# Astronomical unit

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Astronomical unit
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, ua, or AU
Conversions
1 au, ua, or AU in ...... is equal to ...
metric (SI) units   149597870700  m
imperial  &  US  units   9.2956×107  mi
astronomical units    4.8481×10−6  pc
1.5813×10−5  ly

The astronomical unit (symbol: au, [1] [2] [3] ua, [4] or AU) is a unit of length, roughly the distance from Earth to the Sun and equal to about 150 million kilometres (93 million miles). 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, since 2012 it has been defined as exactly 1.495978707×1011 m. [5] 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] .

## 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. [8] In the non-normative Annex C to ISO 80000-3 (2006), the symbol of the astronomical unit is "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] as did the American Astronomical Society (AAS) in the manuscript preparation guidelines for its principal journals. [3] In the 2014 revision and 2019 edition of the SI Brochure, the BIPM used the unit symbol "au". [9] [10]

## 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. [11]

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". [7] [12] [13] 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"; [14] 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 the TDB scale leads to a value for the speed of light in astronomical units per day (of 86,400 seconds). 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). [15]

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 defined as the distance travelled in a vacuum by light in 1/299792458 second. 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. [16] 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 = 149597870700±3 m, [17] based on a comparison of JPL and IAA–RAS ephemerides. [18] [19] [20]

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. [9] or an increase of 9 metres.

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). [17] [21] 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. [17]

 1 astronomical unit = 149597870700 metres (exactly) ≈ 92.955807 million miles ≈ 499.00478384 light-seconds ≈ 4.8481368 millionths (4.8481368×10−6) of a parsec ≈ 15.812507 millionths (15.812507×10−6) 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.

## 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 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". [22] 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, [23] and "vigorous debate" ensued [24] until August 2012 when 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. [25]

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

The book On the Sizes and Distances of the Sun and Moon , which has long been ascribed to Aristarchus, says that he calculated the distance to the Sun to be between 18 and 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. [26]

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. [31]

Distance to the Sun
estimated by
EstimateIn au
Solar
parallax
Earth
Aristarchus (3rd century BCE)
(in On the Sizes and Distances)
380–1,5200.016–0.065
Archimedes (3rd century BCE)
(in The Sand Reckoner)
40″10,0000.426
Hipparchus (2nd century BCE)7'4900.021
Posidonius (1st century BCE)
(quoted by coeval Cleomedes)
10,0000.426
Ptolemy (2nd century)2' 50″1,2100.052
Godefroy Wendelin (1635)15″14,0000.597
Jeremiah Horrocks (1639)15″14,0000.597
Christiaan Huygens (1659)(8.2″) [32] 25,0861.068
Cassini & Richer (1672)9½″21,7000.925
Jérôme Lalande (1771)8.6″24,0001.023
Simon Newcomb (1895)8.80″23,4400.9994
Arthur Hinks (1909)8.807″23,4200.9985
H. Spencer Jones (1941)8.790″23,4661.0005
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. [33] [34] 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. [35] [36] 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 1210 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. [35]

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. [37] 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. [38]

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. [39] 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 [40] ). 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 arcseconds, similar to Wendelin's figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by

${\displaystyle A=\cot \alpha \approx 1\,{\textrm {radian}}/\alpha .}$

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, [41] 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.

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+1/2", 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 . 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 [42] 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. [43] The various results were collated by Jérôme Lalande to give a figure for the solar parallax of 8.6″.

DateMethodA/GmUncertainty
1895aberration149.250.12
1941parallax149.6740.016
1976telemetry149.597 8700.000 001
2009telemetry149.597 870 7000.000 000 003

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 kilometres. 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, [44] which remained in place for the calculation of ephemerides until 1964. [45] The name "astronomical unit" appears first to have been used in 1903. [46] [ 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. [47] Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931. [40] [48]

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. [49]

## Developments

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

${\displaystyle A^{3}={\frac {GM_{\odot }D^{2}}{k^{2}}}}$

where G is the Newtonian gravitational constant, M is the solar mass, k is the numerical value of Gaussian gravitational constant and D is the time period of one day. The Sun is constantly losing mass by radiating away energy, [50] 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. [51]

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 GM 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. [52] [53]

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. [54]

## Examples

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.

ObjectLength or distance (au)RangeComment and reference pointRefs
Light-second 0.002 distance light travels in one second
Lunar distance 0.0026average distance from Earth (which the Apollo missions took about 3 days to travel)
Solar radius 0.005 radius of the Sun (695500 km, 432450 mi, a hundred times the radius of Earth or ten times the average radius of Jupiter)
Light-minute 0.12  distance light travels in one minute
Mercury 0.39  average distance from the Sun
Venus 0.72  average distance from the Sun
Earth 1.00  average distance of Earth's orbit from the Sun (sunlight travels for 8 minutes and 19 seconds before reaching Earth)
Mars 1.52  average distance from the Sun
Light-hour 7.2   distance light travels in one hour
Kuiper belt 30     Inner edge begins at roughly 30 au [55]
Eris 67.8  average distance from the Sun
Voyager 2 122   distance from the Sun in 2019 [56]
Voyager 1 147   distance from the Sun in 2019 [56]
Light-day 173     distance light travels in one day
Light-year 63241     distance light travels in one Julian year (365.25 days)
Oort cloud 75000     ± 25000distance of the outer limit of Oort cloud from the Sun (estimated, corresponds to 1.2 light-years)
Parsec 206265     one 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] [57]
Proxima Centauri 268000     ± 126distance to the nearest star to the Solar System
Galactic Centre 1700000000     distance 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.

## Related Research Articles

The term ephemeris time can in principle refer to time in connection with any astronomical 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 in the 1970s. This time scale was proposed in 1948, to overcome the drawbacks 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.

Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. Due to foreshortening, nearby objects show a larger parallax than farther objects when observed from different positions, so parallax can be used to determine distances.

The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System. A parsec is obtained by the use of parallax and trigonometry, and is defined as the distance at which one astronomical unit subtends an angle of one arcsecond, i.e. 1/3600th of a degree. This corresponds to 648000/π astronomical units, i.e. 1 pc = 1 au/tan(1"). One parsec is approximately equal to 31 trillion kilometres (3.1×1013 km) or 19 trillion miles (1.9×1013 mi), and equates to about 3.26 light-years. The nearest star, Proxima Centauri, is about 1.3 parsecs (4.2 light-years) from the Sun. Most of the stars visible to the unaided eye in the night sky are within 500 parsecs of the Sun.

The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is defined as 299792458 metres per second. It is exact because by international agreement a metre is defined as the length of the path travelled by light in vacuum during a time interval of ​1299792458 second. According to special relativity, c is the upper limit for the speed at which conventional matter and information can travel. Though this speed is most commonly associated with light, it is also the speed at which all massless particles and field perturbations travel in vacuum, including electromagnetic radiation and gravitational waves. Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer. Particles with nonzero rest mass can approach c, but can never actually reach it. In the special and general theories of relativity, c interrelates space and time, and also appears in the famous equation of mass–energy equivalence E = mc2.

The gravitational constant, denoted by the 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 general theory of relativity.

Luminosity is an absolute measure of radiated electromagnetic power (light), the radiant power emitted by a light-emitting object.

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

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 299,792,458 metres (983,571,056 ft).

Radar astronomy is a technique of observing nearby astronomical objects by reflecting microwaves off target objects and analyzing the reflections. This research has been conducted for six decades. Radar astronomy differs from radio astronomy in that the latter is a passive observation and the former an active one. Radar systems have been used for a wide range of solar system studies. The radar transmission may either be pulsed or continuous.

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.

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.

Solar radius is a unit of distance used to express the size of stars in astronomy relative to the Sun. The solar radius is usually defined as the radius to the layer in the Sun's photosphere where the optical depth equals 2/3:

In astronomy, a Julian year is a unit of measurement of time defined as exactly 365.25 days of 86400 SI seconds each. The length of the Julian year is the average length of the year in the Julian calendar that was used in Western societies until some centuries ago, and from which the unit is named. Nevertheless, because astronomical Julian years are measuring duration rather than designating dates, this Julian year does not correspond to years in the Julian calendar or any other calendar. Nor does it correspond to the many other ways of defining a year.

Lunar distance, also called Earth–Moon distance, Earth–Moon characteristic distance, or distance to the Moon, is a unit of measure in astronomy. It is the average distance from the center of Earth to the center of the Moon. More technically, it is the mean semi-major axis of the geocentric lunar orbit. It may also refer to the time-averaged distance between the centers of the Earth and the Moon, or less commonly, the instantaneous Earth–Moon distance. The lunar distance is approximately 400000 km, or a quarter of a million miles.

In celestial mechanics, the standard gravitational parameterμ of a celestial body is the product of the gravitational constant G and the mass M of the body.

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.

Jupiter mass, also called Jovian mass, is the unit of mass equal to the total mass of the planet Jupiter. This value may refer to the mass of the planet alone, or the mass of the entire Jovian system to include the moons of Jupiter. Jupiter is by far the most massive planet in the Solar System. It is approximately 2.5 times as massive as all of the other planets in the Solar System combined.

The light-year is a unit of length used to express astronomical distances and measures about 9.46 trillion kilometres (9.46 x 1012 km) or 5.88 trillion miles (5.88 x 1012 mi). As defined by the International Astronomical Union (IAU), a light-year is the distance that light travels in vacuum in one Julian year (365.25 days). Because it includes the word "year", the term light-year may be misinterpreted as a unit of time.

Planetary mass is a measure of the mass of a planet-like 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 (M) 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"

## References

1. RESOLUTION B2 on the re-definition of the astronomical unit of length (PDF), Beijing, China: International Astronomical Union, 31 August 2012, The XXVIII General Assembly of International Astronomical Union … 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. Retrieved 20 March 2015. The units of length/distance are Å, nm, µm, mm, cm, m, km, au, light-year, pc.
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