheliocentric gravitational constant(the productGM☉) is equal to (0.01720209895)2au3/d2,when the length is used to describe the positions of objects in the Solar System.

Subsequent explorations of the Solar System byspace probesmade it possible to obtain precise measurements of the relative positions of theinner planetsand other objects by means ofradarandtelemetry.As with all radar measurements, these rely on measuring the time taken forphotonsto be reflected from an object. Because all photons move at thespeed of lightin 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 forrelativistic time dilation.Comparison of the ephemeris positions with time measurements expressed inBarycentric Dynamical Time(TDB) leads to a value for the speed of light in astronomical units per day (of86,400 s). By 2009, the IAU had updated its standard measures to reflect improvements, and calculated the speed of light at173.1446326847(69) au/d(TDB).[18]

In 1983, the CIPM modified theInternational System of Units(SI) to make the metre defined as the distance travelled in a vacuum by light in 1 /299,792,458s. 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 asc0=299,792,458 m/s,a standard also adopted by theIERSnumerical standards.[19]From this definition and the 2009 IAU standard, the time for light to traverse an astronomical unit is found to beτA=499.0047838061±0.00000001s,which is slightly more than 8 minutes 19 seconds. By multiplication, the best IAU 2009 estimate wasA=c0τA=149,597,870,700±3 m,[20]based on a comparison of Jet Propulsion Laboratory andIAA–RASephemerides.[21][22][23]

In 2006, the BIPM reported a value of the astronomical unit as1.49597870691(6)×1011m.[8]In the 2014 revision of the SI Brochure, the BIPM recognised the IAU's 2012 redefinition of the astronomical unit as149,597,870,700 m.[10]

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 (exactly149,597,870,700 m).[20][24]The new definition recognizes as a consequence that the astronomical unit has reduced importance, limited in use to a convenience in some applications.[20]

1 astronomical unit =149,597,870,700metres(by definition)
= 149,597,870.7kilometres(exactly)
≈ 92,955,807.2730miles
≈499.004783836light-seconds
≈1.58125074098×10−5light-years
≈4.84813681113×10−6parsecs

This definition makes the speed of light, defined as exactly299,792,458 m/s,equal to exactly299,792,458×86,400÷149,597,870,700or about173.144632674240au/d, some 60 parts pertrillionless than the 2009 estimate.

Usage and significance

[edit]

With the definitions used before 2012, the astronomical unit was dependent on theheliocentric gravitational constant,that is the product of thegravitational constant,G,and thesolar mass,M☉.NeitherGnorM☉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 lawexpressed 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 ofgeneral 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 between0.9832898912and1.0167103335au) 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 ofproper length.Indeed, theInternational 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".[25]As such, a distance within the Solar System without specifying theframe of referencefor 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,[26]and "vigorous debate" ensued[27]until August 2012 when the IAU adopted the current definition of 1 astronomical unit =149,597,870,700metres.

The astronomical unit is typically used forstellar systemscale distances, such as the size of a protostellar disk or theheliocentric distanceof an asteroid, whereas other units are used forother distances in astronomy.The astronomical unit is too small to be convenient for interstellar distances, where theparsecandlight-yearare widely used. The parsec (parallaxarcsecond) is defined in terms of the astronomical unit, being the distance of an object with a parallax of1″.The light-year is often used in popular works, but is not an approved non-SI unit and is rarely used by professional astronomers.[28]

When simulating anumerical model of the Solar System,the astronomical unit provides an appropriate scale that minimizes (overflow,underflowandtruncation) errors infloating pointcalculations.

History

[edit]

The bookOn the Sizes and Distances of the Sun and Moon,which is ascribed toAristarchus,says the distance to the Sun is 18 to 20 times thedistance to the Moon,whereas the true ratio is about389.174.The latter estimate was based on the angle between thehalf-moonand the Sun, which he estimated as87°(the true value being close to89.853°). Depending on the distance that van Helden assumes Aristarchus used for the distance to the Moon, his calculated distance to the Sun would fall between380and1,520Earth radii.[29]

According toEusebiusin thePraeparatio evangelica(Book XV, Chapter 53),Eratosthenesfound the distance to the Sun to be "σταδιων μυριαδας τετρακοσιας και οκτωκισμυριας" (literally "ofstadiamyriads400 and80,000″) but with the additional note that in the Greek text thegrammatical agreementis betweenmyriads(notstadia) on the one hand and both400and80,000on the other: all three are accusative plural, while σταδιων is genitive plural ( "of stadia" ). All three words (or all four includingstadia) areinflected.This has been translated either as4080000stadia(1903 translation byEdwin Hamilton Gifford), or as804,000,000stadia(edition ofÉdourad des Places[de],dated 1974–1991). Using the Greek stadium of 185 to 190 metres,[30][31]the former translation comes to754,800 kmto775,200 km,which is far too low, whereas the second translation comes to 148.7 to 152.8 billion metres (accurate within 2%).[32]Hipparchusalso gave an estimate of the distance of Earth from the Sun, quoted byPappusas equal to 490 Earth radii. According to the conjectural reconstructions ofNoel SwerdlowandG. J. Toomer,this was derived from his assumption of a "least perceptible" solar parallax of7′.[33]

A Chinese mathematical treatise, theZhoubi Suanjing(c. 1st century BCE), shows how the distance to the Sun can be computed geometrically, using the different lengths of the noontime shadows observed at three places1,000liapart and the assumption that Earth is flat.[34]

Distance to the Sun
estimated by 		Estimate In au Percentage error
Solar
parallax 		Earth
radii
Aristarchus(3rd century BCE)(inOn Sizes) 13′24″–7′12″ 256.5–477.8 0.011–0.020 -98.9% to -98%
Archimedes(3rd century BCE)(inThe Sand Reckoner) 21″ 10,000 0.426 -57.4%
Hipparchus(2nd century BCE) 7′ 490 0.021 -97.9%
Posidonius(1st century BCE)(quoted by coevalCleomedes) 21″ 10,000 0.426 -57.4%
Ptolemy(2nd century) 2′ 50″ 1,210 0.052 -94.8%
Godefroy Wendelin(1635) 15″ 14,000 0.597 -40.3%
Jeremiah Horrocks(1639) 15″ 14,000 0.597 -40.3%
Christiaan Huygens(1659) 8.2″ 25,086[35] 1.068 6.8%
Cassini&Richer(1672) 9.5″ 21,700 0.925 -7.5%
Flamsteed(1672) 9.5″ 21,700 0.925 -7.5%
Jérôme Lalande(1771) 8.6″ 24,000 1.023 2.3%
Simon Newcomb(1895) 8.80″ 23,440 0.9994 -0.06%
Arthur Hinks(1909) 8.807″ 23,420 0.9985 -0.15%
H. Spencer Jones(1941) 8.790″ 23,466 1.0005 0.05%
Modernastronomy 8.794143″ 23,455 1.0000

In the 2nd century CE,Ptolemyestimated the mean distance of the Sun as1,210timesEarth's radius.[36][37]To determine this value, Ptolemy started by measuring the Moon's parallax, finding what amounted to a horizontal lunar parallax of 1° 26′, which was much too large. He then derived a maximum lunar distance of⁠64+1/6⁠Earth radii. Because of cancelling errors in his parallax figure, his theory of the Moon's orbit, and other factors, this figure was approximately correct.[38][39]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 be1,210Earth 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.[38]

After Greek astronomy was transmitted to the medieval Islamic world, astronomers made some changes to Ptolemy's cosmological model, but did not greatly change his estimate of the Earth–Sun distance. For example, in his introduction to Ptolemaic astronomy,al-Farghānīgave a mean solar distance of1,170Earth radii, whereas in hiszij,al-Battānīused a mean solar distance of1,108Earth radii. Subsequent astronomers, such asal-Bīrūnī,used similar values.[40]Later in Europe,CopernicusandTycho Brahealso used comparable figures (1,142and1,150Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century.[41]

Johannes Keplerwas the first to realize that Ptolemy's estimate must be significantly too low (according to Kepler, at least by a factor of three) in hisRudolphine Tables(1627).Kepler's laws of planetary motionallowed 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 thetelescopeallowed far more accurate measurements of angles than is possible with the naked eye. Flemish astronomerGodefroy Wendelinrepeated 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 thetransit of Venus.[42]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, thesolar parallaxα(which cannot be measured directly due to the brightness of the Sun[43]).Jeremiah Horrockshad attempted to produce an estimate based on his observation of the1639 transit(published in 1662), giving a solar parallax of15″,similar to Wendelin's figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by

The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of15″is equivalent to an Earth–Sun distance of13,750Earth radii.

Christiaan Huygensbelieved that the distance was even greater: by comparing the apparent sizes of Venus andMars,he estimated a value of about24,000Earth radii,[35]equivalent to a solar parallax of8.6″.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.

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 RicherandGiovanni Domenico Cassinimeasured the parallax of Mars betweenParisandCayenneinFrench Guianawhen Mars was at its closest to Earth in 1672. They arrived at a figure for the solar parallax of9.5″,equivalent to an Earth–Sun distance of about22,000Earth 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 colleagueJean Picardin 1669 as3,269,000toises.This same year saw another estimate for the astronomical unit byJohn Flamsteed,which accomplished it alone by measuring themartiandiurnal parallax.[44]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 byJames Gregoryand published in hisOptica Promata(1663). It was strongly advocated byEdmond Halley[45]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 theSeven 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.[46]The various results were collated byJérôme Lalandeto give a figure for the solar parallax of8.6″.Karl Rudolph Powalkyhad made an estimate of8.83″in 1864.[47]

Date Method A/Gm Uncertainty
1895 aberration 149.25 0.12
1941 parallax 149.674 0.016
1964 radar 149.5981 0.001
1976 telemetry 149.597870 0.000001
2009 telemetry 149.597870700 0.000000003

Another method involved determining the constant ofaberration.Simon Newcombgave great weight to this method when deriving his widely accepted value of8.80″for the solar parallax (close to the modern value of8.794143″), although Newcomb also used data from the transits of Venus. Newcomb also collaborated withA. A. Michelsonto 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 ofastronomical constantsin 1896,[48]which remained in place for the calculation of ephemerides until 1964.[49]The name "astronomical unit" appears first to have been used in 1903.[50][failed verification]

The discovery of thenear-Earth asteroid433 Erosand its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement.[51]Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931.[43][52]

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.[53]

Developments

[edit]
Theastronomical unitis used as the baseline of the triangle to measurestellar parallaxes(distances in the image are not to scale)

The unit distanceA(the value of the astronomical unit in metres) can be expressed in terms of other astronomical constants:

whereGis theNewtonian constant of gravitation,M☉is the solar mass,kis the numerical value of Gaussian gravitational constant andDis the time period of one day.[1] The Sun is constantly losing mass by radiating away energy,[54]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.[55]

As the speed of light has an exact defined value in SI units and the Gaussian gravitational constantkis fixed in theastronomical system of units,measuring the light time per unit distance is exactly equivalent to measuring the productG×M☉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 thesecular increasein the unit distance was much larger than can be accounted for by solar radiation, +15±4metres per century.[56][57]

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.[58]

Examples

[edit]

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.

Object or length Length or
distance
in au 		Range Comment and reference point Refs
Light-second 0.002 – Distance light travels in one second –
Lunar distance 0.0026 – Average distance from Earth (which theApollo missionstook about 3 days to travel) –
Solar radius 0.005 – Radius of theSun(695500km,432450mi,a hundred times the radius of Earth or ten times the average radius of Jupiter) –
Light-minute 0.12 – Distance light travels in one minute –
Mercury 0.39 – Average distance from the Sun –
Venus 0.72 – Average distance from the Sun –
Earth 1.00 – Average distance ofEarth's orbitfrom the Sun (sunlighttravels for 8 minutes and 19 seconds before reaching Earth) –
Mars 1.52 – Average distance from the Sun –
Jupiter 5.2 – Average distance from the Sun –
Light-hour 7.2 – Distance light travels in one hour –
Saturn 9.5 – Average distance from the Sun –
Uranus 19.2 – Average distance from the Sun –
Kuiper belt 30 – Inner edge begins at approximately 30 au [59]
Neptune 30.1 – Average distance from the Sun –
Eris 67.8 – Average distance from the Sun –
Voyager 2 134 – Distance from the Sun in August 2023 [60]
Voyager 1 161 – Distance from the Sun in August 2023 [60]
Light-day 173 – Distance light travels in one day –
Light-year 63,241 – Distance light travels in oneJulian year(365.25 days) –
Oort cloud 75,000 ±25,000 Distance of the outer limit of Oort cloud from the Sun (estimated, corresponds to 1.2 light-years) –
Parsec 206,265 – Oneparsec.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 au/tan(1″) [6][61]
Proxima Centauri 268,000 ± 126 Distance to the nearest star to the Solar System –
Galactic Centreof theMilky Way 1,700,000,000 – Distance from the Sun to the centre of the Milky Way –
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

[edit]

References

[edit]
  1. ^abcOn the re-definition of the astronomical unit of length(PDF).XXVIII General Assembly of International Astronomical Union. Beijing, China: International Astronomical Union. 31 August 2012. Resolution B2.... recommends... 5. that the unique symbol "au" be used for the astronomical unit.
  2. ^"Monthly Notices of the Royal Astronomical Society: Instructions for Authors".Oxford Journals.Archived fromthe originalon 22 October 2012.Retrieved20 March2015.The units of length/distance are Å, nm, μm, mm, cm, m, km, au, light-year, pc.
  3. ^ab"Manuscript Preparation: AJ & ApJ Author Instructions".American Astronomical Society.Archived fromthe originalon 21 February 2016.Retrieved29 October2016.Use standard abbreviations for... natural units (e.g., au, pc, cm).
  4. ^Le Système international d’unités[The International System of Units](PDF)(in French and English) (9th ed.), International Bureau of Weights and Measures, 2019, p. 145,ISBN978-92-822-2272-0
  5. ^On the re-definition of the astronomical unit of length(PDF).XXVIII General Assembly of International Astronomical Union. Beijing: International Astronomical Union. 31 August 2012. Resolution B2.... recommends [adopted] that the astronomical unit be re-defined to be a conventional unit of length equal to exactly 149,597,870,700 metres, in agreement with the value adopted in IAU 2009 Resolution B2
  6. ^abLuque, B.; Ballesteros, F.J. (2019)."Title: To the Sun and beyond".Nature Physics.15:1302.doi:10.1038/s41567-019-0685-3.
  7. ^abCommission 4: Ephemerides/Ephémérides (1976).item 12: Unit distance(PDF).XVIth General Assembly of the International Astronomical Union. IAU (1976) System of Astronomical Constants. Grenoble, FR. Commission 4, part III, Recommendation 1, item 12.Archived(PDF)from the original on 9 October 2022.{{cite conference}}:CS1 maint: numeric names: authors list (link)
  8. ^abBureau International des Poids et Mesures(2006),The International System of Units (SI)(PDF)(8th ed.), Organisation Intergouvernementale de la Convention du Mètre, p. 126, archived fromthe original(PDF)on 9 October 2022
  9. ^"Instructions to Authors".Monthly Notices of the Royal Astronomical Society.Oxford University Press.Retrieved5 November2020.The units of length/distance are Å, nm, µm, mm, cm, m, km, au, light-year, pc.
  10. ^ab"The International System of Units (SI)".SI Brochure (8th ed.). BIPM. 2014 [2006].Retrieved3 January2015.
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  14. ^"HORIZONS System".Solar system dynamics.NASA: Jet Propulsion Laboratory. 4 January 2005.Retrieved16 January2012.
  15. ^Hussmann, H.; Sohl, F.; Oberst, J. (2009)."§ 4.2.2.1.3: Astronomical units".In Trümper, Joachim E. (ed.).Astronomy, astrophysics, and cosmology – Volume VI/4BSolar System.Springer. p. 4.ISBN978-3-540-88054-7.
  16. ^Williams Gareth V. (1997)."Astronomical unit".In Shirley, James H.; Fairbridge, Rhodes Whitmore (eds.).Encyclopedia of planetary sciences.Springer. p. 48.ISBN978-0-412-06951-2.
  17. ^International Bureau of Weights and Measures(2006),The International System of Units (SI)(PDF)(8th ed.), p. 126,ISBN92-822-2213-6,archived(PDF)from the original on 4 June 2021,retrieved16 December2021
  18. ^"Selected Astronomical Constants"(PDF).The Astronomical Almanac Online.USNO–UKHO.2009. p. K6. Archived fromthe original(PDF)on 26 July 2014.
  19. ^Petit, Gérard; Luzum, Brian, eds. (2010).Table 1.1: IERS numerical standards(PDF).IERS technical note no. 36: General definitions and numerical standards(Report).International Earth Rotation and Reference Systems Service.Archived(PDF)from the original on 9 October 2022.For complete document seeGérard Petit; Brian Luzum, eds. (2010).IERS Conventions (2010): IERS technical note no. 36(Report). International Earth Rotation and Reference Systems Service.ISBN978-3-89888-989-6.Archived fromthe originalon 30 June 2019.Retrieved16 January2012.
  20. ^abcCapitaine, Nicole; Klioner, Sergei;McCarthy, Dennis(2012).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(PDF)(Report). Vol. 7. Beijing, China. p. 40.Bibcode:2012IAUJD...7E..40C.Archived(PDF)from the original on 9 October 2022.Retrieved16 May2013.
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