Astronomical unit

Last updated

Astronomical unit
Astronomical unit.png
The grey line indicates the Earth–Sun distance, which on average is about 1 astronomical unit.
General information
Unit system Astronomical system of units
(Accepted for use with the SI)
Unit of length
Symbolau or AU or AU
1 au or AU or AU in ...... is equal to ...
    metric (SI) units   1.495978707×1011  m
    imperial  &  US  units   9.2956×107  mi
    astronomical units    4.8481×10−6  pc
   1.5813×10−5  ly
   215.03  R

The astronomical unit (symbol: au, [1] [2] [3] [4] or AU) is a unit of length defined to be exactly equal to 149,597,870,700 m. [5] Historically, the astronomical unit was originally 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. [6] One au is equivalent to 499 light-seconds to within 10 parts per million.

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. [7] In the astronomical literature, the symbol AU was (and remains) 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". [8] In the non-normative Annex C to ISO 80000-3:2006 (now withdrawn), the symbol of the astronomical unit was also ua.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". [1] The scientific journals published by the American Astronomical Society and the Royal Astronomical Society subsequently adopted this symbol. [3] [9] In the 2014 revision and 2019 edition of the SI Brochure, the BIPM used the unit symbol "au". [10] [11] ISO 80000-3:2019, which replaces ISO 80000-3:2006, does not mention the astronomical unit. [12] [13]

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. [14]

In 1976, to establish an even 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". [7] [15] [16] 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"; [17] 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 86,400 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). [18]

In 1983, the CIPM modified the International System of Units (SI) to make the metre defined as the distance travelled in a vacuum by light in 1 / 299,792,458 s. 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 = 299,792,458 m/s, a standard also adopted by the IERS numerical standards. [19] From this definition and the 2009 IAU standard, the time for light to traverse an astronomical unit is found to be τA = 499.0047838061±0.00000001 s, which is slightly more than 8 minutes 19 seconds. By multiplication, the best IAU 2009 estimate was A = c0τA = 149,597,870,700±3 m, [20] based on a comparison of Jet Propulsion Laboratory and IAA–RAS ephemerides. [21] [22] [23]

In 2006, the BIPM reported a value of the astronomical unit as 1.49597870691(6)×1011 m. [8] In the 2014 revision of the SI Brochure, the BIPM recognised the IAU's 2012 redefinition of the astronomical unit as 149,597,870,700 m. [10]

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 149,597,870,700 m). [20] [24] 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. [20]

1 astronomical unit = 149,597,870,700 metres (by definition)
= 149,597,870.7 kilometres (exactly)
92,955,807.2730 miles
499.004783836 light-seconds
1.58125074098×10−5 light-years
4.84813681113×10−6 parsecs

This definition makes the speed of light, defined as exactly 299,792,458 m/s, equal to exactly 299,792,458 × 86,400 ÷ 149,597,870,700 or about 173.144632674240 au/d, some 60 parts per trillion less than the 2009 estimate.

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, M. Neither G nor M 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 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 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". [25] 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, [26] and "vigorous debate" ensued [27] until August 2012 when the IAU adopted the current definition of 1 astronomical unit = 149,597,870,700 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″. The light-year is often used in popular works, but is not an approved non-SI unit and is rarely used by professional astronomers. [28]

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.


The book On the Sizes and Distances of the Sun and Moon , which is ascribed to Aristarchus, says the distance to the Sun is 18 to 20 times the distance to the Moon, whereas the true ratio is about 389.174. The latter estimate was based on the angle between the half-moon and the Sun, which he estimated as 87° (the true value being close to 89.853°). Depending on the distance that van Helden assumes Aristarchus used for the distance to the Moon, his calculated distance to the Sun would fall between 380 and 1,520 Earth radii. [29]

According to Eusebius in the Praeparatio evangelica (Book XV, Chapter 53), Eratosthenes found the distance to the Sun to be "σταδιων μυριαδας τετρακοσιας και οκτωκισμυριας" (literally "of stadia myriads 400 and 80,000″) but with the additional note that in the Greek text the grammatical agreement is between myriads (not stadia) on the one hand and both 400 and 80,000 on the other, as in Greek, unlike English, all three (or all four if one were to include stadia) words are inflected. This has been translated either as 4080000 stadia (1903 translation by Edwin Hamilton Gifford), or as 804,000,000stadia (edition of Édourad des Places  [ de ], dated 1974–1991). Using the Greek stadium of 185 to 190 metres, [30] [31] the former translation comes to 754,800 km to 775,200 km, which is far too low, whereas the second translation comes to 148.7 to 152.8 billion metres (accurate within 2%). [32] Hipparchus also 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 7 . [33]

A Chinese mathematical treatise, the Zhoubi Suanjing (c.1st century BCE), shows how the distance to the Sun can be computed geometrically, using the different lengths of the noontime shadows observed at three places 1,000 li apart and the assumption that Earth is flat. [34]

Distance to the Sun
estimated by
EstimateIn auPercentage error
Aristarchus (3rd century BCE)
(in On Sizes)  
13′24″7′12″256.5477.80.0110.020-98.9% to -98%
Archimedes (3rd century BCE)
(in The Sand Reckoner)
Hipparchus (2nd century BCE)7′4900.021-97.9%
Posidonius (1st century BCE)
(quoted by coeval Cleomedes)
Ptolemy (2nd century)2′ 50″1,2100.052-94.8%
Godefroy Wendelin (1635)15″14,0000.597-40.3%
Jeremiah Horrocks (1639)15″14,0000.597-40.3%
Christiaan Huygens (1659)8.2″25,086 [35] 1.0686.8%
Cassini & Richer (1672)9.5″21,7000.925-7.5%
Flamsteed (1672)9.5″21,7000.925-7.5%
Jérôme Lalande (1771)8.6″24,0001.0232.3%
Simon Newcomb (1895)8.80″23,4400.9994-0.06%
Arthur Hinks (1909)8.807″23,4200.9985-0.15%
H. Spencer Jones (1941)8.790″23,4661.00050.05%
modern astronomy 8.79414323,4551.0000

In the 2nd century CE, Ptolemy estimated the mean distance of the Sun as 1,210 times Earth's radius. [36] [37] To determine this value, Ptolemy started by measuring the Moon's parallax, finding what amounted to a horizontal lunar parallax of 1° 26′, which was much too large. He then derived a maximum lunar distance of 64+1/6 Earth radii. Because of cancelling errors in his parallax figure, his theory of the Moon's orbit, and other factors, this figure was approximately correct. [38] [39] He then measured the apparent sizes of the Sun and the Moon and concluded that the apparent diameter of the Sun was equal to the apparent diameter of the Moon at the Moon's greatest distance, and from records of lunar eclipses, he estimated this apparent diameter, as well as the apparent diameter of the shadow cone of Earth traversed by the Moon during a lunar eclipse. Given these data, the distance of the Sun from Earth can be trigonometrically computed to be 1,210 Earth radii. This gives a ratio of solar to lunar distance of approximately 19, matching Aristarchus's figure. Although Ptolemy's procedure is theoretically workable, it is very sensitive to small changes in the data, so much so that changing a measurement by a few per cent can make the solar distance infinite. [38]

After Greek astronomy was transmitted to the medieval Islamic world, astronomers made some changes to Ptolemy's cosmological model, but did not greatly change his estimate of the Earth–Sun distance. For example, in his introduction to Ptolemaic astronomy, al-Farghānī gave a mean solar distance of 1,170 Earth radii, whereas in his zij , al-Battānī used a mean solar distance of 1,108 Earth radii. Subsequent astronomers, such as al-Bīrūnī, used similar values. [40] Later in Europe, Copernicus and Tycho Brahe also used comparable figures (1,142 and 1,150 Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century. [41]

Johannes Kepler was the first to realize that Ptolemy's estimate must be significantly too low (according to Kepler, at least by a factor of three) in his Rudolphine Tables (1627). Kepler's laws of planetary motion allowed astronomers to calculate the relative distances of the planets from the Sun, and rekindled interest in measuring the absolute value for Earth (which could then be applied to the other planets). The invention of the telescope allowed far more accurate measurements of angles than is possible with the naked eye. Flemish astronomer Godefroy Wendelin repeated Aristarchus’ measurements in 1635, and found that Ptolemy's value was too low by a factor of at least eleven.

A somewhat more accurate estimate can be obtained by observing the transit of Venus. [42] By measuring the transit in two different locations, one can accurately calculate the parallax of Venus and from the relative distance of Earth and Venus from the Sun, the solar parallax α (which cannot be measured directly due to the brightness of the Sun [43] ). Jeremiah Horrocks had attempted to produce an estimate based on his observation of the 1639 transit (published in 1662), giving a solar parallax of 15 , similar to Wendelin's figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by

The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of 15″ is equivalent to an Earth–Sun distance of 13,750 Earth radii.

Christiaan Huygens believed that the distance was even greater: by comparing the apparent sizes of Venus and Mars, he estimated a value of about 24,000 Earth radii, [35] equivalent to a solar parallax of 8.6″. Although Huygens' estimate is remarkably close to modern values, it is often discounted by historians of astronomy because of the many unproven (and incorrect) assumptions he had to make for his method to work; the accuracy of his value seems to be based more on luck than good measurement, with his various errors cancelling each other out.

Transits of Venus across the face of the Sun were, for a long time, the best method of measuring the astronomical unit, despite the difficulties (here, the so-called "black drop effect") and the rarity of observations. Venustransit 2004-06-08 07-44.jpg
Transits of Venus across the face of the Sun were, for a long time, the best method of measuring the astronomical unit, despite the difficulties (here, the so-called "black drop effect") and the rarity of observations.

Jean Richer and Giovanni Domenico Cassini measured the parallax of Mars between Paris and Cayenne in French Guiana when Mars was at its closest to Earth in 1672. They arrived at a figure for the solar parallax of 9.5″, equivalent to an Earth–Sun distance of about 22,000 Earth radii. They were also the first astronomers to have access to an accurate and reliable value for the radius of Earth, which had been measured by their colleague Jean Picard in 1669 as 3,269,000 toises . This same year saw another estimate for the astronomical unit by John Flamsteed, which accomplished it alone by measuring the martian diurnal parallax. [44] Another colleague, Ole Rømer, discovered the finite speed of light in 1676: the speed was so great that it was usually quoted as the time required for light to travel from the Sun to the Earth, or "light time per unit distance", a convention that is still followed by astronomers today.

A better method for observing Venus transits was devised by James Gregory and published in his Optica Promata (1663). It was strongly advocated by Edmond Halley [45] and was applied to the transits of Venus observed in 1761 and 1769, and then again in 1874 and 1882. Transits of Venus occur in pairs, but less than one pair every century, and observing the transits in 1761 and 1769 was an unprecedented international scientific operation including observations by James Cook and Charles Green from Tahiti. Despite the Seven Years' War, dozens of astronomers were dispatched to observing points around the world at great expense and personal danger: several of them died in the endeavour. [46] The various results were collated by Jérôme Lalande to give a figure for the solar parallax of 8.6″. Karl Rudolph Powalky had made an estimate of 8.83″ in 1864. [47]


Another method involved determining the constant of aberration. 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 8.794143), although Newcomb also used data from the transits of Venus. Newcomb also collaborated with A. A. Michelson to measure the speed of light with Earth-based equipment; combined with the constant of aberration (which is related to the light time per unit distance), this gave the first direct measurement of the Earth–Sun distance in metres. Newcomb's value for the solar parallax (and for the constant of aberration and the Gaussian gravitational constant) were incorporated into the first international system of astronomical constants in 1896, [48] which remained in place for the calculation of ephemerides until 1964. [49] The name "astronomical unit" appears first to have been used in 1903. [50] [ failed verification ]

The discovery of the near-Earth asteroid 433 Eros and its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement. [51] Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931. [43] [52]

Direct radar measurements of the distances to Venus and Mars became available in the early 1960s. Along with improved measurements of the speed of light, these showed that Newcomb's values for the solar parallax and the constant of aberration were inconsistent with one another. [53]


The astronomical unit is used as the baseline of the triangle to measure stellar parallaxes (distances in the image are not to scale) Stellarparallax parsec1.svg
The astronomical unit is used as the baseline of the triangle to measure stellar parallaxes (distances in the image are not to scale)

The unit distance A (the value of the astronomical unit in metres) can be expressed in terms of other astronomical constants:

where G is the Newtonian constant of gravitation, M is the solar mass, k is the numerical value of Gaussian gravitational constant and D is the time period of one day. [1] The Sun is constantly losing mass by radiating away energy, [54] so the orbits of the planets are steadily expanding outward from the Sun. This has led to calls to abandon the astronomical unit as a unit of measurement. [55]

As the speed of light has an exact defined value in SI units and the Gaussian gravitational constant k is fixed in the astronomical system of units, measuring the light time per unit distance is exactly equivalent to measuring the product G×M in SI units. Hence, it is possible to construct ephemerides entirely in SI units, which is increasingly becoming the norm.

A 2004 analysis of radiometric measurements in the inner Solar System suggested that the secular increase in the unit distance was much larger than can be accounted for by solar radiation, +15±4 metres per century. [56] [57]

The measurements of the secular variations of the astronomical unit are not confirmed by other authors and are quite controversial. Furthermore, since 2010, the astronomical unit has not been estimated by the planetary ephemerides. [58]


The following table contains some distances given in astronomical units. It includes some examples with distances that are normally not given in astronomical units, because they are either too short or far too long. Distances normally change over time. Examples are listed by increasing distance.

Object or lengthLength or distance in auRangeComment and reference pointRefs
Light-second 0.002distance light travels in one second
Lunar distance 0.0026average distance from Earth (which the Apollo missions took about 3 days to travel)
Solar radius 0.005radius of the Sun (695500 km, 432450 mi, a hundred times the radius of Earth or ten times the average radius of Jupiter)
Light-minute 0.12distance light travels in one minute
Mercury 0.39average distance from the Sun
Venus 0.72average distance from the Sun
Earth 1.00average distance of Earth's orbit from the Sun (sunlight travels for 8 minutes and 19 seconds before reaching Earth)
Mars 1.52average distance from the Sun
Jupiter 5.2average distance from the Sun
Light-hour 7.2distance light travels in one hour
Saturn 9.5average distance from the Sun
Uranus 19.2average distance from the Sun
Kuiper belt 30Inner edge begins at approximately 30 au [59]
Neptune 30.1average distance from the Sun
Eris 67.8average distance from the Sun
Voyager 2 134distance from the Sun in August 2023 [60]
Voyager 1 161distance from the Sun in August 2023 [60]
Light-day 173distance light travels in one day
Light-year 63,241distance light travels in one Julian year (365.25 days)
Oort cloud 75,000± 25,000distance of the outer limit of Oort cloud from the Sun (estimated, corresponds to 1.2 light-years)
Parsec 206,265one parsec. The parsec is defined in terms of the astronomical unit, is used to measure distances beyond the scope of the Solar System and is about 3.26 light-years: 1 pc = 1 au/tan(1″) [6] [61]
Proxima Centauri 268,000± 126distance to the nearest star to the Solar System
Galactic Centre of the Milky Way 1,700,000,000distance from the Sun to the centre of the Milky Way
Note: figures in this table are generally rounded, estimates, often rough estimates, and may considerably differ from other sources. Table also includes other units of length for comparison.

See also

Related Research Articles

In astronomy, absolute magnitude is a measure of the luminosity of a celestial object on an inverse logarithmic astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent magnitude that the object would have if it were viewed from a distance of exactly 10 parsecs, without extinction of its light due to absorption by interstellar matter and cosmic dust. By hypothetically placing all objects at a standard reference distance from the observer, their luminosities can be directly compared among each other on a magnitude scale. For Solar System bodies that shine in reflected light, a different definition of absolute magnitude (H) is used, based on a standard reference distance of one astronomical unit.

The term ephemeris time can in principle refer to time in association with any ephemeris. In practice it has been used more specifically to refer to:

  1. a former standard astronomical time scale adopted in 1952 by the IAU, and superseded during the 1970s. This time scale was proposed in 1948, to overcome the disadvantages of irregularly fluctuating mean solar time. The intent was to define a uniform time based on Newtonian theory. Ephemeris time was a first application of the concept of a dynamical time scale, in which the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via the dynamical theory of its motion.
  2. a modern relativistic coordinate time scale, implemented by the JPL ephemeris time argument Teph, in a series of numerically integrated Development Ephemerides. Among them is the DE405 ephemeris in widespread current use. The time scale represented by Teph is closely related to, but distinct from, the TCB time scale currently adopted as a standard by the IAU.
<span class="mw-page-title-main">Parsec</span> Unit of length used in astronomy

The parsec is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to 3.26 light-years or 206,265 astronomical units (AU), i.e. 30.9 trillion kilometres. The parsec unit is obtained by the use of parallax and trigonometry, and is defined as the distance at which 1 AU subtends an angle of one arcsecond. The nearest star, Proxima Centauri, is about 1.3 parsecs from the Sun: from that distance, the gap between the Earth and the Sun spans slightly less than 1/3600 of one degree of view. Most stars visible to the naked eye are within a few hundred parsecs of the Sun, with the most distant at a few thousand parsecs, and the Andromeda Galaxy at over 700,000 parsecs.

Terrestrial Time (TT) is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of Earth. For example, the Astronomical Almanac uses TT for its tables of positions (ephemerides) of the Sun, Moon and planets as seen from Earth. In this role, TT continues Terrestrial Dynamical Time, which succeeded ephemeris time (ET). TT shares the original purpose for which ET was designed, to be free of the irregularities in the rotation of Earth.

<span class="mw-page-title-main">Gravitational constant</span> Physical constant relating the gravitational force between objects to their mass and distance

The gravitational constant, denoted by the capital letter G, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity.

A time standard is a specification for measuring time: either the rate at which time passes or points in time or both. In modern times, several time specifications have been officially recognized as standards, where formerly they were matters of custom and practice. An example of a kind of time standard can be a time scale, specifying a method for measuring divisions of time. A standard for civil time can specify both time intervals and time-of-day.

<span class="mw-page-title-main">Luminosity</span> Measurement of radiant electromagnetic power emitted by an object

Luminosity is an absolute measure of radiated electromagnetic energy (light) per unit time, and is synonymous with the radiant power emitted by a light-emitting object. In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a star, galaxy, or other astronomical objects.

<span class="mw-page-title-main">Solar mass</span> Standard unit of mass in astronomy

The solar mass (M) is a standard unit of mass in astronomy, equal to approximately 2×1030 kg. It is approximately equal to the mass of the Sun. It is often used to indicate the masses of other stars, as well as stellar clusters, nebulae, galaxies and black holes. This equates to about two nonillion (short scale), two quintillion (long scale) kilograms, 2000 quettagrams, or 2 quettakilograms:

The light-second is a unit of length useful in astronomy, telecommunications and relativistic physics. It is defined as the distance that light travels in free space in one second, and is equal to exactly 299792458 m.

<span class="mw-page-title-main">Gaussian gravitational constant</span> Constant used in orbital mechanics

The Gaussian gravitational constant is a parameter used in the orbital mechanics of the Solar System. It relates the orbital period to the orbit's semi-major axis and the mass of the orbiting body in Solar masses.

Barycentric Dynamical Time is a relativistic coordinate time scale, intended for astronomical use as a time standard to take account of time dilation when calculating orbits and astronomical ephemerides of planets, asteroids, comets and interplanetary spacecraft in the Solar System. TDB is now defined as a linear scaling of Barycentric Coordinate Time (TCB). A feature that distinguishes TDB from TCB is that TDB, when observed from the Earth's surface, has a difference from Terrestrial Time (TT) that is about as small as can be practically arranged with consistent definition: the differences are mainly periodic, and overall will remain at less than 2 milliseconds for several millennia.

The astronomical system of units, formerly called the IAU (1976) System of Astronomical Constants, is a system of measurement developed for use in astronomy. It was adopted by the International Astronomical Union (IAU) in 1976 via Resolution No. 1, and has been significantly updated in 1994 and 2009.

<span class="mw-page-title-main">Cosmic distance ladder</span> Succession of methods by which astronomers determine the distances to celestial objects

The cosmic distance ladder is the succession of methods by which astronomers determine the distances to celestial objects. A direct distance measurement of an astronomical object is possible only for those objects that are "close enough" to Earth. The techniques for determining distances to more distant objects are all based on various measured correlations between methods that work at close distances and methods that work at larger distances. Several methods rely on a standard candle, which is an astronomical object that has a known luminosity.

<span class="mw-page-title-main">Lunar distance</span> Distance from center of Earth to center of Moon

The instantaneous Earth–Moon distance, or distance to the Moon, is the distance from the center of Earth to the center of the Moon. Lunar distance, or Earth–Moon characteristic distance, is a unit of measure in astronomy. More technically, it is the semi-major axis of the geocentric lunar orbit. The lunar distance is on average approximately 385,000 km (239,000 mi), or 1.28 light-seconds; this is roughly 30 times Earth's diameter or 9.5 times Earth's circumference. Around 389 lunar distances make up an AU astronomical unit.

In celestial mechanics, the standard gravitational parameterμ of a celestial body is the product of the gravitational constant G and the total mass M of the bodies. For two bodies, the parameter may be expressed as G(m1 + m2), or as GM when one body is much larger than the other:

An astronomical constant is any of several physical constants used in astronomy. Formal sets of constants, along with recommended values, have been defined by the International Astronomical Union (IAU) several times: in 1964 and in 1976. In 2009 the IAU adopted a new current set, and recognizing that new observations and techniques continuously provide better values for these constants, they decided to not fix these values, but have the Working Group on Numerical Standards continuously maintain a set of Current Best Estimates. The set of constants is widely reproduced in publications such as the Astronomical Almanac of the United States Naval Observatory and HM Nautical Almanac Office.

<span class="mw-page-title-main">Light-year</span> Distance that light travels in one year

A light-year, alternatively spelled light year (ly), is a unit of length used to express astronomical distances and is equal to exactly 9,460,730,472,580.8 km, which is approximately 5.88 trillion mi. As defined by the International Astronomical Union (IAU), a light-year is the distance that light travels in a vacuum in one Julian year. Because it includes the word "year", the term is sometimes misinterpreted as a unit of time.

In astronomy, planetary mass is a measure of the mass of a planet-like astronomical object. Within the Solar System, planets are usually measured in the astronomical system of units, where the unit of mass is the solar mass (M), the mass of the Sun. In the study of extrasolar planets, the unit of measure is typically the mass of Jupiter (MJ) for large gas giant planets, and the mass of Earth (ME) for smaller rocky terrestrial planets.

The International Astronomical Union at its XVIth General Assembly in Grenoble in 1976, accepted a whole new consistent set of astronomical constants recommended for reduction of astronomical observations, and for computation of ephemerides. It superseded the IAU's previous recommendations of 1964, became in effect in the Astronomical Almanac from 1984 onward, and remained in use until the introduction of the IAU (2009) System of Astronomical Constants. In 1994 the IAU recognized that the parameters became outdated, but retained the 1976 set for sake of continuity, but also recommended to start maintaining a set of "current best estimates".

<span class="mw-page-title-main">Parallax in astronomy</span> Change in the apparent position of celestial bodies when seen from two different positions

The most important fundamental distance measurements in astronomy come from trigonometric parallax, as applied in the stellar parallax method. As the Earth orbits the Sun, the position of nearby stars will appear to shift slightly against the more distant background. These shifts are angles in an isosceles triangle, with 2 AU making the base leg of the triangle and the distance to the star being the long equal-length legs. The amount of shift is quite small, even for the nearest stars, measuring 1 arcsecond for an object at 1 parsec's distance, and thereafter decreasing in angular amount as the distance increases. Astronomers usually express distances in units of parsecs ; light-years are used in popular media.


  1. 1 2 3 On the re-definition of the astronomical unit of length (PDF). XXVIII General Assembly of International Astronomical Union. Beijing, China: International Astronomical Union. 31 August 2012. Resolution B2. ... recommends ... 5. that the unique symbol "au" be used for the astronomical unit.
  2. "Monthly Notices of the Royal Astronomical Society: Instructions for Authors". Oxford Journals. Archived from the original on 22 October 2012. Retrieved 20 March 2015. The units of length/distance are Å, nm, μm, mm, cm, m, km, au, light-year, pc.
  3. 1 2 "Manuscript Preparation: AJ & ApJ Author Instructions". American Astronomical Society. Archived from the original on 21 February 2016. Retrieved 29 October 2016. Use standard abbreviations for ... natural units (e.g., au, pc, cm).
  4. Le Système international d’unités [The International System of Units](PDF) (in French and English) (9th ed.), International Bureau of Weights and Measures, 2019, p. 145, ISBN   978-92-822-2272-0
  5. On the re-definition of the astronomical unit of length (PDF). XXVIII General Assembly of International Astronomical Union. Beijing: International Astronomical Union. 31 August 2012. Resolution B2. ... recommends [adopted] that the astronomical unit be re-defined to be a conventional unit of length equal to exactly 149,597,870,700 metres, in agreement with the value adopted in IAU 2009 Resolution B2
  6. 1 2 Luque, B.; Ballesteros, F.J. (2019). "Title: To the Sun and beyond". Nature Physics . 15: 1302. doi: 10.1038/s41567-019-0685-3 .
  7. 1 2 Commission 4: Ephemerides/Ephémérides (1976). item 12: Unit distance (PDF). XVIth General Assembly of the International Astronomical Union. IAU (1976) System of Astronomical Constants. Grenoble, FR. Commission 4, part III, Recommendation 1, item 12. Archived (PDF) from the original on 9 October 2022.{{cite conference}}: CS1 maint: numeric names: authors list (link)
  8. 1 2 Bureau International des Poids et Mesures (2006), The International System of Units (SI) (PDF) (8th ed.), Organisation Intergouvernementale de la Convention du Mètre, p. 126, archived from the original (PDF) on 9 October 2022
  9. "Instructions to Authors". Monthly Notices of the Royal Astronomical Society. Oxford University Press. Retrieved 5 November 2020. The units of length/distance are Å, nm, µm, mm, cm, m, km, au, light-year, pc.
  10. 1 2 "The International System of Units (SI)". SI Brochure (8th ed.). BIPM. 2014 [2006]. Retrieved 3 January 2015.
  11. "The International System of Units (SI)" (PDF). SI Brochure (9th ed.). BIPM. 2019. p. 145. Archived (PDF) from the original on 9 October 2022. Retrieved 1 July 2019.
  12. "ISO 80000-3:2019". International Organization for Standardization. 19 May 2020. Retrieved 3 July 2020.
  13. "Part 3: Space and time". Quantities and units. International Organization for Standardization. ISO 80000-3:2019(en). Retrieved 3 July 2020.
  14. "HORIZONS System". Solar system dynamics. NASA: Jet Propulsion Laboratory. 4 January 2005. Retrieved 16 January 2012.
  15. Hussmann, H.; Sohl, F.; Oberst, J. (2009). Astronomical units". In Trümper, Joachim E. (ed.). Astronomy, astrophysics, and cosmology – Volume VI/4B Solar System. Springer. p. 4. ISBN   978-3-540-88054-7.
  16. Williams Gareth V. (1997). "Astronomical unit". In Shirley, James H.; Fairbridge, Rhodes Whitmore (eds.). Encyclopedia of planetary sciences. Springer. p. 48. ISBN   978-0-412-06951-2.
  17. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 126, ISBN   92-822-2213-6, archived (PDF) from the original on 4 June 2021, retrieved 16 December 2021
  18. "Selected Astronomical Constants" (PDF). The Astronomical Almanac Online. USNOUKHO. 2009. p. K6. Archived from the original (PDF) on 26 July 2014.
  19. Petit, Gérard; Luzum, Brian, eds. (2010). Table 1.1: IERS numerical standards (PDF). IERS technical note no. 36: General definitions and numerical standards (Report). International Earth Rotation and Reference Systems Service. Archived (PDF) from the original on 9 October 2022. For complete document see Gérard Petit; Brian Luzum, eds. (2010). IERS Conventions (2010): IERS technical note no. 36 (Report). International Earth Rotation and Reference Systems Service. ISBN   978-3-89888-989-6. Archived from the original on 30 June 2019. Retrieved 16 January 2012.
  20. 1 2 3 Capitaine, Nicole; Klioner, Sergei; McCarthy, Dennis (2012). IAU Joint Discussion 7: Space-time reference systems for future research at IAU General Assembly – The re-definition of the astronomical unit of length: Reasons and consequences (PDF) (Report). Vol. 7. Beijing, China. p. 40. Bibcode:2012IAUJD...7E..40C. Archived (PDF) from the original on 9 October 2022. Retrieved 16 May 2013.
  21. IAU WG on NSFA current best estimates (Report). Archived from the original on 8 December 2009. Retrieved 25 September 2009.
  22. Pitjeva, E.V.; Standish, E.M. (2009). "Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the Astronomical Unit". Celestial Mechanics and Dynamical Astronomy . 103 (4): 365–72. Bibcode:2009CeMDA.103..365P. doi:10.1007/s10569-009-9203-8. S2CID   121374703.
  23. "The final session of the [IAU] General Assembly" (PDF). Estrella d'Alva. 14 August 2009. p. 1. Archived from the original (PDF) on 6 July 2011.
  24. Brumfiel, Geoff (14 September 2012). "The astronomical unit gets fixed: Earth–Sun distance changes from slippery equation to single number". Nature. doi:10.1038/nature.2012.11416. S2CID   123424704 . Retrieved 14 September 2012.
  25. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 166–67, ISBN   92-822-2213-6, archived (PDF) from the original on 4 June 2021, retrieved 16 December 2021
  26. Huang, T.-Y.; Han, C.-H.; Yi, Z.-H.; Xu, B.-X. (1995). "What is the astronomical unit of length?". Astronomy and Astrophysics . 298: 629–33. Bibcode:1995A&A...298..629H.
  27. Dodd, Richard (2011).  6.2.3: Astronomical unit: Definition of the astronomical unit, future versions". Using SI Units in Astronomy. Cambridge University Press. p. 76. ISBN   978-0-521-76917-4. and also p. 91, Summary and recommendations.
  28. Dodd, Richard (2011).  6.2.8: Light-year". Using SI Units in Astronomy. Cambridge University Press. p. 82. ISBN   978-0-521-76917-4.
  29. van Helden, Albert (1985). Measuring the Universe: Cosmic dimensions from Aristarchus to Halley. Chicago: University of Chicago Press. pp. 5–9. ISBN   978-0-226-84882-2.
  30. Engels, Donald (1985). "The Length of Eratosthenes' Stade". The American Journal of Philology. 106 (3): 298–311. doi:10.2307/295030. JSTOR   295030.
  31. Gulbekian, Edward (1987). "The origin and value of the stadion unit used by Eratosthenes in the third century B.C." Archive for History of Exact Sciences. 37 (4): 359–63. doi:10.1007/BF00417008. S2CID   115314003.
  32. Rawlins, D. (March 2008). "Eratosthenes' Too-Big Earth & Too-Tiny Universe" (PDF). DIO. 14: 3–12. Bibcode:2008DIO....14....3R. Archived (PDF) from the original on 9 October 2022.
  33. Toomer, G.J. (1974). "Hipparchus on the distances of the sun and moon". Archive for History of Exact Sciences. 14 (2): 126–42. Bibcode:1974AHES...14..126T. doi:10.1007/BF00329826. S2CID   122093782.
  34. Lloyd, G. E. R. (1996). Adversaries and Authorities: Investigations into Ancient Greek and Chinese Science. Cambridge University Press. pp. 59–60. ISBN   978-0-521-55695-8.
  35. 1 2 Goldstein, S. J. (1985). "Christiaan Huygens' measurement of the distance to the Sun". The Observatory. 105: 32. Bibcode:1985Obs...105...32G.
  36. Goldstein, Bernard R. (1967). "The Arabic version of Ptolemy's planetary hypotheses". Trans. Am. Philos. Soc. 57 (4): 9–12. doi:10.2307/1006040. JSTOR   1006040.
  37. van Helden, Albert (1985). Measuring the Universe: Cosmic Dimensions from Aristarchus to Halley. Chicago: University of Chicago Press. pp. 15–27. ISBN   978-0-226-84882-2.
  38. 1 2 van Helden 1985, pp. 16–19.
  39. Ptolemy's Almagest, translated and annotated by G. J. Toomer, London: Duckworth, 1984, p. 251. ISBN   0-7156-1588-2.
  40. van Helden 1985, pp. 29–33.
  41. van Helden 1985, pp. 41–53.
  42. Bell, Trudy E. (Summer 2004). "Quest for the astronomical unit" (PDF). The Bent of Tau Beta Pi. p. 20. Archived from the original (PDF) on 24 March 2012. Retrieved 16 January 2012 – provides an extended historical discussion of the transit of Venus method.
  43. 1 2 Weaver, Harold F. (March 1943). The Solar Parallax. Astronomical Society of the Pacific Leaflets (Report). Vol. 4. pp. 144–51. Bibcode:1943ASPL....4..144W.
  44. Van Helden, A. (2010). Measuring the universe: cosmic dimensions from Aristarchus to Halley. University of Chicago Press. Ch. 12.
  45. Halley, E. (1716). "A new method of determining the parallax of the Sun, or his distance from the Earth". Philosophical Transactions of the Royal Society. 29 (338–350): 454–64. doi: 10.1098/rstl.1714.0056 . S2CID   186214749.
  46. Pogge, Richard (May 2004). "How far to the Sun? The Venus transits of 1761 & 1769". Astronomy. Ohio State University. Retrieved 15 November 2009.
  47. Newcomb, Simon (1871). "The Solar Parallax". Nature. 5 (108): 60–61. Bibcode:1871Natur...5...60N. doi:10.1038/005060a0. ISSN   0028-0836. S2CID   4001378.
  48. Conférence internationale des étoiles fondamentales, Paris, 18–21 May 1896
  49. Resolution No. 4 of the XIIth General Assembly of the International Astronomical Union, Hamburg, 1964
  50. "astronomical unit", Merriam-Webster's Online Dictionary
  51. Hinks, Arthur R. (1909). "Solar parallax papers No. 7: The general solution from the photographic right ascensions of Eros, at the opposition of 1900". Monthly Notices of the Royal Astronomical Society. 69 (7): 544–67. Bibcode:1909MNRAS..69..544H. doi: 10.1093/mnras/69.7.544 .
  52. Spencer Jones, H. (1941). "The solar parallax and the mass of the Moon from observations of Eros at the opposition of 1931". Mem. R. Astron. Soc. 66: 11–66. ISSN   0369-1829.
  53. Mikhailov, A. A. (1964). "The Constant of Aberration and the Solar Parallax". Sov. Astron. 7 (6): 737–39. Bibcode:1964SvA.....7..737M.
  54. Noerdlinger, Peter D. (2008). "Solar Mass Loss, the Astronomical Unit, and the Scale of the Solar System". Celestial Mechanics and Dynamical Astronomy . 0801: 3807. arXiv: 0801.3807 . Bibcode:2008arXiv0801.3807N.
  55. "AU may need to be redefined". New Scientist . 6 February 2008.
  56. Krasinsky, G.A.; Brumberg, V.A. (2004). "Secular increase of astronomical unit from analysis of the major planet motions, and its interpretation". Celestial Mechanics and Dynamical Astronomy . 90 (3–4): 267–88. Bibcode:2004CeMDA..90..267K. doi:10.1007/s10569-004-0633-z. S2CID   120785056.
  57. Anderson, John D. & Nieto, Michael Martin (2009). "Astrometric Solar-System Anomalies;§ 2: Increase in the astronomical unit". American Astronomical Society. 261: 189–97. arXiv: 0907.2469 . Bibcode:2009IAU...261.0702A. doi:10.1017/s1743921309990378. S2CID   8852372.
  58. Fienga, A.; et al. (2011). "The INPOP10a planetary ephemeris and its applications in fundamental physics". Celestial Mechanics and Dynamical Astronomy . 111 (3): 363. arXiv: 1108.5546 . Bibcode:2011CeMDA.111..363F. doi:10.1007/s10569-011-9377-8. S2CID   122573801.
  59. Stern, Alan; Colwell, Joshua E. (1997). "Collisional erosion in the primordial Edgeworth-Kuiper belt and the generation of the 30–50 au Kuiper gap". The Astrophysical Journal. 490 (2): 879–82. Bibcode:1997ApJ...490..879S. doi: 10.1086/304912 . S2CID   123177461.
  60. 1 2 Voyager Mission Status.
  61. "Measuring the Universe – The IAU and astronomical units". International Astronomical Union. Retrieved 22 July 2021.

Further reading