# astronomical unit

Convert between astronomical units and other major units of astronomical distance.

A unit of distance = 149 597 870 700 meters, by vote of the 28th General Assembly of the International Astronomical Union in August 2012¹. Symbol, au; formerly A, AU or a.u.. The value had previously been adopted in IAU 2009 Resolution B2. (The symbol “ua”, specified by the BIPM for use with SI, has not been accepted by astronomers.) Formerly, in concept, the astronomical unit was roughly equal to the average distance from the earth to the sun.

In 1976 the 16th General Assembly of the IAU defined the astronomical unit of length (as part of the International System of Astronomical Constants) as “that length for which the Gaussian gravitational constant (k) takes the value 0.0172 020 989 5 when the units of measurement are the astronomical units of length, mass and time.”²

The astronomical unit of time is the day, defined as 86,400 seconds (the second as defined in SI), and the astronomical unit of mass is the mass of the sun, by definition 1.9891 × 1030 kilograms. The value chosen for the Gaussian gravitational constant made an astronomical unit approximately the earth-sun distance. The value of the astronomical unit in meters, using the 1976 definition, is  1.495 978 70 × 1011 meters.

The 2012 IAU resolution redefining the astronomical unit also deleted the Gaussian gravitational constant from the system of astronomical constants, since it no longer plays any role.

The astronomical unit was once defined as the radius of a circular orbit in which a body of negligible mass, and free from perturbations, would revolve around the sun in 2π/k days, where k is the Gaussian gravitational constant.

In the preparation of ephemerides in the 1990s, it was found necessary to use the value 1.495 978 706 6 × 1011 meters.

In its early days the astronomical unit was not nearly so precisely defined. In 1922, the Commission des notations, des unités et de l'économie des publications of the International Astronomical Union accepted, and the First General Assembly adopted, the recommendation of an American committee3 that 1) dimensions of celestial bodies, velocities, etc. be described in kilometers, 2) “la distance moyenne du soleil à la terre, ou unité astronomique” [the average distance between the sun and earth, or astronomical unit] be used for distances in the solar system and 3) the parsec be used for distances to stars.4

1. XXVIIIth General Assembly of the International Astronomical Union, in Beijing, China.
Resolution B2.: Recommande 1. que l’unité astronomique soit re-définie comme une unité conventionnelle de longueur égale à 149 597 870 700 m exactement, selon la valeur adoptée dans la Résolution UAI 2009 B2, … 5. que le seul symbole “au” soit utilisé pour l’unité astronomique.

All resolutions are available at the IAU's website http://www.iau.org/administration/resolutions/general_assemblies/

2. International Astronomical Union.
Transactions of the International Astronomical Union, XVIB 58 (1977).

3. Proceedings of the National Academy of Sciences, volume 6, page 360 (1920)

4. A. Fowler, ed.
First General Assembly, held at Rome, May 2nd to May 10th, 1922.
Transactions of the International Astronomical Union. Volume 1.
London: Imperial College Bookstall, no date [1922 ?].
Pages 23, 138, 207.