The astronomical unit
A non-system unit accepted for use · quantity: length
For two thousand years astronomers knew the shape of the Solar System and not its size. Kepler drew his third law in 1619: the squares of the periods go as the cubes of the semi-major axes. From the observations it followed at once that Jupiter is 5.2 times further from the Sun than the Earth is. How many times over — that was known. How much that came to in miles — that was not. The map had been drawn without a scale bar.
The scale bar turned out to be the distance from the Earth to the Sun. It cannot be measured head-on: one cannot walk up to the Sun, and the angle between its two edges is not enough. So for three centuries what was measured was not the Sun but the neighbours: Mars, then Venus, then the echo of a radio pulse. Each time the same quantity came out, an order of magnitude more precise.
In 2012 the measuring came to an end. The International Astronomical Union declared the astronomical unit to be an exact number of metres and closed the question: 149 597 870 700, with no uncertainty. The reason was not precision but that the old definition had begun to drift of its own accord.
01 · Definition
The astronomical unit is 149 597 870 700 metres exactly. That is close to the mean distance from the Earth to the Sun, but the definition no longer refers either to the Earth or to the Sun. The unit is now simply a number.
Before 2012 the definition was a different and far more cunning thing. The astronomical unit was set through the Gaussian gravitational constant: it was the distance at which a test body of negligible mass goes round the Sun in 365.2568983 days. The quantity was not measured with a ruler but derived from the motion of the planets.
Such a definition proved to have two flaws. The first: it is tied to the mass of the Sun, and the Sun is losing mass — some 10¹⁷ kilograms a year go off as radiation and solar wind. The astronomical unit slowly grew because of it, by a few centimetres a century. The second: it is a Newtonian definition, and in the relativistic treatment the unit came out different in different frames of reference.
Resolution B2 removed both troubles in one move: it appointed a number. The au is no longer a measured quantity but a conversion factor between the metre and a scale convenient to astronomers. The gravitational constant of the Sun came to be published separately, as a measured parameter.
A logarithmic scale from Mercury to the edge of the Kuiper belt. The slider sets a mark at any distance, and the sheet works out how long light takes, what the flux from the Sun is there, and what temperature a body without an atmosphere would have.
In half a year the Earth moves across by two astronomical units, and a nearby star traces a tiny ellipse against the distant ones. The distance at which the radius of the Earth's orbit subtends one second of arc was named the parsec — that is 206 265 au. For the nearest star the angle is only 0.77 of a second, and no star has a parallax of a whole second.
02 · Conversion
Enter a distance and the sheet will carry it across the scales
Prefixes are not used with the astronomical unit: there is no such thing as a kiloastronomical unit. Inside the Solar System distances are counted in au and kilometres, beyond it one goes over to parsecs, and to spacecraft the distance is given in seconds of signal travel — that is handier for the people on the ground.
The third family in the table is about the signal. A radio command reaches a craft in the same time light does, and the reply takes twice as long to come back. Hence the rule: the further the probe, the less it is flown by hand.
In 1961 the astronomical unit was measured by radar for the first time: a pulse was sent to Venus and the echo caught a few minutes later. The distance came straight out of the travel time of the signal, with no geometry and no assumptions about masses. The precision rose by three orders at a stroke, and with it the whole scale of the system.
| Note | |||
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| {u} | {name} | {value} | {note} |
03 · Orders of magnitude
from the radius of the Earth to the centre of the Galaxy04 · Measuring instruments
What the scale of the system was measured with
In 1672 Cassini in Paris and Richer in Cayenne measured the position of Mars against the stars at the same moment. The difference of angles on a baseline of 7000 kilometres gave the first honest distance to the Sun: about 140 million kilometres, only 7 % short of the true one.
Halley thought of the trick in 1716: when Venus crosses the disc of the Sun, observers at different latitudes see it travel along different chords. The difference in the duration of the passage gives the parallax. The transits of 1761 and 1769 drew scores of expeditions across the whole world — Lomonosov watched from Petersburg and noticed the atmosphere of Venus along the way.
The pulse goes out to Venus and comes back in a little over five minutes. The distance follows straight from the time and the speed of light: no geometry, no assumptions about masses. The first such sessions in 1961 gave the unit to within a few hundred kilometres at once.
Today's precision comes from interplanetary craft. A ground antenna catches the shift in the frequency of the signal and from it knows the speed of the probe to fractions of a millimetre a second. Out of thousands of such measurements the ephemerides are built, and from the same source comes the gravitational constant of the Sun.
05 · Writing rules
Lower-case au, no stops and no prefixes
Since 2012 the standard designation is lower-case au without stops. The older AU, a.u. and ua are not used in new writing, though they turn up in old papers. SI prefixes do not apply to the unit: a distance of thousands of au is written out in full.
One more subtlety is the phrase «the mean distance to the Sun». It will not do: the semi-major axis of the Earth's orbit is 1.00000102 au, and a difference of a hundred and fifty kilometres matters in exact work. The astronomical unit is close to that distance, but by definition it is not equal to it.
06 · Neighbouring units
Three units of distance in astronomy stand as a staircase: the au for the Solar System, the parsec for the stars, the light year for popular writing. In scientific papers the light year is almost absent — there it is parsecs throughout.
1.496·10¹¹ m
63 241 au
206 265 au
The parsec is convenient for just this: the distance comes out by dividing the unit by the measured angle. The astronomer converts nothing — he reads the result of the observation directly. Proxima has a parallax of 0.7687 of a second, so it is 1.301 parsecs away, or 268 400 astronomical units.
07 · Historical section
How the scale was sought
Aristarchus waited for the moment when the Moon stood exactly half lit and measured the angle between it and the Sun. The trick is sound: from the angle follows the ratio of the distances. But the angle he got was 87° instead of the true 89.85°, and the Sun came out only 19 times further than the Moon — nearly twenty times nearer than it is.
Richer sailed for Guiana, Cassini stayed in Paris, and both fixed the position of Mars on one and the same night. A baseline of seven thousand kilometres gave the parallax, and out of it 140 million kilometres to the Sun. For the first time the size of the system was known to within a few per cent.
For two passages of Venus more than a hundred expeditions were fitted out: Cook sailed for Tahiti, Le Gentil spent eleven years on the road and saw nothing either time for the clouds. The result was brought together at 153 million kilometres — 2 % more than the truth.
Radar on Venus closed the question of precision: the distance came to be had from the travel time of the signal. Half a century later it turned out that the definition itself was now in the way, and the IAU appointed the unit an exact number of metres. There was nothing left to measure.
A unit that is no longer measured
For three hundred years the astronomical unit was the chief measured quantity in astronomy. Everything hung on its precision: the distances to the planets, the masses, the luminosities of the stars, the size of the Galaxy. Every refinement rewrote the reference books entire.
In 2012 it was taken out of the measured quantities. The reason is an honest one: a quantity defined through the mass of the Sun is bound to change, because the Sun shines and grows thinner. A unit of length must not breathe. So the IAU did with the au what had been done with the metre before: appointed a number and closed the matter.
The measured part did not vanish, it moved house. What is measured now is the gravitational constant of the Sun and the semi-major axis of the Earth's orbit — 1.00000102 au. The distance to the Sun is still refined every year; only the result is now written not in the definition of the unit but beside it.
Catalogue · units of measurement
A data sheet for every quantity
Seven SI base units, twenty-two derived ones with names of their own, and the non-SI quantities that neither science nor daily life can do without. Each gets its own sheet: definition, conversion, instruments, writing rules, history. In 36 languages.