Astronomical unit
Astronomical unit | |
---|---|
Unit of | length |
Symbol | au or AU or AU |
Conversions | |
1 au or AU or AU in ... | ... is equal to ... |
metric (SI) units | 1.495978707×1011 m |
imperial & US units | 9.2956×107 mi |
astronomical units | 4.8481×10−6 pc 1.5813×10−5 ly 215.03 R☉ |
The astronomical unit (symbol: au,
The astronomical unit is used primarily for measuring distances within the
History of symbol usage
A variety of unit symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the
In 2012, the IAU, noting "that various symbols are presently in use for the astronomical unit", recommended the use of the symbol "au".[1] The scientific journals published by the American Astronomical Society and the Royal Astronomical Society subsequently 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
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.[14]
In 1976, to establish an even precise measure for the astronomical unit, the IAU formally 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 0.01720209895 when 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 an angular frequency of 0.01720209895 radians per day";[17] or alternatively that length for which the heliocentric gravitational constant (the product GM☉) is equal to (0.01720209895)2 au3/d2, when the length is used to describe the positions of objects in the Solar System.
Subsequent explorations of the Solar System by
In 1983, the CIPM modified the
In 2006, the BIPM reported a value of the astronomical unit as 1.49597870691(6)×1011 m.[8] In the 2014 revision of the SI Brochure, the BIPM recognised the IAU's 2012 redefinition of the astronomical unit as 149,597,870,700 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 (exactly 149,597,870,700 m).[20][24] The new definition also recognizes as a consequence that the astronomical unit is now to play a role of reduced importance, limited in its use to that of a convenience in some applications.[20]
1 astronomical unit = 149,597,870,700 metres (by definition) = 149,597,870.7 kilometres (exactly) ≈ 92,955,807.2730 miles ≈ 499.004783836 light-seconds ≈ 1.58125074098×10−5 light-years ≈ 4.84813681113×10−6 parsecs
This definition makes the speed of light, defined as exactly 299,792,458 m/s, equal to exactly 299,792,458 × 86,400 ÷ 149,597,870,700 or about 173.144632674240 au/d, some 60 parts per trillion less than the 2009 estimate.
Usage and significance
With the definitions used before 2012, the astronomical unit was dependent on the
The calculation of ephemerides also requires a consideration of the effects of
The metre is defined to be a unit of
The astronomical unit is typically used for
When simulating a
History
The book
According to
A Chinese mathematical treatise, the Zhoubi 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 places 1,000 li apart and the assumption that Earth is flat.[34]
Distance to the Sun estimated by |
Estimate | In au | Percentage error | |
---|---|---|---|---|
Solar
parallax |
Earth
radii | |||
On Sizes )
|
13′ 24″–7′ 12″ | 256.5–477.8 | 0.011–0.020 | -98.9% to -98% |
Archimedes (3rd century BCE) (in The 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 coeval Cleomedes) |
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% |
modern astronomy | 8.794143″ | 23,455 | 1.0000 |
In the 2nd century CE,
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,
A somewhat more accurate estimate can be obtained by observing the
The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of 15″ is equivalent to an Earth–Sun distance of 13,750 Earth radii.
Christiaan Huygens believed that the distance was even greater: by comparing the apparent sizes of Venus and Mars, he estimated a value of about 24,000 Earth radii,[35] equivalent to a solar parallax of 8.6″. 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.
, 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
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 of
The discovery of the
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
The unit distance A (the value of the astronomical unit in metres) can be expressed in terms of other astronomical constants:
where G is the
As the speed of light has an exact defined value in SI units and the Gaussian gravitational constant k is fixed in the astronomical system of units, measuring the light time per unit distance is exactly equivalent to measuring the product G×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 the secular increase in the unit distance was much larger than can be accounted for by solar radiation, +15±4 metres 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
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 the Apollo missions took about 3 days to travel) | – |
Solar radius | 0.005 | – | radius of the Sun (695500 km, 432450 mi, 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 of Earth's orbit from the Sun (sunlight travels 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 one Julian 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 | – | one parsec. The parsec is defined in terms of the astronomical unit, is used to measure distances beyond the scope of the Solar System and is about 3.26 light-years: 1 pc = 1 au/tan(1″) | [6][61] |
Proxima Centauri | 268,000 | ± 126 | distance to the nearest star to the Solar System | – |
Galactic Centre of the Milky 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
References
- ^ a b c On 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.
- ^ "Monthly Notices of the Royal Astronomical Society: Instructions for Authors". Oxford Journals. Archived from the original on 22 October 2012. Retrieved 20 March 2015.
The units of length/distance are Å, nm, μm, mm, cm, m, km, au, light-year, pc.
- ^ a b "Manuscript Preparation: AJ & ApJ Author Instructions". American Astronomical Society. Archived from the original on 21 February 2016. Retrieved 29 October 2016.
Use standard abbreviations for ... natural units (e.g., au, pc, cm).
- ISBN 978-92-822-2272-0
- ^ 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
- ^ .
- ^ a b Commission 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) - ^ Bureau 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 from the original(PDF) on 9 October 2022
- ^ "Instructions to Authors". Monthly Notices of the Royal Astronomical Society. Oxford University Press. Retrieved 5 November 2020.
The units of length/distance are Å, nm, µm, mm, cm, m, km, au, light-year, pc.
- ^ a b "The International System of Units (SI)". SI Brochure (8th ed.). BIPM. 2014 [2006]. Retrieved 3 January 2015.
- ^ "The International System of Units (SI)" (PDF). SI Brochure (9th ed.). BIPM. 2019. p. 145. Archived (PDF) from the original on 9 October 2022. Retrieved 1 July 2019.
- ^ "ISO 80000-3:2019". International Organization for Standardization. 19 May 2020. Retrieved 3 July 2020.
- ^ "Part 3: Space and time". Quantities and units. International Organization for Standardization. ISO 80000-3:2019(en). Retrieved 3 July 2020.
- ^ "HORIZONS System". Solar system dynamics. NASA: Jet Propulsion Laboratory. 4 January 2005. Retrieved 16 January 2012.
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- ISBN 978-3-89888-989-6. Archived from the originalon 30 June 2019. Retrieved 16 January 2012.
- ^ Bibcode:2012IAUJD...7E..40C. Archived(PDF) from the original on 9 October 2022. Retrieved 16 May 2013.
- ^ IAU WG on NSFA current best estimates (Report). Archived from the original on 8 December 2009. Retrieved 25 September 2009.
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- ^ "The final session of the [IAU] General Assembly" (PDF). Estrella d'Alva. 14 August 2009. p. 1. Archived from the original (PDF) on 6 July 2011.
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- ISBN 978-0-521-76917-4. and also p. 91, Summary and recommendations.
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- ^ Bibcode:1985Obs...105...32G.
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- ^ a b van Helden 1985, pp. 16–19.
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- ^ van Helden 1985, pp. 29–33.
- ^ van Helden 1985, pp. 41–53.
- ^ Bell, Trudy E. (Summer 2004). "Quest for the astronomical unit" (PDF). The Bent of Tau Beta Pi. p. 20. Archived from the original (PDF) on 24 March 2012. Retrieved 16 January 2012 – provides an extended historical discussion of the transit of Venus method.
- ^ Bibcode:1943ASPL....4..144W.
- ^ Van Helden, A. (2010). Measuring the universe: cosmic dimensions from Aristarchus to Halley. University of Chicago Press. Ch. 12.
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- ^ Pogge, Richard (May 2004). "How far to the Sun? The Venus transits of 1761 & 1769". Astronomy. Ohio State University. Retrieved 15 November 2009.
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Further reading
- Williams, D.; Davies, R. D. (1968). "A radio method for determining the astronomical unit". .
External links
- The IAU and astronomical units
- Recommendations concerning Units (HTML version of the IAU Style Manual)
- Chasing Venus, Observing the Transits of Venus
- Transit of Venus