An
astronomical unit (abbreviated as
AU,
au,
a.u., or sometimes
ua) is a
unit of
length roughly equal to the mean distance between the
Earth and the
Sun. The
International Astronomical Union current best estimate (2009) is metres, approximately 150 million
kilometres or 93 million
miles.
The symbol
ua is recommended by the
International Bureau of Weights and Measures,
but
au is more common in
Anglosphere countries. The
International Astronomical Union recommends
au, while
international standard ISO 31-1 uses
AU. In general, capital letters are only used for the symbols of units which are named after individual scientists, while
au or
a.u. can also mean
atomic unit or even arbitrary unit; however, the use of
AU to refer to the astronomical unit is widespread. The
astronomical constant whose value is one astronomical unit is referred to as
unit distance and given the symbol
A.
Definition
Originally, the AU was defined as the length of the
semi-major axis of the Earth's elliptical orbit around the Sun. In 1976, the International Astronomical Union revised the definition of the AU for greater precision, defining it as that length for which the
Gaussian gravitational constant (
k) takes the value when the units of measurement are the astronomical units of length, mass and time.
[Resolution No. 10 of the , Grenoble, 1976.] An equivalent definition is the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with a mean motion of radians per day, or that length for which the
heliocentric gravitational constant (the product
GM☉) is equal to ()
2 AU
3/d
2. It is approximately equal to the mean Earth–Sun distance.
Modern determinations
Very precise measurements of the relative positions of the
inner planets can be made by
radar and by
telemetry from
space probes. As with all radar measurements, these rely on measuring the time taken for light to be reflected from an object. These measured positions are then compared with those calculated by the laws of celestial mechanics: the calculated positions are often referred to as an
ephemeris, and are usually calculated in astronomical units. The comparison gives the
speed of light in astronomical units, which is AU/d (
TDB). As the speed of light in metres per second (
cSI) is fixed in the
International System of Units, this measurement of the speed of light in AU/d (
cAU) also determines the value of the astronomical unit in metres (
A):
The
International Astronomical Union (IAU) currently accepted best estimate (2009) of the value of the astronomical unit in metres is
A = m, based on a comparison of
JPL and
IAA–RAS ephemerides.
[.]Usage
By definition, the astronomical unit is dependent on the
heliocentric gravitational constant, that is the product of the
gravitational constant G and the solar mass
M☉. Neither
G nor
M☉ can be measured to high accuracy in SI units, but the value of their product is known very precisely from observing the relative positions of planets (
Kepler's Third Law expressed in terms of Newtonian gravitation). Only the product is required to calculate planetary positions for an ephemeris, which explains why 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 the surface of the Earth (
terrestrial time, TT) are not constant when compared to the motions of the planets: the terrestrial second (TT) appears to be longer in Northern Hemisphere winter and shorter in Northern Hemisphere summer when compared to the "planetary second" (conventionally measured in
barycentric dynamical time, TDB). This is because the distance between the Earth and the Sun is not fixed (it varies between AU and AU) and, when the Earth is closer to the Sun (
perihelion), the Sun's gravitational field is stronger and the 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." As such, the metre is undefined for the purposes of measuring distances within the solar system. The 1976 definition of the astronomical unit is incomplete, in particular because it does not specify the
frame of reference in which time is to be measured, but has proved practical for the calculation of ephemerides: a fuller definition that is consistent with general relativity has been proposed.
[.]History
Aristarchus of Samos estimated the distance to the Sun to be about 20 times the
distance to the moon, whereas the true ratio is about 390. His estimate was based on the angle between the
half moon and the Sun, which he estimated as 87°.
According to
Eusebius of Caesarea in the
Praeparatio Evangelica,
Eratosthenes found the distance to the sun to be "σταδιων μυριαδας τετρακοσιας και οκτωκισμυριας" (literally "of
stadia myriads 400 and 80000"). This has been translated either as 4,080,000
stadia (1903 translation by
Edwin Hamilton Gifford), or as 804,000,000
stadia (edition of
Édouard des Places, dated 1974-1991). Using the Greek stadium of 185 to 190 metres, the former translation comes to a far too low 755,000 km whereas the second translation comes to 148.7 to 152.8 million km (accurate within 2%).
A similar measurement to that of Eratosthenes is reported in a
Chinese mathematical treatise, the
Zhoubi suanjing (1st century BCE), although contrary to Eratosthenes, it assumed that the Earth was flat.
In the 2nd century CE,
Ptolemy estimated the distance as 1,210 times the
Earth radius, again about 20 times the distance to the Moon. This value was used by European and Islamic astronomers for more 1400 years.
Johannes Kepler appears to have been the first to realise that it must be 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 the 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 Ptolomy'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. By measuring the transit in two different locations, one can accurately calculate the
parallax of Venus and from the relative distance of the Earth and Venus from the Sun, the
solar parallax α (which cannot be measured directly).
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
The smaller the solar parallax, the greater the distance between the Sun and the Earth: a solar parallax of 15" is equivalent to an Earth–Sun distance of 13,750 Earth radii.
Christiaan Huygens believed the distance was even greater: by comparing the apparent sizes of Venus and
Mars, he estimated a value of about 24,000 Earth radii, 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 false) assumptions he had to make for his method to work: the accuracy of his value seems to 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 9½", 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 the Earth, which had been measured by their colleague
Jean Picard in 1669 as 3,269 thousand
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.
thumb|right|Transits of Venus across the face of the Sun were for long the best method of measuring the astronomical unit, despite the difficulties (here, the so called "black drop effect") and the rarity of observations.
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 the observations of the transits in 1761 and 1769 was an unprecedented international scientific operation. 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 8.6″.
Another method involved determining the constant of
aberration, and
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, 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 the Earth in 1900–1901 allowed a considerable improvement in parallax measurement.
Developments
The unit distance
A (the value of the astronomical unit in metres) can be expressed in term of other
astronomical constants:
where
G is the
Newtonian gravitational constant,
M☉ is the
solar mass,
k is the
Gaussian gravitational constant and
D 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. There have also been calls to redefine the astronomical unit in terms of a fixed number of metres.
As the
speed of light has a 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 increasing becoming the norm.
In 2004, an 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. Later estimates based on both radiometric and angular observations lowered this estimate to +7±2 metres per century, but this is still far larger than can be accounted for by solar radiation and current theories of gravitation. The possible variation in the gravitational constant based on radiometric measurements is of the order of parts in 10
12 per century, or lower. It has been suggested that the observed increase could be explained by the
DGP model.
Examples
The distances are approximate mean distances. It has to be taken into consideration that the distances between
celestial bodies change in
time due to their
orbits and other factors.
- The Moon is 0.0026 ± 0.0001 AU from the Earth
- The Earth is 1.00 ± 0.02 AU from the Sun
- Mars is 1.52 ± 0.14 AU from the Sun
- Jupiter is 5.20 ± 0.05 AU from the Sun
- Pluto is 39.5 ± 9.8 AU from the Sun
- Ending of Kuiper Belt at 50-55 AU
- 90377 Sedna's orbit ranges between 76 and 942 AU from the Sun; Sedna is currently () about 88 AU from the Sun
- 110 AU: As of June 2009, Voyager 1 is the furthest of any human-made objects from the Sun: it is currently travelling at about 3½ AU/yr
- 20,000 AU: Ending of Hills Cloud/"Inner Oort Cloud", beginning of "Outer Oort Cloud"
- 50,000 AU: possible closest estimate of the "Outer Oort Cloud" limits (0.8 ly)
- 100,000 AU: possible farthest estimate of the "Outer Oort Cloud" limits (1.6 ly)
- The mean diameter of Betelgeuse is 5.5 AU (822 800 000 km)
- The distance from the Sun to the centre of the Milky Way is approximately 1.7 AU
Conversion factors
See also
