The symbol ua is recommended by the Bureau International des Poids et Mesures but in anglophone countries the reverse - au - is more common. The International Astronomical Union recommends au and 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.
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 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). This definition gives a value that is slightly less than the mean Earth-Sun distance. An alternative way of stating the definition is that an AU is the distance at which the heliocentric gravitational constant (the product GM☉) is equal to (0.017 202 098 95)² AU³/d².
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%).
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 kilometres.
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. 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.
Some conversion factors: