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In astronomy distances are generally expressed in non-metric units like: light-years, astronomical units (AU), parsecs, etc. Why don't they use meters (or multiples thereof) to measure distances, as these are the SI unit for distance? Since the meter is already used in particle physics to measure the size of atoms, why couldn't it be used in astrophysics to measure the large distances in the Universe?

For example:

  • The ISS orbits about 400 km above Earth.
  • The diameter of the Sun is 1.39 Gm (gigameters).
  • The distance to the Andromeda Galaxy is 23 Zm (zettameters).
  • At its furthest point, Pluto is 5.83 Tm (terameters) from the Sun.

Edit: some have answered that meters are too small and therefore not intuitive for measuring large distances, however there are plenty of situations where this is not a problem, for example:

  • Bytes are used for measuring gigantic amounts of data, for example terabytes (1e+12) or petabytes (1e+15)
  • The energy released by large explosions is usually expressed in megatons, which is based on grams (1e+12)
  • The SI unit Hertz is often expressed in gigahertz (1e+9) or terahertz (1e+12) for measuring network frequencies or processor clock speeds.

If the main reason for not using meters is historical, is it reasonable to expect that SI-unites will become the standard in astronomy, like most of the world switched from native to SI-units for everyday measurements?

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    $\begingroup$ Because it's not useful to do so. $\endgroup$ – eyeballfrog Mar 20 '17 at 22:23
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    $\begingroup$ What do you think an Angstrom or a Fermi are? Or a barn? Physicists don't always specify stuff in SI either and for the same reason. $\endgroup$ – Rob Jeffries Mar 21 '17 at 6:35
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    $\begingroup$ For the same reason that you buy rice in KG, not by the grain. $\endgroup$ – dotancohen Mar 21 '17 at 8:33
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    $\begingroup$ Because you want units to relate to objects being measured. If I told you I'm $1.13*10^{35}$ Plank lengths tall, would it help you to picture how tall I am? $\endgroup$ – Dmitry Grigoryev Mar 21 '17 at 11:45
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    $\begingroup$ @MartinArgerami True, but if someone tells me they are 57 feet tall, I'll spot a mistake right away (and I think an American won't believe me if I tell them I'm 18 meters tall). With Plank lengths, even a mistake by an order of magnitude may not be obvious. $\endgroup$ – Dmitry Grigoryev Mar 21 '17 at 12:29

12 Answers 12

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In addition to the answer provided by @HDE226868, there are historical reasons. Before the advent of using radar ranging to find distances in the solar system, we had to use other clever methods for finding the distance from the Earth to the sun; for example, measuring the transit of Venus across the surface of the sun. These methods are not as super accurate as what is available today, so it makes sense to specify distances, that are all based on measuring parallaxes, in terms of the uncertain, but fixed, Earth-Sun distance. That way, if future measurements change the conversion value from AU to meters, you don't have to change as many papers and textbooks.

Not to mention that such calibration uncertainties introduce correlated errors into an analysis that aren't defeatable using large sample sizes.

I can't speak authoritatively on the actual history, but solar system measurements were all initially done in terms of the Earth/sun distance. For example, a little geometry shows that it's pretty straightforward to back out the size of Venus's and Mercury's orbit in AU from their maximum solar elongation. I don't know how they worked out the orbital radii of Mars, etc, but they were almost certainly done in AU long before the AU was known, and all of that before the MKS system existed, let alone became standardized.

For stars, the base of what is known as the "cosmological distance ladder" (that is "all distance measures" in astronomy) rests on measuring the parallax angle: $$\tan \pi_{\mathrm{angle}} = \frac{1 AU}{D}.$$ To measure $D$ in 'parsecs' is to setup the equation so that the angle being measured in arcseconds fits the small angle approximation. That is: $$\frac{D}{1\, \mathrm{parsec}} = \frac{\frac{\pi}{180\times60\times60}}{\tan\left(\pi_{\mathrm{angle}} \frac{\pi\, \mathrm{radians}}{180\times60\times60 \, \mathrm{arcsec}}\right)}$$

Astronomers also have a marked preference for the close cousin of mks/SI units, known as cgs. As far as I can tell, this is due to the influence of spectroscopists who liked the "Gaussian units" part of it for electromagnetism because it set Coulomb's constant to 1, simplifying calculations.

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    $\begingroup$ I would say that this is the correct answer, whereas the one provided by HDE 226868 is not. In terms of human comprehensibility, measuring e.g. the solar system is AU is no more or less intuitive than measuring it in gigameters (or perhaps terameters; 1 AU ≈ 150 Gm = 0.15 Tm). However, the non-metric units still persist due to historical inertia, and the fact that they were (and sometimes still are) more convenient in cases where some distance can be measured in some particular units more accurately than the length of those units themselves can be measures in meters. $\endgroup$ – Ilmari Karonen Mar 20 '17 at 20:08
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    $\begingroup$ I like this answer. You could extend it by mentioning that the favoured measure of stellar distance is the parsec, since it can be calculated exactly in terms of AU, (648000 AU = \pi parsec) $\endgroup$ – James K Mar 20 '17 at 22:00
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    $\begingroup$ Another historical parallel to this situation comes from chemistry, where there is a strong preference to talk about the "moles" of a substance rather than a certain number of molecules of that substance. It's not just that the number of moles is less likely to require scientific notation to express; it's also that for a surprisingly long time (until the early 20th century), chemists didn't actually know how many molecules were in a mole. $\endgroup$ – Michael Seifert Mar 21 '17 at 13:50
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    $\begingroup$ In general, physicists don't like raw numbers. They really like to express quantities as dimensionless numbers that express some property of a system. It makes it easier to reason about things. So, if you are considering a planetary system, working in AU (i.e. expressing distances as a multiple of earth's orbit) is a very reasonable thing to do. $\endgroup$ – drxzcl Mar 21 '17 at 13:53
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    $\begingroup$ Astronomers don't seriously use pi_angle for parallax angle, do they? That seems potentially confusing =). $\endgroup$ – Chris Chudzicki Mar 21 '17 at 16:54
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I would suggest it also makes the material more reachable for the human mind.

I just can't work with insanely large or small numbers. They convey no meaning.

But 1 AU is easy, even if I don;t know exactly what that is in meters, I know what it means and it is a convenient scale for the mind.

Likewise when we talk about stellar distances, what use is the distance in meters (or AU) ? It makes more sense to work with light years. Again most people know what that means even if they don't know exactly what it is in meters.

And when we go cosmic you're also talking about colossal times in the past, so light years do convey a double meaning here. If I told you the distance in meters, that doesn't instantly tell you how far back in time it is as well.

So I think it's a matter on convenience and comprehension.

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    $\begingroup$ What about bytes? Nobody seems to have a problem using bytes for extremely large numbers, wether it's KB, MB, GB, TB, PB, etc. Nobody thinks these units are unintuitive or we need a completely different unit once the size exceeds some limit. I'm not sure why this would be different concerning the meter and large measurements. $\endgroup$ – Arne Mar 20 '17 at 21:57
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    $\begingroup$ My view is that KB, MB, TB and so on are not really understood at all by most people. What's a byte ? What's a TB ? For the majority they're little more than marketing labels. I think the only people who understand them are professionals who have to. And to a computer type (guilty) those measurements are pretty straightforward. YMMV. $\endgroup$ – StephenG Mar 20 '17 at 23:21
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    $\begingroup$ @Arne: As a computer science major, I would like to point out that we (computer scientists) use a non-SI number of bytes in talking about memory. KB, MB, GB, TB, PB, etc. are not SI units. For example, 1 MB = 1024 KB, not 1000 like it would in an SI system. We use base 2, not base 10. $\endgroup$ – sharur Mar 20 '17 at 23:45
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    $\begingroup$ @pipe KiB, MiB, ... are by definition base-2. KB, MB, ... are ambiguous, and can use either base-2 or base-10 in common usage. $\endgroup$ – a CVn Mar 21 '17 at 15:52
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    $\begingroup$ @pipe: On the contrary, base 2 is built into the hardware at its most basic level. What's borderline fraud are the marketers who use powers of 10 to exaggerate the size of their memory. $\endgroup$ – jamesqf Mar 21 '17 at 23:47
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Along with the other answers, there is one other reason, specifically when measuring the distances to other galaxies.

When stating the distance to other galaxies, Astronomers rarely ever state the distance in any unit of length, they tend to use redshifts (z). This unit is not actually a unit of length (it is a dimensionless ratio of wavelengths), nor does it linearly convert to a distance (z=2 is not twice as far as z=1), nor is there an excepted conversion between redshift and distance (it depends on what model of the universe you assume).

Redshift is used because it can be very accurately measured. There are features in a star or a galaxies spectra that we know the exact wavelength that they are emitted at and so the redshift can be calculated exactly by:

$$ z=\frac{\lambda_{obs}}{\lambda_{em}}-1 $$

This is an observed, exact (within experimental error) property. Converting this to a distance is confusing: are you talking about the distance the object is away from us instantaneously now, or instantaneously when the photon that you see was emitted, or the distance the photon you see travelled? Do you wish to take into consideration local movement as well as Hubble (universe) expansion? Add on to this the shape of the universe, the rate of expansion of the universe, the rate of change of the expansion of the universe (dark energy/Hubble constants/other effects), and you see that any conversion to an actual distance is problematic and would require that you define exactly what type of conversion and with what assumptions. It is easier to stay with the well-defined easy-to-measure redshift.

A good (degree-level) work that summarises all the different types of cosmological distances and their calculations is Hogg 2000.

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  • $\begingroup$ Jonathan: in Hogg Introduction, Is it correct the all distance are measured along a null radial line? Gravitational lensing came to my mind... In the sense that obviously a photon terminate at me as observer, but I would expect (in principle, not in the absolute sense... Difference can be negligible) that it does after having "curved". I hope is clear what I mean. $\endgroup$ – Alchimista Oct 20 '17 at 13:58
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Another not yet mentioned reason:

There were no usable SI prefixes for such distances.

If you want to use an unit, you need something which allows to express a specific quantity without too many leading or trailing zeroes. I do not express human height as 1 670 000 µm or the size of a bacteria as 0.000 02 m.

If you look up the table of prefixes you see that giga and tera was defined the first time 1960. But definition does not include usage and those definitions were exactly as exotic as octillion; sure it exists as definition, but noone uses it or knows of its existence. During academic studies in physics in the 90s (!) it still was not widely known, 30 years after introduction. Still many scientists do not use giga- or tera- at all. Hint by gerrit: Physicists used frequencies with the giga-/tera- prefix, I forgot that.

1 AU is then 150 gigameter or 0.15 terameter. If you are using light years, 1 light year is already 9500 terameter which is not a convenient unit. Thirty years later they finally introduced some usable metric prefixes, but I still have to find someone who uses exa-, peta-, yotta- or zetta-.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – called2voyage Jun 18 '18 at 12:43
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Perhaps one needs to go back in time and think about why the cubit (length of forearm), league (distance walked in one hour), foot, (metre - one ten-millionth of a quadrant of the Earth?? and so perhaps should not be i this list) etc were chosen as the units of distance?
They were easily understood and reproducible whilst at the same time being of a scale comparable with distances to be measured.
So in the modern world people have chosen further units of distance which initially had those characteristics.

Once these new units gain favour and papers, textbooks etc are written it is difficult to get rid of them and some would say - "Why bother?".

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Several excellent answers have already been given. But no one has talked about logarithmic perception. (https://en.wikipedia.org/wiki/Weber%E2%80%93Fechner_law)

We perceive everything logarithmic-ally. For humans, the difference between $10 metres$ and $100 metres$ is the same as between $100 metres$ and $1 km$.

Weber-Fechner Law

An illustration of the Weber–Fechner law. On each side, the lower square contains 10 more dots than the upper one. However the perception is different: On the left side, the difference between upper and lower square is clearly visible. On the right side, both squares look almost the same.

Hence it is much better to measure distance on astronomical scales in parsecs than metres because humans understand the difference between $1$ and $10$ parsecs better than they would do if the same data was presented in meters.

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    $\begingroup$ "humans understand the difference between 1 and 10 parsecs better than they would do if the same data was presented in meters." Just add one of the SI prefixes for meters and you end up with the same numerical situation. This doesn't really explain why parsecs and not petameters (Pm). $\endgroup$ – Trilarion Jul 24 '17 at 9:20
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    $\begingroup$ You could have named parsecs as petameters. We just decided that parsec sounded better. $\endgroup$ – Agile_Eagle Jul 24 '17 at 16:10
  • $\begingroup$ also parsec is convenient since its definition makes it very easy to compute distance using parallax $\endgroup$ – Agile_Eagle Jul 24 '17 at 16:56
  • $\begingroup$ I fully agree, it was very convenient. I think that in the end it's mostly a matter of convention. $\endgroup$ – Trilarion Jul 24 '17 at 19:27
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I do not know how it is in your country, but here in Russia, astronomical articles and news very often report astronomical distances in kilometers, million kilometers, billion kilometers, trillion kilometers etc. It is just we do not use units like gigameters, petameters and the like, but kilometer is the standard unit in astronomy.

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    $\begingroup$ I think you're talking about articles in popular publications, but not professional astronomical journals. $\endgroup$ – Walter Mar 25 '17 at 18:41
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Units like metres are simply too small to be used when measuring distances on an astronomical scale. While one could, in theory, use metres in conjunction with scientific notation, it is unnecessarily difficult. One Astronomical Unit is the distance between the Earth and the Sun, this acts as a sort of a cosmic metre stick.

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    $\begingroup$ Except the distance between the Sun and the Earth keeps changing, so the AU needed to be defined in some invariant units anyway... $\endgroup$ – a CVn Mar 22 '17 at 13:58
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    $\begingroup$ The AU is the semi-major axis, which is pretty close to invariant. $\endgroup$ – userLTK Mar 27 '17 at 12:43
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    $\begingroup$ "Units like metres are simply too small..." Then use a prefix to make them larger like for example a petameter (Pm). I don't see the big disadvantage. $\endgroup$ – Trilarion Jul 24 '17 at 9:24
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Astronomers don't and cannot measure distances. Distances are merely inferred from what actually has been measured, such as an angle, a relative luminosity, a time period, etc.. Most astronomical distance determinations ultimately hinge on the Earth-Sun distance (astronomical unit), which therefore is of fundamental importance (and only in modern time is known with good accuracy). For nearby stars, the parallax angle is directly related to the distance, but the distance inferred from that is not a proper measured distance: its uncertainty is not normally distributed (think about a negative parallax measurement).

Astronomers know, of course, how many meters a parsec is, and know that using meters for galactic distances is only confusing, because you have to make sure you get the correct number of 0000 all the time (or the correct power of ten).

Finally, unlike particle physics, astronomy as a science predates the meter system, at least its wider use. Changing from a well working system to something else only for the sake of conformity with SI, but for the price of inconvenience and confusion seems a stupid idea.

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  • $\begingroup$ "Distances are merely inferred from what actually has been measured..." Isn't this always like this? Observations are rarely direct and often you have to infer the value you are interested in in some way or another. This doesn't make it a less valid measurement. It's simply wrong to state that you cannot measure distances in astronomy. $\endgroup$ – Trilarion Jul 24 '17 at 9:17
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In my opinion the answer is convention (and people prefering small numbers of digits).

There isn't really more to it. Any prefix to a length is equally well valid as long as you get the conversion right and people in your field know about it.

Physically there is no difference between 1 m and 1,000,000 µm.

So all questions of the type: "Why is this prefix chosen instead of that for measuring XYZ?" have the same answer. It comes down to what is more convenient and is ultimatively quite subjective.

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It's tough to relate something like a terameter to "real lengths", because of the lack of knowledge of physical objects to compare them to. Also, because after a while, these units become just "so many more zeros". So I would suggest the following:

Space Marginal Unit (SMU): 1,000,000 meters, or roughly the distance of from one end of France to the other. The minimum distance two spacecraft would have to be from each other before they would have to coordinate trajectories or go into docking manuvers. (Give me a bit of suspension of disbelief here folks.)

Length of Earth Orbit (LEO): 1,000,000,000,000 meters, the distance the Earth travels in one year. (The distance is actually about 6% less than that, but the LEO is something that can be visualized.)

Kaid: 1,000,000,000,000,000,000 meters. That's a bit more than the distance from here to the star Alkaid.

The above readily lend themselves to everyday conversation -- if we ever get to a point where we talk about such things everyday!

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    $\begingroup$ What about scientific notation ? we can use that in place of zeroes, no ? $\endgroup$ – A---B Mar 22 '17 at 12:00
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    $\begingroup$ I don't see how this answers the question. Also, LEO is the common abbreviation for Low Earth Orbit, which is something very unlike the Earth's orbit around the Sun. $\endgroup$ – a CVn Mar 22 '17 at 13:57
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    $\begingroup$ "It's tough to relate something like a terameter to "real lengths"" Really? For me a parsec is equally tough to relate it to a length that I can feel. My simple view is that some stars and galaxies are just really, really far away. And that 1 terameter is clearly defined and therefore must have a meaning. $\endgroup$ – Trilarion Jul 24 '17 at 9:27
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The simple answer is: the larger units such as AU or light years are easier for the human brain to remember. And, we should avoid putting units with to many zeros trailing after the first few digits, for example:1,000,000,000,000,000,000,000,000,000,000 meters. we could use AU or for even higher distances, light years. If it was shorter, well we cold still use meters but with an exponent.

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  • $\begingroup$ 1 AU is about 0.15 Tm, if you use the right prefix you don't have excessive zeroes. The size of a water molecule is 0.275 nm, we don't say 0.000000000275 meters. $\endgroup$ – Arne Jun 17 '18 at 10:12

protected by called2voyage Mar 27 '17 at 14:47

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