TheInfoList

The astronomical unit (symbol: au, or or AU) is a
unit of length A unit of length refers to any arbitrarily chosen and accepted reference standard for measurement of length. The most common units in modern use are the metric system, metric units, used in every country globally. In the United States the U.S. c ...
, roughly the distance from
Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remaining 70.8% is Water distribution on Earth, covered wi ...

to the
Sun The Sun is the star A star is an astronomical object consisting of a luminous spheroid of plasma (physics), plasma held together by its own gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many othe ...

and equal to about or ~8 light minutes. The actual distance varies by about 3% as Earth orbits the Sun, from a maximum (
aphelion upright=1.15, The two-body system of interacting primary body A primary (also called a gravitational primary, primary body, or central body) is the main physical body of a gravity, gravitationally bound, multi-object system. This object consti ...

) to a minimum (
perihelion upright=1.15, The two-body system of interacting primary body (yellow); both are in elliptic orbits around their center of mass">common center of mass (or barycenter), (red +). ∗Periapsis and apoapsis as distances: The smallest and largest ...

) and back again once each year. The was originally conceived as the average of Earth's aphelion and perihelion; however, since 2012 it has been defined as exactly . The astronomical unit is used primarily for measuring distances within the
Solar System The Solar SystemCapitalization Capitalization ( North American English) or capitalisation ( British English) is writing a word with its first letter as a capital letter (uppercase letter) and the remaining letters in lower case, in writin ...

or around other stars. It is also a fundamental component in the definition of another unit of astronomical length, the
parsec The parsec (symbol: pc) is a used to measure the large distances to s outside the , approximately equal to or (au), i.e. . Parsec is obtained by the use of and , and is defined as the distance at which 1 au an angle of one ( of a ). This ...

.

# 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 The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) is a nongovernmental organisation with the objective of advancing astronomy Astronomy (from el, ἀστρονομία, literally mea ...
(IAU) had used the symbol ''A'' to denote a length equal to the astronomical unit. In the astronomical literature, the symbol AU was (and remains) common. In 2006, the
International Bureau of Weights and Measures The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation An intergovernmental organization (IGO) is an organization composed primarily of sovereign state ...
(BIPM) had recommended ua as the symbol for the unit. In the non-normative Annex C to
ISO 80000-3 ISO 80000 or IEC 80000 is an international standard introducing the International System of Quantities The International System of Quantities (ISQ) is a set of quantities and the equation In mathematics, an equation is a statement that assert ...
:2006 (now withdrawn), 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". The
scientific journal In academic publishing Academic publishing is the subfield of publishing which distributes academic research and scholarship. Most academic work is published in academic journal articles, books or thesis' form. The part of academic written ...
American Astronomical Society The American Astronomical Society (AAS, sometimes spoken as "double-A-S") is an American society of professional astronomers and other interested individuals, headquartered in Washington, DC ) , image_skyline = , imag ...
and the
Royal Astronomical Society (Whatever shines should be observed) , predecessor = , successor = , formation = , founder = , extinction = , merger = , merged = , type = NGO, learned society A learned society (; also ...
subsequently adopted this symbol. In the 2014 revision and 2019 edition of the SI Brochure, the BIPM used the unit symbol "au". ISO 80000-3:2019, which replaces ISO 80000-3:2006, does not mention the astronomical unit.

# Development of unit definition

Earth's orbit Earth orbits the Sun at an average distance of 149.60 million km (92.96 million mi), and one complete orbit takes  days (1 sidereal year), during which time Earth has traveled 940 million km (584 million mi). Jean Meeus, ''Astron ...
around the Sun is an
ellipse In , an ellipse is a surrounding two , such that for all points on the curve, the sum of the two distances to the focal points is a constant. As such, it generalizes a , which is the special type of ellipse in which the two focal points are t ...

. The
semi-major axis In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space ...
of this
elliptic orbit In astrodynamics Orbital mechanics or astrodynamics is the application of ballistics Ballistics is the field of mechanics concerned with the launching, flight behavior and impact effects of projectiles, especially ranged weapon munitio ...

is defined to be half of the straight
line segment 250px, The geometric definition of a closed line segment: the intersection of all points at or to the right of ''A'' with all points at or to the left of ''B'' In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' ...

that joins the
perihelion and aphelion Apsis ( el, ἀψίς; plural apsides , Greek: ἀψῖδες; "orbit") denotes either of the two extreme points (i.e., the farthest or nearest point) in the orbit of a planetary body about its primary (astronomy), primary body (or simply ...
. 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 Parallax is a displacement or difference in the apparent positionThe apparent place of an object Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Entity, something that is tangible and within the ...

(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 Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theory ...

's
theory of relativity The theory of relativity usually encompasses two interrelated theories by Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born , widely acknowledged to be one of the greatest physicists of all time ...
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 Celestial mechanics is the branch of astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and cel ...
, which govern the motions of objects in space. The expected positions and distances of objects at an established time are calculated (in ) from these laws, and assembled into a collection of data called an
ephemeris In and , an ephemeris (plural: ephemerides) is a book with tables that gives the of naturally occurring as well as in the , i.e., the (and possibly ) over . The is and . Historically, positions were given as printed tables of values, given ...
.
NASA The National Aeronautics and Space Administration (NASA; ) is an independent agencies of the United States government, independent agency of the Federal government of the United States, U.S. federal government responsible for the civilian Li ...

Jet Propulsion Laboratory The Jet Propulsion Laboratory (JPL) is a federally funded research and development center Federally funded research and development centers (FFRDCs) are public-private partnerships which conduct research and development Research is " cr ...
HORIZONS System provides one of several ephemeris computation services. 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 The Gaussian gravitational constant (symbol ) is a parameter used in the orbital mechanics of the solar system The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astrono ...
(''k'') takes the value when the units of measurement are the astronomical units of length, mass and time". Equivalently, by this definition, one is "the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass, moving with an
angular frequency In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ ...
of "; or alternatively that length for which the heliocentric gravitational constant (the product ''G'') is equal to ()2 au3/d2, when the length is used to describe the positions of objects in the Solar System. Subsequent explorations of the Solar System by
space probe A space probe or a spaceprobe is a robotic spacecraft that doesn't Earth orbit, orbit the Earth (planet), Earth, but instead explores farther into outer space. A space probe may approach the Moon; travel through interplanetary space; planetary ...
s made it possible to obtain precise measurements of the relative positions of the
inner planets The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...
and other objects by means of
radar Radar (radio detection and ranging) is a detection system that uses radio waves to determine the distance (''ranging''), angle, or velocity of objects. It can be used to detect aircraft, Marine radar, ships, spacecraft, guided missiles, motor ...

and
telemetry Telemetry is the or other data at remote points and their automatic to receiving equipment () for monitoring. The word is derived from the roots ''tele'', "remote", and ''metron'', "measure". Systems that need external instructions and da ...
. As with all radar measurements, these rely on measuring the time taken for
photons The photon ( el, φῶς, phōs, light) is a type of elementary particle. It is the quantum of the electromagnetic field including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photo ...
to be reflected from an object. Because all photons move at the
speed of light The speed of light in vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "Void (astronomy), void". An approximation to such vacuum is a region with a gaseous pressure m ...
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 TimeBarycentric Dynamical Time (TDB, from the French Temps Dynamique Barycentrique) is a relativistic coordinate time scale, intended for astronomical use as a time standard A time standard is a specification for measuring time: either the rate at whi ...
(TDB) leads to a value for the speed of light in astronomical units per day (of ). By 2009, the IAU had updated its standard measures to reflect improvements, and calculated the speed of light at (TDB). In 1983, the CIPM modified the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms_and_initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wi ...
(SI) to make the metre defined as the distance travelled in a vacuum by light in 1 /  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 ''c''0 = , a standard also adopted by the
IERS The International Earth Rotation and Reference Systems Service (IERS), formerly the International Earth Rotation Service, is the body responsible for maintaining global and standards, notably through its (EOP) and (ICRS) groups. History The ...
numerical standards. For complete document see From this definition and the 2009 IAU standard, the time for light to traverse an astronomical unit is found to be ''τ''A = , which is slightly more than 8 minutes 19 seconds. By multiplication, the best IAU 2009 estimate was ''A'' = ''c''0''τ''A = , based on a comparison of Jet Propulsion Laboratory and IAA–RAS ephemerides. In 2006, the BIPM reported a value of the astronomical unit as . In the 2014 revision of the SI Brochure, the BIPM recognised the IAU's 2012 redefinition of the astronomical unit as . This estimate was still derived from observation and measurements subject to error, and based on techniques that did not yet standardize all relativistic effects, and thus were not constant for all observers. In 2012, finding that the equalization of relativity alone would make the definition overly complex, the IAU simply used the 2009 estimate to redefine the astronomical unit as a conventional unit of length directly tied to the metre (exactly ). The new definition 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. : This definition makes the speed of light, defined as exactly , equal to exactly  ×  ÷  or about  /d, some 60 parts per
trillion A trillion is a number with two distinct definitions: * 1,000,000,000,000, i.e. one million million, or (ten to the twelfth power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted ...
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 , ''G'', and the
solar mass The solar mass () is a standard unit of mass in astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial obje ...
, . Neither ''G'' nor can be measured to high accuracy separately, but the value of their product is known very precisely from observing the relative positions of planets (
Kepler's Third Law In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses ma ...
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 General relativity, also known as the general theory of relativity, is the geometric Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...
. In particular, time intervals measured on Earth's surface (
Terrestrial Time Terrestrial Time (TT) is a modern astronomical time standard defined by the International Astronomical Union The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) exists to promote and safeguard t ...
, TT) are not constant when compared with the motions of the planets: the terrestrial second (TT) appears to be longer near January and shorter near July when compared with the "planetary second" (conventionally measured in TDB). This is because the distance between Earth and the Sun is not fixed (it varies between and ) and, when Earth is closer to the Sun (
perihelion upright=1.15, The two-body system of interacting primary body (yellow); both are in elliptic orbits around their center of mass">common center of mass (or barycenter), (red +). ∗Periapsis and apoapsis as distances: The smallest and largest ...

), 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 Proper length or rest length is the length of an object in the object's rest frame. The measurement of lengths is more complicated in the theory of relativity than in classical mechanics. In classical mechanics, lengths are measured based on t ...
, but the SI definition does not specify the
metric tensor In the mathematical Mathematics (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population ...
to be used in determining it. Indeed, the
International Committee for Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence Générale des Poids et Mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established in ...
(CIPM) notes that "its definition applies only within a spatial extent sufficiently small that the effects of the non-uniformity of the gravitational field can be ignored". As such, 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 physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...

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 and also p. 91, ''Summary and recommendations''. until August 2012 when the IAU adopted the current definition of 1 astronomical unit =
metre The metre ( Commonwealth spelling) or meter (American spelling Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English ...
s. 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 . The astronomical unit is too small to be convenient for interstellar distances, where the
parsec The parsec (symbol: pc) is a used to measure the large distances to s outside the , approximately equal to or (au), i.e. . Parsec is obtained by the use of and , and is defined as the distance at which 1 au an angle of one ( of a ). This ...

and
light-year A light-year, alternatively spelt lightyear, is a unit of length A unit of length refers to any arbitrarily chosen and accepted reference standard for measurement of length. The most common units in modern use are the metric system, metric un ...
are widely used. The parsec (parallax
arcsecond A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree Degree may refer to: As a unit of measurement * Degree symbol (°), a notation used in scie ...
) is defined in terms of the astronomical unit, being the distance of an object with a parallax of . The light-year is often used in popular works, but is not an approved non-SI unit and is rarely used by professional astronomers. When simulating a numerical model of the Solar System, the astronomical unit provides an appropriate scale that minimizes ( overflow, underflow and
truncation In mathematics and computer science, truncation is limiting the number of numerical digit, digits right of the decimal point. Truncation and floor function Truncation of positive real numbers can be done using the floor function. Given a numb ...
) errors in
floating point In computing Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes and development of both computer hardware , hardware and soft ...
calculations.

# History

The book '' On the Sizes and Distances of the Sun and Moon'', which is ascribed to , says the distance to the Sun is 18 to 20 times the distance to the Moon, whereas the true ratio is about . The latter estimate was based on the angle between the half-moon and the Sun, which he estimated as (the true value being close to ). 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 and Earth radii. According to
Eusebius of Caesarea Eusebius of Caesarea (; grc-gre, Εὐσέβιος τῆς Καισαρείας, ''Eusébios tés Kaisareías''; AD 260/265 – 339/340), also known as Eusebius Pamphili (from the grc-gre, Εὐσέβιος τοῦ Παμϕίλου), ...

in the ''
Praeparatio Evangelica''Preparation for the Gospel'' ( grc-gre, Εὐαγγελικὴ προπαρασκευή, ''Euangelikē proparaskeuē''), commonly known by its Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the ...
'' (Book XV, Chapter 53),
Eratosthenes Eratosthenes of Cyrene (; grc-gre, Ἐρατοσθένης ;  – ) was a Greek polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a ...

found the distance to the Sun to be "σταδιων μυριαδας τετρακοσιας και οκτωκισμυριας" (literally "of ''stadia''
myriad A myriad (from Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: M ...
s 400 and ) 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 ' 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 '' stadia'' (1903 translation by
Edwin Hamilton GiffordEdwin Hamilton Gifford, Doctor of Divinity, DD (18 December 1820 – 4 May 1905) was an eminent Anglican priest and author in the second half of the 19th century. Edwin Gifford was educated at Shrewsbury School, Shrewsbury and St John's College, Cam ...
), or as ''stadia'' (edition of , dated 1974–1991). Using the Greek stadium of 185 to 190 metres, the former translation comes to to , which is far too low, whereas the second translation comes to 148.7 to 152.8 million kilometres (accurate within 2%).
Hipparchus Hipparchus of Nicaea (; el, Ἵππαρχος, ''Hipparkhos'';  BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of precession of the ...
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 Noel Mark Swerdlow (born 1941) is a professor emeritus of history, astronomy and astrophysics at the University of Chicago. He is currently a visiting professor at the California Institute of Technology. Career Swerdlow specializes in the history ...
and G. J. Toomer, this was derived from his assumption of a "least perceptible" solar parallax of . A Chinese mathematical treatise, the ''
Zhoubi Suanjing The ''Zhoubi Suanjing'' () is one of the oldest Chinese mathematics, Chinese mathematical texts. "Zhou" refers to the ancient Zhou dynasty (1046–256 BCE); "Bi" means thigh and according to the book, it refers to the gnomon of the sundial. The ...
'' (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 li apart and the assumption that Earth is flat. In the 2nd century CE,
Ptolemy Claudius Ptolemy (; grc-koi, Κλαύδιος Πτολεμαῖος, , ; la, Claudius Ptolemaeus; AD) was a mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes ...
estimated the mean distance of the Sun as times Earth's radius. 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 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.pp. 16–19, van Helden 1985 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 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. 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 Earth radii, whereas in his ''
zij A zij ( fa, زيج, zīj) is an astronomy in medieval Islam, Islamic astronomical book that tabulates ephemeris, parameters used for astronomy, astronomical calculations of the apparent place, positions of the Sun, Moon, stars, and planets. Etym ...
'', used a mean solar distance of Earth radii. Subsequent astronomers, such as al-Bīrūnī, used similar values. Later in Europe,
Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, link=no, Niclas Koppernigk, modern: ''Nikolaus Kopernikus''; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic Church, C ...

and
Tycho Brahe Tycho Brahe ( ; born Tyge Ottesen Brahe; 14 December 154624 October 1601) was a Danish astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. T ...

also used comparable figures ( and Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century.
Johannes Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer An astronomer is a in the field of who focuses their studies on a specific question or field outside the scope of . They observe s such as s, s, , s and ...

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 The ''Rudolphine Tables'' ( la, Tabulae Rudolphinae) consist of a star catalogue and planetary tables published by Johannes Kepler in 1627, using observational data collected by Tycho Brahe (1546–1601). The tables are named in memory of Rudolf ...

'' (1627).
Kepler's laws of planetary motion In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the Copernican heliocentrism, heliocentric theory of Nicolaus Copernicus, repl ...
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 A telescope is an optical instrument An optical instrument (or "optic" for short) is a device that processes light waves (or photons), either to enhance an image for viewing or to analyze and determine their characteristic properties. Common ...

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 A transit of Venus across the Sun takes place when the planet Venus passes directly between the Sun and a inferior and superior planets, superior planet, becoming visible against (and hence obscuring a small portion of) the solar disk. During ...

. – provides an extended historical discussion of the
transit of Venus A transit of Venus across the Sun takes place when the planet Venus passes directly between the Sun and a inferior and superior planets, superior planet, becoming visible against (and hence obscuring a small portion of) the solar disk. During ...

method.
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 Parallax is a displacement or difference in the apparent position of an object viewed along two different sightline, lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. Due to perspective (graphic ...
(which cannot be measured directly due to the brightness of the Sun).
Jeremiah Horrocks Jeremiah Horrocks (16183 January 1641), sometimes given as Jeremiah Horrox (the Latinised version that he used on the Emmanuel College register and in his Latin manuscripts), – See footnote 1 was an English astronomer An astronomer is a scie ...
had attempted to produce an estimate based on his observation of the 1639 transit (published in 1662), giving a solar parallax of , similar to Wendelin’s figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by :$A = \cot\alpha \approx 1\,\textrm/\alpha.$ The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of is equivalent to an Earth–Sun distance of Earth radii.
Christiaan Huygens Christiaan Huygens ( , also , ; la, Hugenius; 14 April 1629 – 8 July 1695), also spelled Huyghens, was a Dutch mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) i ...

believed that the distance was even greater: by comparing the apparent sizes of Venus and
Mars Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, being larger than only Mercury (planet), Mercury. In English, Mars carries the name of the Mars (mythology), Roman god of war and is often referred to ...

, he estimated a value of about Earth radii, equivalent to a solar parallax of . 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 Jean Richer (1630–1696) was a French astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, pla ...
and
Giovanni Domenico Cassini Giovanni Domenico Cassini, also known as Jean-Dominique Cassini (8 June 1625 – 14 September 1712) was an Italian (naturalised French) mathematician, astronomer An astronomer is a scientist in the field of astronomy who focuses their stu ...

measured the parallax of Mars between
Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,175,601 residents , in an area of more than . Since the 17th century, Paris ha ...

and
Cayenne Cayenne (; ) is the capital city A capital or capital city is the holding primary status in a , , , , or other , usually as its seat of the government. A capital is typically a that physically encompasses the government's offices and me ...
in
French Guiana French Guiana ( or ; french: link=no, Guyane ) is an overseas department/region and single territorial collectivity A single territorial collectivity (french: collectivité territoriale ''unique'') is a chartered subdivision of France ...

when Mars was at its closest to Earth in 1672. They arrived at a figure for the solar parallax of , equivalent to an Earth–Sun distance of about 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 Jean Picard (21 July 1620 – 12 July 1682) was a France, French astronomer and priest born in La Flèche, where he studied at the Jesuit Collège Royal Henry-Le-Grand. He is principally notable for his accurate measure of the size of the Ear ...

in 1669 as ''
toise A toise (; symbol: T) is a unit of measure for length Length is a measure of distance Distance is a numerical measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (rese ...
s''. This same year saw another estimate for the astronomical unit by
John Flamsteed John Flamsteed FRS (19 August 1646 – 31 December 1719) was an English astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astr ...

, which accomplished it alone by measuring the
martian Image:Woking tripod.JPG, 200px, Sculpture of a Martian (The War of the Worlds), Wellsian Martian Tripod in the town of Woking, England A Martian is an inhabitant of the planet Mars or a Colonization of Mars, human colonist on Mars. Although the ...

diurnal parallax Parallax () is a displacement or difference in the apparent position of an object viewed along two different sightline, lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. Due to perspective (grap ...

. Another colleague, , 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 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. The various results were collated by Jérôme Lalande to give a figure for the solar parallax of . Karl Rudolph Powalky had made an estimate of in 1864. Another method involved determining the constant of aberration of light, aberration. Simon Newcomb gave great weight to this method when deriving his widely accepted value of for the solar parallax (close to the modern value of ), although Newcomb also used data from the transits of Venus. Newcomb also collaborated with Albert Abraham Michelson, 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, which remained in place for the calculation of ephemerides until 1964. The name "astronomical unit" appears first to have been used in 1903. The discovery of the near-Earth asteroid 433 Eros and its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement. Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931. 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.

# Developments

The unit distance (the value of the astronomical unit in metres) can be expressed in terms of other astronomical constants: :$A^3 = \frac$ where is the Newtonian gravitational constant, is the solar mass, is the numerical value of Gaussian gravitational constant and is the time period of one day. The Sun is constantly losing mass by radiating away energy, 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. As the speed of light has an exact defined value in SI units and the Gaussian gravitational constant is fixed in the astronomical system of units, measuring the light time per unit distance is exactly equivalent to measuring the product × 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 variation, secular increase in the unit distance was much larger than can be accounted for by solar radiation, + metres per century. 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.

# 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.

* Orders of magnitude (length) * Gigametre

*