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# Astronomical unit

The astronomical unit (AU or au or a.u. or rarely ua) is a unit of distance, approximately equal to the mean distance between Earth and Sun. The currently accepted value of the AU is 149,597,870,691 ± 30 metres (about 150 million kilometres or 93 million miles).

The abbreviation "ua" is recommended by the Bureau International des Poids et Mesures [1], but this is almost universally ignored. The International Astronomical Union website continues to recommend "au" [2].

Earth's orbit is not a circle but an ellipse; originally, the AU was defined as the length of the semimajor axis of said orbit. For greater precision, the International Astronomical Union in 1976 defined the AU as the distance from the Sun at which a particle of negligible mass, in an unperturbed circular orbit, would have an orbital period of 365.2568983 days (a Gaussian year). More accurately, it is the distance such that the heliocentric gravitational constant is equal to (0.017 202 098 95)˛ AUł/d˛.

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.

The first good measurement on the distance between Earth and the Sun was made by Eratosthenes in around 200 BC, by studying lunar eclipses, his result was 804,000,000 stadia. If we use the common attic stadion this translates to roughly 148,740,000,000 m.

A somewhat more accurate estimate can be obtained by observing the transit of Venus. This method was devised by Edmond Halley, and 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 19001901 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 kilometers. 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.

It is known that the mass of the Sun is very slowly decreasing, and therefore the orbital period of a body at a given distance is increasing. This implies that the AU is getting smaller (by about one centimetre per year) over time.

## 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 (2005) about 90 AU from the Sun.
• As of February 2005, Voyager 1 (the farthest human-made object) is 94 AU from the Sun.
• The mean diametre of the Solar system, including the Oort cloud, is ~100,000 AU.
• Proxima Centauri (the nearest star) is ~268,000 AU away from the Sun.
• The mean diametre of Betelgeuse is 2.57 AU.
• The distance from the Sun to the centre of the Milky Way is ~1,700,000,000 AU.

Some conversion factors:

See also: parsec and light year, conversion of units, orders of magnitude

## 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