An
astronomical unit (abbreviated as
AU,
au,
a.u., or
sometimes
ua) is a
unit of
length
equal to approximately 149.60 million
kilometres (93 million
miles).
It is defined by the
International Astronomical
Union, and is defined as the mean distance between the
Earth and the
Sun over one Earth
orbit.
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. 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):
- A = 86\,400 \frac{c_{\rm SI}}{c_{\rm AU}}
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.
| |
Solar
parallax |
Earth
radii |
| Ptolemy (2nd cent.) |
2′ 50″ |
1,210 |
| Godefroy Wendelin (1635) |
15″ |
14,000 |
| Jeremiah Horrocks (1639) |
15″ |
14,000 |
| Christiaan Huygens
(1659) |
8.6″ |
24,000 |
| Cassini & Richer (1672) |
9½″ |
21,700 |
| Jérôme Lalande
(1771) |
8.6″ |
24,000 |
| Simon Newcomb (1895) |
8.80″ |
23,440 |
| Arthur Hinks (1909) |
8.807″ |
23,420 |
| H. Spencer Jones (1941) |
8.790″ |
23,466 |
| modern |
8.794143″ |
23,455 |
|
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 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. 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
- A = {1\over{\tan\alpha}}
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.
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″.
| Date |
Method |
A/Gm |
Uncertainty |
| 1895 |
aberration |
149.25 |
0.12 |
| 1941 |
parallax |
149.674 |
0.016 |
| 1964 |
radar |
149.5981 |
0.001 |
| 1976 |
telemetry |
149.597 870 |
0.000 001 |
| 2009 |
telemetry |
149.597 870 700 |
0.000 000 003 |
|
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. 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
A (the value of the astronomical unit in
metres) can be expressed in term of other
astronomical constants:
- A^3 = \frac{D^2}{G M_\odot k^2}
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
- The Kuiper Belt begins at roughly 35
AU
- Beginning of Scattered disk at 45
AU (10 AU overlap with Kuiper Belt)
- 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
- 94 AU: Termination
shock between Solar winds/Interstellar winds/Interstellar medium
- 100 AU: Heliosheath
- 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
- 100-1000 AU: Mostly populated by objects from the Scattered Disc
- 1000-3000 AU: Beginning of Hills
cloud/"Inner Oort Cloud"
- 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)
- 125,000 AU: maximum extent of influence of the Sun's gravitational field (Hill/Roche sphere). beyond this is true interstellar medium. This distance is
roughly 1.8-2.0 light-years
- Proxima Centauri (the nearest
star to Earth, excluding
our own Sun) is ~268 000 AU away from the Sun
- 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
Notes and references
- .
- See, for example, the Merriam-Webster's
Collegiate Dictionary, the American Heritage
Dictionary, and the Oxford English
Dictionary.
- Resolution No. 10 of the XVIth General Assembly of the International Astronomical
Union, Grenoble, 1976.
- .
- " 2009 Selected Astronomical Constants" in .
- .
- .
- .
- .
- .
- .
- .
- .
- .
- .
- .
- .
- .
- .
- Conférence internationale des étoiles fondamentales, Paris,
18–21 May 1896.
- Resolution No. 4 of the XIIth General Assembly of the International Astronomical
Union, Hamburg, 1964.
- Merriam-Webster's Online Dictionary.
- .
- .
- .
- .
- .
- .
- .
- .
- .
- .
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