The astronomical unit (symbol: au or AU) is a unit of length defined as . Historically, the astronomical unit was conceived as the average Earth-Sun distance (the average of Earth's aphelion and perihelion), before its modern redefinition in 2012.
The astronomical unit is used primarily for measuring distances within the Solar System or around other stars. It is also a fundamental component in the definition of another unit of astronomical length, the parsec. One au is approximately equivalent to 499 light-seconds.
History of symbol usage A variety of unit symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union (IAU) had used the symbol A to denote a length equal to the astronomical unit. In the astronomical literature, the symbol AU is common. In 2006, the International Bureau of Weights and Measures (BIPM) had recommended ua as the symbol for the unit, from the French "unité astronomique". In the non-normative Annex C to ISO 80000-3:2006 (later withdrawn), the symbol of the astronomical unit was also ua.
In 2012, the IAU, noting "that various symbols are presently in use for the astronomical unit", recommended the use of the symbol "au". The scientific journals published by the American Astronomical Society and the Royal Astronomical Society subsequently adopted this symbol. In the 2014 revision and 2019 edition of the SI Brochure, the BIPM used the unit symbol "au". ISO 80000-3:2019, which replaces ISO 80000-3:2006, does not mention the astronomical unit.
Development of unit definition
Earth's orbit around the Sun is an ellipse. The semi-major axis of this elliptic orbit is defined to be half of the straight line segment that joins the perihelion and aphelion. The centre of the Sun lies on this straight line segment, but not at its midpoint. Because ellipses are well-understood shapes, measuring the points of its extremes defined the exact shape mathematically, and made possible calculations for the entire orbit as well as predictions based on observation. In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, defining times and places for observing the largest parallax (apparent shifts of position) in nearby stars. Knowing Earth's shift and a star's shift enabled the star's distance to be calculated. But all measurements are subject to some degree of error or uncertainty, and the uncertainties in the length of the astronomical unit only increased uncertainties in the stellar distances. Improvements in precision have always been a key to improving astronomical understanding. Throughout the twentieth century, measurements became increasingly precise and sophisticated, and ever more dependent on accurate observation of the effects described by Einstein's theory of relativity and upon the mathematical tools it used.
Improving measurements were continually checked and cross-checked by means of improved understanding of the laws of celestial mechanics, which govern the motions of objects in space. The expected positions and distances of objects at an established time are calculated (in au) from these laws, and assembled into a collection of data called an ephemeris. NASA's Jet Propulsion Laboratory HORIZONS System provides one of several ephemeris computation services.
In 1976, to establish a more precise measure for the astronomical unit, the IAU formally adopted a new definition. Although directly based on the then-best available observational measurements, the definition was recast in terms of the then-best mathematical derivations from celestial mechanics and planetary ephemerides. It stated that "the astronomical unit of length is that length (A) for which the Gaussian gravitational constant (k) takes the value when the units of measurement are the astronomical units of length, mass and time". Equivalently, by this definition, one au is "the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass, moving with an angular frequency of "; or alternatively that length for which the heliocentric gravitational constant (the product G) is equal to ()2 au3/d2, when the length is used to describe the positions of objects in the Solar System.
Subsequent explorations of the Solar System by space probes made it possible to obtain precise measurements of the relative positions of the inner planets and other objects by means of radar and telemetry. As with all radar measurements, these rely on measuring the time taken for photons to be reflected from an object. Because all photons move at the speed of light in vacuum, a fundamental constant of the universe, the distance of an object from the probe is calculated as the product of the speed of light and the measured time. However, for precision the calculations require adjustment for things such as the motions of the probe and object while the photons are transiting. In addition, the measurement of the time itself must be translated to a standard scale that accounts for relativistic time dilation. Comparison of the ephemeris positions with time measurements expressed in Barycentric Dynamical Time (TDB) leads to a value for the speed of light in astronomical units per day (of ). In 2009, the IAU reported the "light-time for unit distance" as (TDB).
In 1983, the BIPM modified the International System of Units (SI) to make the metre defined as the distance travelled in a vacuum by light in 1 / . This replaced the previous definition, valid between 1960 and 1983, which was that the metre equalled a certain number of wavelengths of a certain emission line of krypton-86. (The reason for the change was an improved method of measuring the speed of light.) The speed of light could then be expressed exactly as c0 = , a standard also adopted by the IERS numerical standards. For complete document see From this definition and the 2009 IAU standard, the time for light to traverse an astronomical unit is found to be τA = , which is slightly more than 8 minutes 19 seconds. By multiplication, the best IAU 2009 estimate was A = c0τA = , based on a comparison of Jet Propulsion Laboratory and IAA–RAS ephemerides.
In 2006, the BIPM reported a value of the astronomical unit as . In the 2014 revision of the SI Brochure, the BIPM recognised the IAU's 2012 redefinition of the astronomical unit as .
This estimate was still derived from observation and measurements subject to error, and based on techniques that did not yet standardize all relativistic effects, and thus were not constant for all observers. In 2012, finding that the equalization of relativity alone would make the definition overly complex, the IAU simply used the 2009 estimate to redefine the astronomical unit as a conventional unit of length directly tied to the metre (exactly ). The new definition recognizes as a consequence that the astronomical unit has reduced importance, limited in use to a convenience in some applications.
{| style="border-spacing:0" |- |rowspan=7 style="vertical-align:top; padding-right:0"|1 astronomical unit |= metres (by definition) |- |= (exactly) |- |≈ |- |≈ light-seconds |- |≈ |- |≈
Usage and significance With the definitions used before 2012, the astronomical unit was dependent on the heliocentric gravitational constant, that is the product of the gravitational constant, G, and the solar mass, . Neither G nor can be measured to high accuracy separately, 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, so ephemerides are 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 Earth's surface (Terrestrial Time, TT) are not constant when compared with the motions of the planets: the terrestrial second (TT) appears to be longer near January and shorter near July when compared with the "planetary second" (conventionally measured in TDB). This is because the distance between Earth and the Sun is not fixed (it varies between and ) and, when Earth is closer to the Sun (perihelion), the Sun's gravitational field is stronger and 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 with the "planetary metre" on a periodic basis.
The metre is defined to be a unit of proper length. 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". As such, a distance within the Solar System without specifying the frame of reference for the measurement is problematic. The 1976 definition of the astronomical unit was incomplete because it did not specify the frame of reference in which to apply the measurement, but proved practical for the calculation of ephemerides: a fuller definition that is consistent with general relativity was proposed, and "vigorous debate" ensued and also p. 91, Summary and recommendations. until August 2012 when the IAU adopted the current definition of 1 astronomical unit = metres.
The astronomical unit is typically used for stellar system scale distances, such as the size of a protostellar disk or the heliocentric distance (distance from the Sun's centre) of an asteroid, whereas other units are used for other distances in astronomy. The astronomical unit is too small to be convenient for interstellar distances, where the parsec and light-year are widely used. The parsec (parallax arcsecond) is defined in terms of the astronomical unit, being the distance of an object with a parallax of . The light-year is often used in popular works, but is not an approved non-SI unit and is rarely used by professional astronomers.
When simulating a numerical model of the Solar System, the astronomical unit provides an appropriate scale that minimizes (overflow, underflow and truncation) errors in floating point calculations.
History Many early measurements of the Earth-Sun distance are wildly incorrect, primarily because the measurements rely on the ratio of the diameter of the Earth to the distance of the Sun. Since this ratio is 1/12000, small errors in the size of the Earth lead to large errors in the Earth-Sun distance.Hughes, D. W. (2001). Six stages in the history of the astronomical unit. Journal of Astronomical History and Heritage (ISSN 1440-2807), Vol. 4, No. 1, p. 15-28 (2001)., 4, 15-28.
Around 280 BCE, Aristarchus carefully measured the Moon-Earth-Sun angle when the Moon is in its first quarter and used this to estimate the distance to the Sun. The exact timing and angle measurement are essential. He estimated the angle at as (the true value being close to ) and reported in On the Sizes and Distances of the Sun and Moon the distance to the Sun is 18 to 20 times the distance to the Moon, whereas the true ratio is about . Depending on the distance that Aristarchus used for the distance to the Moon, his calculated distance to the Sun would fall between and Earth radii.
Hipparchus gave an estimate of the distance of Earth from the Sun, quoted by Pappus as equal to 490 Earth radii. According to the conjectural reconstructions of Noel Swerdlow and G. J. Toomer, this was derived from his assumption of a "least perceptible" solar parallax of .
A Chinese mathematical treatise, the Zhoubi Suanjing (), shows how the distance to the Sun can be computed geometrically, using the different lengths of the noontime shadows observed at three places li apart and the assumption that Earth is flat.