### Why don't astronomers use meters to measure astronomical distances?

• 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?

As you noted, we do. They're just in groups of 1,000 or greater.

Because it's not useful to do so.

Planetary distances are most often measured in Astronomical Units (AU), not km. Like light years, the unit tells you something useful about the distance, e.g. 1 AU is the average distance from the Earth to the Sun.

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.

For the same reason that you buy rice in KG, not by the grain.

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?

@DmitryGrigoryev: that depends on how common it is to use those units for that kind of measure, so it is a matter of tradition. I grew up with the metric system, and to this day it is not very helpful if they tell me that someone is 5'7'' tall; but I can assure you that it is exactly the opposite for someone who grew up in America.

@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.

I actually know a guy who likes to measure length in attoparsecs.

@JohnEye I think we all know That Guy.

Astrophysicists never use light-years, journalists use light-years because they think it is a sciency-concept that the public can understand. Amusingly if anyone actually understands the *distance* of a light-year, they would have no problem with the *distance* of a parsec.

I my thesis, I used centimeters. I did calculations of H2 clouds 10^18 cm in size.

@dotancohen Your "buy rice in KG" is a good example of what the question is asking: we don't mind lugging around an extra factor of 1000 there, even though the metric unit is inconvenient (we use kilogram rather than the metric unit of gram). If we can speak in kilograms and not think it inconvenient, why not speak in gigametres or petametres?

@ShreevatsaR: We buy rice by the **kilogram**, not the **kilograin**. I get what you are saying, but the amount of grains we eat don't really, matter. What matters is the mass of food that we eat. By measuring rice in kilograms and also potatoes in kilograms, we can compare portions. Similarly, the AU and lightyear give us a better way to compare distances than do the SI prefixes with the meter.

@dotancohen I didn't mention grains in my comment. I only pointed out that we _do_ indeed buy rice by the **kilo**gram, not gram. If we can measure different quantities in kilograms (an SI prefix with the gram), we can also measure different distances in (say) terametres (and compare them that way).

@dotancohen "Similarly, the AU and lightyear give us a better way to compare distances than do the SI prefixes with the meter." I fail to see how this is better? But I agree that kilogram is better than kilograin. I would conclude that then petameters must be better than some obscure other unit, because it only matters that it's a length (a really long length but way beyond our imagination anyway). AU and pc are there because they were first and have historical relevance. In the end it's all convention. But I wouldn't bet in 100 years people will still use it.

"Megatons" is actually a good example of a non-SI unit. A megaton is not a unit of mass, it's a unit of energy = 4.184 gigajoules. (It's indirectly based on energy released from the explosion of a "TNT-equivalent" mass, but as an energy unit it's clearly not a standard, power-of-ten SI unit.)

My favourite are Light Years and AU... Rather than raw maths, most humans can create a clearer mind-map and logical framework with comparative images. originally using feet, steps, hands, counting 20's because of fingers... It's natural for humans to use earth-sun and light-year to logically interpret space distances. AU is especially easy. Parsecs are simple images too when you imagine AU's. They are only weird when you are fresh out of prelim science studies.. Syllabels with TERS dont lend themselves to stars conversations, it's also preferential linguistics, same reason how french say 97.

IIRC, AU are useful because for the longest time we weren't sure how exactly far away the sun is, but we did know distances of other planets compared to the earth thanks to Kepler's third law. And the math of Kepler's law becomes easier when you reduce the earth's distance to 1.

1 TM (terameter) would be $\approx$ 6 AU. 1 EM (exameter) would by $\approx$ 11 ly. 1 YM (yottameter) would be 11million light years, still a thousandth of the visible Universe, but the scale ends here.

The radius of the visible Universe would be $\approx$ 1200 YM. I think it wouldn't be so bad. However, using the Planck units is not possible, because they all depend on the gravitational constant, and we know it only with $\approx$ 5 digits precision. The SI meter depends only the SI second and on the speed of light, both are known very precisely. Maybe if once we will be able to know also G with at least 10-12 digits precision, a new scale based on purely the Planck units will become useful.

5 years ago

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:
$$\frac{D}{1\, \mathrm{parsec}} = \frac{\frac{\pi}{180\times60\times60}}{\tan\left(\pi_{\mathrm{angle}} \frac{\pi\, \mathrm{radians}}{180\times60\times60 \, \mathrm{arcsec}}\right)}.$$
In other words, $$1\operatorname{parsec} = \frac{180\times 3600}{\pi} \operatorname{AU}$$.

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.

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.

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)

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.

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.

Astronomers don't seriously use pi_angle for parallax angle, do they? That seems potentially confusing =).

No, they don't, @ChrisChudzicki, it's usually just $\pi$. They also don't usually use radians, so I added the subscript to disambiguate. See: https://en.wikipedia.org/wiki/List_of_common_astronomy_symbols

Astronomers really like Gaussian units for a number of reasons. Electric and magnetic fields have the same units! This makes complete sense since they are the same thing in different frames. The only constant in Maxwell's equations is the speed of light!

@KAI It only makes sense for electric and magnetic fields to have the same units in unit systems where the speed of light is unitless. The relationship between them, in terms of units, is fundamentally no different than the relationship between momentum and energy, etc. Put another way, the vector potential and the electric potential should differ by a factor of $c$.

Isn't it also a question of accuracy ? I remember school, where we studied why units were important : e.g. in a road distance of 58 km (beware this is a compound unit, thus we can see it as "another unit than meters with the same root and a 1000x factor"), it does not matter if you have +/- 0.05km, but if you say that distance is 58000 meters, the acceptable accuracy would be something like +/- 0.05m. Applying this to AU, it does not matter if there is a +/-50000km error in the measure, it is an order of magnitude. Please correct me if I'm not right.

@Benj You are not right. I don't know how old the conventions are, but the sig-fig conventions and scientific notation both handle specifying astronomical distances in AU and meters equally well. Granted, you save a little writing when discussing solar system objects and nearby stars when using AU and parsecs, respectively, but that's a matter of convenience not a technical necessity. That said, you can't underestimate the value of convenience, especially in the pre-computer world.

@SeanLake that's not incompatible and you're rigth the convenience aspect is a real point