The plate is the measurement itself, taken apart. At the lower left lies the crimson orbit of the Earth, and a blue marker travels along it: half a year one way, half a year back. The golden disc at the centre of the orbit is the Sun, and the caption beneath it says that the radius of this orbit is the astronomical unit — the very base of the triangle. From the marker to the star runs a turquoise sightline, and you can see it swing as the Earth moves; a second, dashed line is left for comparison — the direction half a year earlier. The star itself, upper right, rocks in time, tracing a tiny ellipse on the sky drawn in crimson dashes: that is the parallactic shift, and the angle between the sightlines is labelled one second. Around it twinkle the field stars against which the shift is noticed. Beneath it all lies a ruler of light-years, and the golden mark on it reaches three point two six — the number of light-years in one parsec. The large letters in the middle are the symbol, the same in every locale, and beneath them stands the value in metres.
Distance · astronomy and cosmology
Parsec
Non-SI unit · quantity: distance · defined through an angle of one second
The only way to measure the distance to a star without leaving home is to wait half a year. In that time the Earth moves to the other side of its orbit, and a nearby star shifts slightly against the distant ones: first to the left, then to the right. Half of that shift, expressed in arcseconds, is called the parallax, and the distance is already contained in it. The parsec is the distance at which the parallax equals exactly one second.
Hence the name: “parallax” plus “second”, glued together in 1913, when astronomers grew tired of writing long phrases in their catalogues. With the name came the main convenience: the distance in parsecs equals one divided by the parallax in seconds, so the observer converts nothing at all — he simply inverts the measured number. A parsec holds a little over three light-years and exactly two hundred and six thousand two hundred and sixty-four point eight astronomical units.
The angles here are monstrously small: one second is a two-centimetre coin seen from four kilometres, and even the nearest star has a parallax of less than a second. That is why the whole history of the unit is a history of instruments able to notice ever finer trembling: Bessel in 1838 caught a third of a second, the Hipparcos satellite reached a thousandth in the nineties, and Gaia measures fractions of a hundred-thousandth of a second, pushing the limit of direct measurement to the far side of the Galaxy.
The symbol is written in lowercase Latin letters without a full stop: pc, and just the same with prefixes — kpc, Mpc, Gpc, where the prefix keeps its own case. In Russian it is written «пк», and it must not be confused with «пс», the picosecond. The plural is parsecs: “eight kiloparsecs to the centre of the Galaxy”.
The parsec is a distance, not a time and not a speed, although the cinema once claimed otherwise: Han Solo boasted of making the Kessel Run in less than twelve parsecs, and the line immortalised the mistake. Nor should the parsec be confused with the light-year: a parsec holds a little over three light-years, and astronomers prefer the first precisely because it comes straight from the measured angle, whereas the second requires knowing the speed of light and the length of the year.
01 · Definition
one second of arc — one parsecThe parsec is the distance from which the radius of Earth’s orbit is seen at an angle of one arcsecond. The definition is fixed exactly: the parsec equals six hundred and forty-eight thousand divided by pi astronomical units, and since the astronomical unit itself has been an exact number of metres since 2012, the parsec is exact as well.
The factor looks mysterious, but it comes from simple trigonometry: a radian contains two hundred and six thousand two hundred and sixty-four seconds and a bit, and the same number results when six hundred and forty-eight thousand is divided by pi. At such small angles the tangent equals the angle itself, and so the cumbersome relation reduces to what the unit was invented for: the distance in parsecs is the reciprocal of the parallax in seconds.
This reciprocal relation works wonderfully conveniently and just as wonderfully cruelly. Conveniently, because an observer who obtains a parallax in hundredths of a second immediately reads a distance in hundreds of parsecs. Cruelly, because the relative error of the distance equals the relative error of the angle, and the angle shrinks with distance: twice as far — half the trembling, and twice the error with the same instrument.
That is why the direct method always has a horizon, and it is set not by physics but by the resolving power of the instrument. Ground-based telescopes worked reliably out to tens of parsecs, Hipparcos pushed the limit to a hundred, Gaia to tens of thousands, and beyond that it is no longer angles but standard candles that take over: Cepheids, supernovae and the whole cosmological ladder, whose first rung is still calibrated by parallaxes.
Half a year there, half a year back
The left window shows the sky as the chosen instrument sees it: the golden star slowly circles a crimson ellipse because the Earth moves along its orbit, while the faint background stars stay put. The size of the ellipse is the parallax, and it is smaller the farther away the star is; the circle around the golden dot shows how finely the instrument can tell positions apart at all — when the ellipse sinks inside that circle, there is nothing left to measure. On the right is the same quantity on a graph: the turquoise curve is the inverse dependence of parallax on distance, the horizontal line is the instrument’s precision, and the vertical band marks the limit beyond which the distance error exceeds one tenth. The buttons switch between instruments of different eras, and you can see how in two hundred years the limit of direct measurement moved from tens of parsecs to tens of thousands.
02 · Conversion
distances · angles · the scales of the UniverseFrom angle to metres and back
All conversions in the first tab are exact, since the astronomical unit, the parsec and the light-year are all defined through fixed numbers rather than through measurements. Only the distances to the objects themselves remain approximate — they are what is being measured.
The second tab converts distance into an angle and back, the third lays out the scale from the stellar neighbourhood to the observable limit.
The inverse relation between angle and distance behaves treacherously when errors are large: if the parallax is measured to worse than twenty per cent, simple inversion gives a systematically overestimated distance, and astronomers turn to statistical estimates. On cosmological scales the word “distance” itself splits into several different quantities, because the Universe expands while the light is on its way.
| Quantity | Value | Note |
|---|---|---|
| {k} | {v} | {note} |
{text}
04 · Measuring instruments
heliometer · Hipparcos · Gaia · radio interferometerTwo hundred years of chasing a second
The heliometer and patience
Bessel’s instrument worked like this: the objective was cut in half, and the halves could be shifted with a screw, bringing the image of the star under study into coincidence with the image of a neighbour. The difference in screw readings gave the angle between them, and because it was a difference that was measured, both the trembling of the air and the setting errors dropped out of the result. A whole year of observations in a row — and it became clear that the star sixty-one Cygni traces an ellipse on the sky a third of a second across.
The Hipparcos satellite
The main enemy of astrometry is the atmosphere, and it could only be beaten by leaving the air behind. Hipparcos spun slowly, looking in different directions of the sky with two fields of view at once, and so measured large angles between stars far apart from each other, and a single catalogue was stitched together from these angles. The result: one hundred and eighteen thousand stars with parallaxes accurate to about a thousandth of a second, and the first reliable calibration of the distance scale within the Galaxy.
Gaia and microarcseconds
Today’s limit of direct measurement is set by the Gaia observatory: for bright stars it determines the parallax to an accuracy of some twenty millionths of a second, fifty times better than Hipparcos. This takes the direct method from the Sun’s neighbourhood to the scale of the whole Galaxy: for a star on its far side the parallax is still measurable, if with a noticeable error. The precision, however, falls with brightness, and so the catalogue is uneven: for faint stars the angle is known far less well than for bright ones.
Very-long-baseline radio interferometer
In the radio band angular resolution is set not by the size of the dish but by the distance between the antennas, and so a network of telescopes spread across different continents resolves details of tens of microarcseconds. What is observed is not the stars themselves but compact maser sources in star-forming regions — their positions can be measured especially precisely. This is how parallaxes were obtained for objects on the far side of the Galaxy, and optical astrometry was checked by a completely independent method along the way.
05 · Writing rules
lowercase letters, prefixes, a unit of distanceA parsec cannot measure time
The symbol consists of two lowercase letters, prefixes go in front of them by the general rules, and the quantity always remains a distance. And if a text gives a parallax, it is useful to state in which fractions of a second it is given: thousandths or millionths.
The first mistake is famous the world over and survives because the line in the film was later explained by the peculiarities of navigating hyperspace. The second swaps the parsec for the picosecond, and the numbers between them differ by twenty-eight orders of magnitude. The third breaks the case rule: a capital “P” would mean peta, and “Pc” means nothing at all. The fourth leaves the angle without a unit, although parallaxes are published sometimes in seconds, sometimes in thousandths of them. The fifth turns a distance into a time: light really does take three and a quarter years to cross a parsec, but the parsec itself is measured in metres, not in years.
06 · Neighbouring units
astronomical unit · light-year · redshiftThe parsec has two neighbouring units of length and one quantity that replaces it on large scales. The first two differ in where they come from: one from the Solar System, the other from the speed of light. The third is no longer a length but a property of the arriving light.
The radius of Earth’s orbit, from which the parsec is derived. Since 2012 it has equalled an exact number of metres, and so the parsec inherited that exactness: all the uncertainty stays in the measured angles, not in the definition.
The distance light travels in a Julian year. It hardly ever appears in scientific papers, but it is indispensable in popular writing, because it tells at once how far into the past we are looking.
On cosmological scales it is redshift that gets published, not parsecs: while the light was travelling, space stretched, and a single distance turns into several different ones. Redshift is measured directly and is therefore more reliable than any of them.
07 · Historical section
archive · 1838 → 1913 → 1993 → todayA word glued together from an angle and a star
{title}
{text}
The turquoise curve is the parallax, falling in inverse proportion to distance. The crimson horizontal is what the instrument can resolve. Their intersection gives the golden dashed line: to the right of it the measured angle is already smaller than its own error, and the distance has to be estimated rather than measured. The whole of astrometry for two centuries has been about pushing the crimson line lower and the golden one further to the right.
A unit whose standard is geometry
In the Simetrium catalogue this is a rare case of a unit that has no physical standard and cannot have one, and loses nothing by it. The parsec is defined geometrically: take a known base, lay off an angle of one second — and the distance follows by itself. What must be kept is not an artefact but two numbers, the length of the astronomical unit and the number of seconds in a radian, and both are fixed exactly, so the unit itself is known with all conceivable rigour.
The uncertainty lives not in the unit but in the measurements: an angle of hundredths of a second has to be fished out of trembling air or out of satellite data, and the astrometrist’s whole work is a fight for the last fractions of that angle. The beauty of the method is that it relies on nothing but geometry: not on a model of the star, not on an assumption about its luminosity, not on cosmology. That is why parallaxes serve as the first rung of the distance ladder, and everything else — Cepheids, supernovae, redshifts — is calibrated against them.
Hence the parsec’s place in science: it is neither the largest nor the most precise unit, but it is the most honest one. It records exactly what the observer really measured — the angle at which the orbit of his own planet is seen. Astronomy has tried more than once to speak of distances otherwise, without tying them to something measurable, and each time it came back to this triangle with one second at its apex.
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 does without. Each gets its own sheet: definition, conversion, instruments, writing rules, history. In 36 languages.
Astronomy and distances
the open data sheet is highlightedSI base units
highlighted are those through which the parsec is expressedObjects and their parallaxes
angles, light-years and instrument limits computed by the sheet| Object | distance | parallax | ly | Hipparcos | Gaia | Measured by |
|---|---|---|---|---|---|---|
| {name} | {d} | {plx} | {ly} | {hip} | {gaia} | {how} |
The last two columns are the relative distance error that instruments of two eras would give: a thousandth of a second for Hipparcos and twenty millionths for Gaia. They show where the limit of the direct method lies in each era: Hipparcos could still reliably reach the Pleiades, the centre of the Galaxy became attainable only for Gaia, and at Andromeda the parallax stops working even for Gaia — there the Cepheids take over.