Astronomical unit

The astronomical unit (AU or au or a.u. or sometimes ua) is a unit of length nearly equal to the semi-major axis of Earth's orbit around the Sun. The currently accepted value of the AU is 149 597 870 691 ± 30 metres (about 150 million kilometres or 93 million miles).

The symbol "ua" is recommended by the Bureau International des Poids et Mesures [1], but in the United States and other anglophone countries the reverse usage is more common. The International Astronomical Union recommends "au" [2] and international standard ISO 31-1 uses "AU".

The distance

Originally, the AU was defined as the length of the semimajor axis of the Earth's elliptical orbit. In 1976, the International Astronomical Union revised the definition of the AU for greater precision, defining it as the distance from the centre of the Sun at which a particle of negligible mass, in an unperturbed circular orbit, would have an orbital period of 365.2568983 days (one Gaussian year). More accurately, it is the distance at which the heliocentric gravitational constant (the product GM_☉) is equal to (0.017 202 098 95)² AU³/d².

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 E. H. Gifford), or as 804,000,000 stadia (edition of Edouard des Places, dated 1974-1991). Using the Greek stadium of 185 metres, the former translation comes to a far-too-low 755,000 km, whereas the second translation comes to a very accurate 149 million km.

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 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. This 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. More recently very precise measurements have been carried out by radar and by telemetry from space probes.

While the value of the astronomical unit is now known to great precision, the value of the mass of the Sun is not, because of uncertainty in the value of the gravitational constant. Because the gravitational constant is known to only five or six significant digits while the positions of the planets are known to 11 or 12 digits, calculations in celestial mechanics are typically performed in solar masses and astronomical units rather than in kilograms and kilometres. This approach makes all results dependent on the gravitational constant. A conversion to SI units would separate the results from the gravitational constant, at the cost of introducing additional uncertainty by assigning a specific value to that unknown constant.

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.
• 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.
• As of August 2006, Voyager 1 is 100 AU from the Sun, the furthest of any man-made object.
• Proxima Centauri (the nearest star) is ~268 000 AU away from the Sun.
• The mean diameter of Betelgeuse is 2.57 AU.
• The distance from the Sun to the centre of the Milky Way is approximately 1.7×10⁹ AU.
• The Earth is actually 147,104,753 km away from the Sun on 29 December and 152,091,803 km away from the Sun on 30 June.

Some conversion factors:

• 1 AU = 149 597 870.691 ± 0.030 km ≈ 92 955 807 miles ≈ 8.317 light minutes ≈ 499 light-seconds
• 1 light-second ≈ 0.002 AU
• 1 gigameter ≈ 0.00(6) AU
• 1 light-minute ≈ 0.120 AU
• 1 microparsec ≈ 0.206 AU
• 1 terameter ≈ 6.685 AU
• 1 light-hour ≈ 7.214 AU
• 1 light-day ≈ 173.263 AU
• 1 milliparsec ≈ 206.265 AU
• 1 light-week ≈ 1212.84 AU
• 1 light-month ≈ 5197.9 AU
• 1 light-year ≈ 63 241 AU
• 1 parsec ≈ 206 265 AU

See also

• Conversion of units
• Light year
• Orders of magnitude
• Parsec

References

• E. Myles Standish. "Report of the IAU WGAS Sub-group on Numerical Standards". In Highlights of Astronomy, I. Appenzeller, ed. Dordrecht: Kluwer Academic Publishers, 1995. (Complete report available online: PostScript. Tables from the report also available: Astrodynamic Constants and Parameters)
• D. D. McCarthy ed., IERS Conventions (1996), IERS Technical Note 21, Observatoire de Paris, July 1996

External links

• Units outside the SI (at the NIST web site)
• Recommendations concerning Units (at the IAU web site)
• Solar Mass Loss, the Astronomical Unit, and the Scale of the Solar System (a discussion of the relation between the AU and other quantities)

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