The astronomical unit (symbol au, AU or ua) is a unit of length, roughly the distance from Earth to the Sun. However, that distance varies as Earth orbits the Sun, from a maximum (aphelion) to a minimum (perihelion) and back again once a year. Originally conceived as the average of Earth's aphelion and perihelion, it is now defined as exactly 149597870700 metres (about 150 million kilometres, or 93 million miles).The astronomical unit is used primarily as a convenient yardstick for measuring distances within the Solar System or around other stars. However, it is also a fundamental component in the definition of another unit of astronomical length, the parsec.
A variety of unit symbols and abbreviations are in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union (IAU) used the symbol A for the AU. In 2006, the International Bureau of Weights and Measures (BIPM) recommended ua as the symbol for the unit. In 2012, the IAU, noting "that various symbols are presently in use for the astronomical unit", recommended the use of the symbol "au". In the 2014 revision of the SI Brochure, the BIPM used the unit symbol "au". The symbol "AU" and abbreviation a.u. are also used. In ISO 80000-3, the symbol of the astronomical unit is "ua"
Earth's orbit around the Sun is an ellipse. The semi-major axis of this ellipse is defined to be half of the straight line segment that joins the aphelion and perihelion. 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 our 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 provides one of several ephemeris computation services.
In 1976, in order to establish a yet 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".[8][14][15] 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 basically 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 the TDB scale 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).
In 1983, the International Committee for Weights and Measures (CIPM) modified the International System of Units (SI, or "modern" metric system) to make the metre independent of physical objects entirely, because other measurements had become too precise for reference to the prototype platinum metre to remain useful. Instead, the metre was redefined in terms of the speed of light in vacuum, which could be independently determined at need. The speed of light could then be expressed exactly as c0 = 299792458 m/s, a standard also adopted by the IERS numerical standards.[18] From this definition and the 2009 IAU standard, the time for light to traverse an AU is found to be τA = 499.0047838061±0.00000001 s, more than 8 minutes. By simple multiplication then, the best IAU 2009 estimate was A = c0τA = 149597870700±3 m, based on a comparison of JPL and IAA–RAS ephemerides.
In 2006, the BIPM reported a value of the astronomical unit as 1.49597870691(6)×1011 m.[9] In the 2014 revision of the SI Brochure, the BIPM recognised the IAU's 2012 redefinition of the astronomical unit as 149597870700 m.
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 149597870700 m). The new definition also recognizes as a consequence that the astronomical unit is now to play a role of reduced importance, limited in its use to that of a convenience in some applications.
1 astronomical unit = 149597870700 metres (exactly)
≈ 92.955807 million miles
≈ 499.004 light-seconds
≈ 4.8481368 millionths of a parsec
≈ 15.812507 millionths of a light-year
This definition makes the speed of light, defined as exactly 299792458 m/s, equal to exactly 299792458 × 86400 ÷ 149597870700 or about 173.144632674240... AU/d, some 60 parts per trillion less than the 2009 estimate.
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 M☉. Neither G nor M☉ can be measured to high accuracy in SI units, 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 to the motions of the planets: the terrestrial second (TT) appears to be longer during the Northern Hemisphere winter and shorter during the Northern Hemisphere summer when compared to the "planetary second" (conventionally measured in barycentric dynamical time, TDB). This is because the distance between Earth and the Sun is not fixed (it varies between 0.9832898912 and 1.0167103335 AU) 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 to the "planetary metre" on a periodic basis.
The metre is defined to be a unit of proper length, but the SI definition does not specify the metric tensor to be used in determining it. 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".[24] As such, the metre is undefined for the purposes of measuring distances within the Solar System. The 1976 definition of the astronomical unit was incomplete because it did not specify the frame of reference in which time is to be measured, but proved practical for the calculation of ephemerides: a fuller definition that is consistent with general relativity was proposed, and "vigorous debate" ensued[26] until in August 2012 the IAU adopted the current definition of 1 astronomical unit = 149597870700 metres.
The astronomical unit is typically used for stellar system scale distances, such as the size of a protostellar disk or the heliocentric distance 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 1 arcsecond. The light year is often used in popular works, but is not an approved non-SI unit and is rarely used by professional astronomers.
Earth's orbit around the Sun is an ellipse. The semi-major axis of this ellipse is defined to be half of the straight line segment that joins the aphelion and perihelion. 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 our 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 provides one of several ephemeris computation services.
In 1976, in order to establish a yet 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".[8][14][15] 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 basically 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 the TDB scale 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).
In 1983, the International Committee for Weights and Measures (CIPM) modified the International System of Units (SI, or "modern" metric system) to make the metre independent of physical objects entirely, because other measurements had become too precise for reference to the prototype platinum metre to remain useful. Instead, the metre was redefined in terms of the speed of light in vacuum, which could be independently determined at need. The speed of light could then be expressed exactly as c0 = 299792458 m/s, a standard also adopted by the IERS numerical standards.[18] From this definition and the 2009 IAU standard, the time for light to traverse an AU is found to be τA = 499.0047838061±0.00000001 s, more than 8 minutes. By simple multiplication then, the best IAU 2009 estimate was A = c0τA = 149597870700±3 m, based on a comparison of JPL and IAA–RAS ephemerides.
In 2006, the BIPM reported a value of the astronomical unit as 1.49597870691(6)×1011 m.[9] In the 2014 revision of the SI Brochure, the BIPM recognised the IAU's 2012 redefinition of the astronomical unit as 149597870700 m.
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 149597870700 m). The new definition also recognizes as a consequence that the astronomical unit is now to play a role of reduced importance, limited in its use to that of a convenience in some applications.
1 astronomical unit = 149597870700 metres (exactly)
≈ 92.955807 million miles
≈ 499.004 light-seconds
≈ 4.8481368 millionths of a parsec
≈ 15.812507 millionths of a light-year
This definition makes the speed of light, defined as exactly 299792458 m/s, equal to exactly 299792458 × 86400 ÷ 149597870700 or about 173.144632674240... AU/d, some 60 parts per trillion less than the 2009 estimate.
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 M☉. Neither G nor M☉ can be measured to high accuracy in SI units, 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 to the motions of the planets: the terrestrial second (TT) appears to be longer during the Northern Hemisphere winter and shorter during the Northern Hemisphere summer when compared to the "planetary second" (conventionally measured in barycentric dynamical time, TDB). This is because the distance between Earth and the Sun is not fixed (it varies between 0.9832898912 and 1.0167103335 AU) 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 to the "planetary metre" on a periodic basis.
The metre is defined to be a unit of proper length, but the SI definition does not specify the metric tensor to be used in determining it. 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".[24] As such, the metre is undefined for the purposes of measuring distances within the Solar System. The 1976 definition of the astronomical unit was incomplete because it did not specify the frame of reference in which time is to be measured, but proved practical for the calculation of ephemerides: a fuller definition that is consistent with general relativity was proposed, and "vigorous debate" ensued[26] until in August 2012 the IAU adopted the current definition of 1 astronomical unit = 149597870700 metres.
The astronomical unit is typically used for stellar system scale distances, such as the size of a protostellar disk or the heliocentric distance 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 1 arcsecond. The light year is often used in popular works, but is not an approved non-SI unit and is rarely used by professional astronomers.
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