Astronomical unit

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"A.U." redirects here. For other uses of the acronym, see AU.
This article is about unit of length. For the full system of units, see Astronomical system of units.
1 astronomical unit =
SI units
149.60×10^6 km 149.60×10^9 m
Astronomical units
4.8481 × 10-6 pc 15.813×10^−6 ly
US customary / Imperial units
92.956×10^6 mi 490.81×10^9 ft

An astronomical unit (abbreviated as AU, au, a.u., or sometimes ua) is a unit of length roughly equal to the mean distance between the Earth and the Sun. It is approximately 150 million kilometres (93 million miles).

The symbol ua is recommended by the International Bureau of Weights and Measures,[1] but au is more common in Anglosphere countries. The International Astronomical Union recommends au,[2] while international standard ISO 31-1 uses AU. In general, capital letters are only used for the symbols of units which are named after individual scientists, while au or a.u. can also mean atomic unit or even arbitrary unit; however, the use of AU to refer to the astronomical unit is widespread.[3] The astronomical constant whose value is one astronomical unit is referred to as unit distance and given the symbol A.

Contents

[edit] Definition

See also: Earth's orbit

Originally, the AU was defined as the length of the semi-major axis of the Earth's elliptical orbit around the Sun. In 1976, the International Astronomical Union revised the definition of the AU for greater precision, defining it as that length for which the Gaussian gravitational constant (k) takes the value 0.017 202 098 95 when the units of measurement are the astronomical units of length, mass and time.[4] An equivalent definition is the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with a mean motion of 0.017 202 098 95 radians per day,[5] or that length for which the heliocentric gravitational constant (the product GM☉) is equal to (0.017 202 098 95)2 AU3/d2. It is approximately equal to the mean Earth–Sun distance.

[edit] Modern determinations

Very precise measurements of the relative positions of the inner planets can be made by radar and by telemetry from space probes. As with all radar measurements, these rely on measuring the time taken for light to be reflected from an object. These measured positions are then compared with those calculated by the laws of celestial mechanics: the calculated positions are often referred to as an ephemeris, and are always calculated in astronomical units. The comparison gives the speed of light in astronomical units, which is 173.144 632 6847(69) AU/d (TDB).[6] As the speed of light in metres per second (cSI) is fixed in the International System of Units, this measurement of the speed of light in AU/d (cAU) also determines the value of the astronomical unit in metres (A):

A = 86\,400 \frac{c_{\rm SI}}{c_{\rm AU}}

The currently accepted estimate of the value of the astronomical unit in metres comes from the D405 ephemeris of the Jet Propulsion Laboratory (1998):[7][8] 149 597 870 691(6) m, based on JPL ephemeris time, which is believed to identical to 2006 barycentric dynamical time (TDB) and hence to the mean duration of the terrestrial second. The 1994 IAU recommended value is 149 597 870 700(30) m based on TDB or 149 597 871 475(30) m in "SI".[9] The latter value is calculated for a hypothetical observer measuring proper length and proper time at the barycentre of the solar system.[9]

The uncertainty in any single ephemeris can be even smaller: JPL D410 ephemeris implies A = 149 597 870 697(1) m, while the EPM2004 ephemeris of the Institute of Applied Astronomy of the Russian Academy of Sciences (IAA–RAS) implies A = 149 597 870 696.0(1) m.[10] However, these estimates of the measurement uncertainty do not fully take into account the possibility of systematic differences between the different measurements. Very recent determinations include τA = 499.004 783 826(10) s (TDB), A = 149 597 870 697(3) m from the IAA–RAS EPM2006 ephemeris[11] and A = 149 597 870 700(3) m based on a comparison of JPL and IAA–RAS ephemerides.[12]

[edit] Usage

By definition, the astronomical unit is dependent on the heliocentric gravitational constant, that is the product of the gravitational constant G and the solar mass M☉. Neither G nor M☉ can be measured to high accuracy in SI units, but the value of their product is known very precisely from observing the relative positions of planets (Kepler's Third Law expressed in terms of Newtonian gravitation). Only the product is required to calculate planetary positions for an ephemeris, which explains why ephemerides are always calculated in astronomical units and not in SI units.

The calculation of ephemerides also requires a consideration of the effects of general relativity. In particular, time intervals measured on the surface of the Earth (terrestrial time, TT) are not constant when compared to the motions of the planets: the terrestrial second (TT) appears to be longer in Northern Hemisphere winter and shorter in Northern Hemisphere summer when compared to the "planetary second" (conventionally measured in barycentric dynamical time, TDB). This is because the distance between the Earth and the Sun is not fixed (it varies between 0.983 289 8912 AU and 1.016 710 3335 AU) and, when the Earth is closer to the Sun (perihelion), the Sun's gravitational field is stronger and the 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 to the "planetary metre" on a periodic basis.

The metre is defined to be a unit of proper length, but the SI definition does not specify the metric tensor to be used in determining it. 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."[13] As such, the metre is undefined for the purposes of measuring distances within the solar system. The 1976 definition of the astronomical unit is incomplete, in particular because it does not specify the frame of reference in which time is to be measured, but has proved practical for the calculation of ephemerides: a fuller definition that is consistent with general relativity has been proposed.[14]

[edit] History

Aristarchus of Samos estimated the distance to the Sun to be about 20 times the distance to the moon, whereas the true ratio is about 390. His estimate was based on the angle between the half moon and the sun, which he estimated as 87°.

According to Eusebius of Caesarea in the Praeparatio Evangelica, Eratosthenes found the distance to the sun to be "σταδιων μυριαδας τετρακοσιας και οκτωκισμυριας" (literally "of stadia myriads 400 and 80000"). This has been translated either as 4,080,000 stadia (1903 translation by Edwin Hamilton Gifford), or as 804,000,000 stadia (edition of Édouard des Places, dated 1974-1991). Using the Greek stadium of 185 to 190 metres, the former translation comes to a far too low 755,000 km whereas the second translation comes to 148.7 to 152.8 million km (accurate within 2%).

A similar measurement to that of Eratosthenes is reported in a Chinese mathematical treatise, the Zhoubi suanjing (1st c. BC), although contrary to Eratosthenes, it assumed that the Earth was flat.[15]

In the 1st century CE, Ptolemy estimated the distance as 1,210 times the Earth radius.[16] In the early 11th century, the medieval Persian astronomer, Abu Rayhan Biruni, discovered that the distance between the Earth and the Sun is much larger than Ptolemy's estimate, on the basis that Ptolemy disregarded the annual solar eclipses.[17][18] In the 14th century, the Arab astronomer Ibn al-Shatir accurately determined the distance between the Sun and the Earth as 23,212 times the Earth radius, which comes very close to the modern value of 23,481 times the Earth radius.[19]

At the time the AU was introduced, its actual value was very poorly known, but planetary distances in terms of AU could be determined from heliocentric geometry and Kepler's laws of planetary motion. The value of the AU was first estimated with reasonable accuracy by Jean Richer and Giovanni Domenico Cassini in 1672. By measuring the parallax of Mars from two locations on the Earth, they arrived at a figure of about 140 million kilometers.

A somewhat more accurate estimate can be obtained by observing the transit of Venus. Jeremiah Horrocks had attempted to produce an estimate based on his observation of the 1639 transit (published in 1662), producing a figure of 95 million kilometres. A better method was devised by James Gregory and published in his Optica Promata. It was strongly advocated by Edmond Halley and was applied to the transits of Venus observed in 1761 and 1769, and then again in 1874 and 1882.

Another method involved determining the constant of aberration, and Simon Newcomb gave great weight to this method when deriving his widely accepted value of 8.80″ for the solar parallax (close to the modern value of 8.794148″). The discovery of the near-Earth asteroid 433 Eros and its passage near the Earth in 1900–1901 allowed a considerable improvement in parallax measurement. The name "astronomical unit" appears first to have been used in 1903.[20]

[edit] Developments

The unit distance A (the value of the astronomical unit in metres) can be expressed in term of other astronomical constants:

A^3 = \frac{D^2}{G M_\odot k^2}

where G is the Newtonian gravitational constant, M☉ is the solar mass, k is the Gaussian gravitational constant and D is the time period of one day. The sun is constantly losing mass by radiating away energy,[21] 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.[22]

However, in 2004, an analysis of radiometric measurements in the inner Solar System suggested that the secular increase in the unit distance was much larger, +15±4 metres per century.[23] Later estimates based on both radiometric and angular observations lowered this estimate to +7±2 metres per century,[24] but this is still far larger than can be accounted for by solar radiation and current theories of gravitation.[25] The possible variation in the gravitational constant based on radiometric measurements is of the order of parts in 1012 per century, or lower.[26] It has been suggested that the observed increase could be explained by the Dvali–Gabadadze–Porrati multi-dimensional braneworld scenario.[27]

There have also been calls to redefine the astronomical unit in terms of a fixed number of metres.[28]

[edit] Examples

The distances are approximate mean distances. It has to be taken into consideration that the distances between celestial bodies change in time due to their orbits and other factors.

  • The Earth is 1.00 ± 0.02 AU from the Sun.
  • The Moon is 0.0026 ± 0.0001 AU from the Earth.
  • Mars is 1.52 ± 0.14 AU from the Sun.
  • Jupiter is 5.20 ± 0.05 AU from the Sun.
  • Pluto is 39.5 ± 9.8 AU from the Sun.
  • The Kuiper Belt begins at roughly 35 AU
  • Beginning of Scattered disk at 45 AU (10 AU overlap with Kuiper Belt)
  • Ending of Kuiper Belt at 50-55 AU
  • 90377 Sedna's orbit ranges between 76 and 942 AU from the Sun; Sedna is currently (as of 2006) about 90 AU from the Sun.
  • 94 AU: Termination shock between Solar winds/Interstellar winds/Interstellar medium.
  • 100 AU: Heliosheath
  • 108 AU: As of November 16, 2008, Voyager 1 is the furthest of any human-made objects from the Sun.
  • 100-150 AU: Ending of Scattered Disc
  • 500-3000 AU: Beginning of Hills cloud/"Inner Oort Cloud"
  • 20,000 AU: Ending of Hills Cloud/"Inner Oort Cloud", beginning of "Outer Oort Cloud"
  • 50,000 AU: possible closest estimate of the "Outer Oort Cloud" limits (0.8 ly)
  • 100,000 AU: possible farthest estimate of the "Outer Oort Cloud" limits (1.6 ly).
  • 125,000 AU: maximum extent of influence of the Sun's gravitational field (Hill/Roche sphere). beyond this is true interstellar space. This distance is roughly 1.8-2.0 light-years.
  • Proxima Centauri (the nearest star to Earth, excluding our own Sun) is ~268 000 AU away from the Sun.
  • The mean diameter of Betelgeuse is 5.5 AU (511,258,000 mi.).
  • The distance from the Sun to the centre of the Milky Way is approximately 1.7 × 109 AU.

[edit] Conversion factors

[edit] See also

time portal

[edit] References

  1. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), p. 126, ISBN 92-822-2213-6, http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf 
  2. ^ The IAU Style Manual (1989): The Preparation of Astronomical Papers and Reports, p. 23, http://www.iau.org/static/publications/stylemanual1989.pdf .
  3. ^ See, for example, the Merriam-Webster's Collegiate Dictionary, the American Heritage Dictionary, and the Oxford English Dictionary.
  4. ^ Resolution No. 10 of the XVIth General Assembly of the International Astronomical Union, Grenoble, 1976.
  5. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), p. 126, ISBN 92-822-2213-6, http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf .
  6. ^ "2009 Selected Astronomical Constants" in The Astronomical Almanac Online, USNO–UKHO, http://asa.usno.navy.mil/ .
  7. ^ Standish, E. M. (1998), JPL Planetary and Lunar Ephemerides, DE405/LE405, JPL IOM 312.F-98-048, http://iau-comm4.jpl.nasa.gov/de405iom/de405iom.pdf .
  8. ^ McCarthy, Dennis D.; Petit, Gérard, ed. (2004), "IERS Conventions (2003)", IERS Technical Note No. 32, Frankfurt: Bundesamts für Kartographie und Geodäsie, ISBN 3-89888-884-3, http://www.iers.org/MainDisp.csl?pid=46-25776 .
  9. ^ a b Standish, E. M. (1995), "Report of the IAU WGAS Sub-group on Numerical Standards", in Appenzeller, I., Highlights of Astronomy, Dordrecht: Kluwer, http://iau-comm4.jpl.nasa.gov/iausgnsrpt.pdf .
  10. ^ Pitjeva, E. V. (2005), "High-Precision Ephemerides of Planets—EPM and Determination of Some Astronomical Constants", Solar Syst. Res. 39 (3): 176–86, doi:10.1007/s11208-005-0033-2, http://iau-comm4.jpl.nasa.gov/EPM2004.pdf .
  11. ^ Pitjeva, E. V. (2007), "Recent Models of the Planet Motions and Fundamental Constants Determined from Position Obeservations of Planets and Spacecraft", in Capitaine, Nicole, Proceedings of the "Journées Systèmes de Référence Spatio-temporels 2007", Observatoire de Paris, p. 65, ISBN 978-2-901057-59-8, http://syrte.obspm.fr/journees2007/PDF/s2_04_Pitjeva.pdf .
  12. ^ Pitjeva, E. V.; Standish, E. M. (2009), "Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the Astronomical Unit", Celest. Mech. Dynam. Astron. 103 (4): 365–72, doi:10.1007/s10569-009-9203-8, http://www.springerlink.com/content/21885q7262104u76/ .
  13. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), pp. 166–67, ISBN 92-822-2213-6, http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf .
  14. ^ Huang, T.-Y.; Han, C.-H.; Yi, Z.-H.; Xu, B.-X. (1995), "What is the astronomical unit of length?", Astron. Astrophys. 298: 629–33, http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1995A%26A...298..629H&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf .
  15. ^ Lloyd, G. E. R. (1996). Adversaries and Authorities: Investigations into Ancient Greek and Chinese Science. Cambridge University Press. pp. 59–60. 
  16. ^ Bernard R. Goldstein, ed., The Arabic Version of Ptolemy's Planetary Hypotheses, Transactions of the American Philosophical Society, 57, 4 (1967), pp. 9-12.
  17. ^ "Khwarizm". Foundation for Science Technology and Civilisation. http://muslimheritage.com/topics/default.cfm?ArticleID=482. Retrieved on 2008-01-22. 
  18. ^ (Saliba 1980, p. 249)
  19. ^ Saliba, George (1995), A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam, New York University Press, p. 173, ISBN 0814780237 
  20. ^ Merriam-Webster's Online Dictionary.
  21. ^ Noedlinger, Peter D., "Solar Mass Loss, the Astronomical Unit, and the Scale of the Solar System", Celest. Mech. Dynam. Astron., http://arxiv.org/ftp/arxiv/papers/0801/0801.3807.pdf 
  22. ^ "AU may need to be redefined", New Scientist, 6 February 2008, http://space.newscientist.com/article/dn13286-astronomical-unit-may-need-to-be-redefined.html?feedId=online-news_rss20 .
  23. ^ Krasinsky, G. A.; Brumberg, V. A. (2004), "Secular increase of astronomical unit from analysis of the major planet motions, and its interpretation", Celest. Mech. Dynam. Astron. 90 (3-4), doi:10.1007/s10569-004-0633-z, http://www.springerlink.com/content/g5051650115444k9/ .
  24. ^ Standish, E. M. (2004), "the Astronomical Unit now", Proc. Int. Astron. Union: 163–79, doi:10.1017/S1743921305001365 .
  25. ^ Lammerzahl, C.; Preuss, O.; Dittus, H., "Is the physics within the Solar system really understood?", Proceedings of the 359th WE-Heraeus Seminar on Lasers, Clocks, and Drag-Free Technologies for Future Exploration in Space and Tests of Gravity, http://arxiv.org/pdf/gr-qc/0604052 .
  26. ^ Pitjeva, E. V. (2005), "Relativistic effects and solar oblateness from radar observations of planets and spacecraft", Astron. Lett. 31 (5): 340–49, doi:10.1134/1.1922533, http://iau-comm4.jpl.nasa.gov/EVP.pdf .
  27. ^ Iorio, Lorenzo (2005), "Secular increase of the astronomical unit and perihelion precessions as tests of the Dvali–Gabadadze–Porrati multi-dimensional braneworld scenario", J. Cosmol. Astroparticle Phys., doi:10.1088/1475-7516/2005/09/006, JCAP09(2005)006, http://arxiv.org/PS_cache/gr-qc/pdf/0508/0508047v2.pdf .
  28. ^ Capitaine, N.; Guinot, B. (2008), "The astronomical units", Proceedings of the "Journées Systèmes de référence spatio-temporels 2008", http://arxiv.org/PS_cache/arxiv/pdf/0812/0812.2970v1.pdf .

[edit] External links

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