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Astronomical unit
The astronomical unit (symbol: au or AU) is a unit of length defined to be exactly equal to 149597870700 m. 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.
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 In the non-normative Annex C to ISO 80000-3:2006 (later withdrawn), the symbol of the astronomical unit was also ua.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.
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 0.01720209895 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 0.01720209895 radians per day"; or alternatively that length for which the heliocentric gravitational constant (the product GM☉) is equal to (0.01720209895)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 86400 s). By 2009, the IAU had updated its standard measures to reflect improvements, and calculated the speed of light at 173.1446326847(69) au/d (TDB).
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Astronomical unit
The astronomical unit (symbol: au or AU) is a unit of length defined to be exactly equal to 149597870700 m. 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.
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.
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 0.01720209895 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 0.01720209895 radians per day"; or alternatively that length for which the heliocentric gravitational constant (the product GM☉) is equal to (0.01720209895)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 86400 s). By 2009, the IAU had updated its standard measures to reflect improvements, and calculated the speed of light at 173.1446326847(69) au/d (TDB).
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