<p>Such units of area, or something similar, <em>are</em> used.</p>
<p>In particular, they crop up in observations, and the astrophysics of discs, which are essentially 2D objects, where a key observational or physical property would be the luminosity or mass per unit area.</p>
<p>The unit per square au would be approriately used for protoplanetary discs, whereas per square light year (or the somewhat bigger per square parsec) would be used for galactic discs.</p>
<p>References to come, but you could look at the <a href="https://en.wikipedia.org/wiki/Kennicutt%E2%80%93Schmidt_law" rel="noreferrer">Kennicutt-Schmidt law</a>, which is the power law proportionality between star formation rate and mass of gas <em>per unit area</em> in a galactic disc. Usually expressed in units of pc<span class="math-container">$^{-2}$</span>, (or kpc<span class="math-container">$^{-2}$</span>) but that's only because
astrophysicists use parsecs rather than light years.</p>
<p>Some other random examples:</p>
<p><a href="https://ui.adsabs.harvard.edu/abs/1989MNRAS.239..571K/abstract" rel="noreferrer">Kuijken &amp; Gilmore (1989)</a> - a well-cited paper in the field. &quot;The mass distribution in the galactic disc. I - A technique to determine the integral surface mass density of the disc near the sun.&quot;</p>
<blockquote>
<p>The results show a total surface mass density of the galactic disk of <span class="math-container">$46\pm 9$</span> solar masses/sq pc.</p>
</blockquote>
<p>Having a bit more trouble finding reference using au<span class="math-container">$^2$</span> - actually, protoplanetary surface mass densities are more often expressed in SI or cgs units (g cm<span class="math-container">$^{-2}$</span>), but I did find that disc angular momentum (SI unit kg m<span class="math-container">$^2$</span> s<span class="math-container">$^{-1}$</span>) is sometimes conveniently expressed as <span class="math-container">$M_\odot$</span> au<span class="math-container">$^2$</span> yr<span class="math-container">$^{-1}$</span>. For example, in <a href="https://ui.adsabs.harvard.edu/abs/2005ApJ...627L.153D/abstract" rel="noreferrer">Davis (2005)</a> &quot;The Surface Density Distribution in the Solar Nebula&quot;</p>
<blockquote>
<p>The augmented system possesses an angular momentum of <span class="math-container">$5.349\times 10^{51}$</span> g cm<span class="math-container">$^2$</span> s<span class="math-container">$^{-1}$</span> (<span class="math-container">$0.379\ M_\odot$</span> AU<span class="math-container">$^2$</span> yr<span class="math-container">$^{-1}$</span>).</p>
</blockquote>

CC BY-SA 4.0
2024-11-21T08:17:39.870Z
2024-11-21T21:47:50.733Z
2024-11-21T21:47:50.733Z
ProfRob
<p>Area shows up in astronomy, but usually only in terms of portions of the sky as seen from a viewpoint. For example, discussions about telescopes and other detection equipment will often talk about how much of the sky it can observe at the same time, which is described in terms of square degrees (or more likely much smaller fractions thereof, like square arcminutes). The ESA's Euclid Telescope has a wide-angle camera that can look at a relatively enormous 0.5 degrees^2, just to mention a recent one. Technically that's really describing an angular area projected through space, but it's about as close as we get.</p>
<p>A concrete area measure like a square lightyear can theoretically exist, it just isn't all that useful astronomically because space is three-dimensional, and a flat plane in space isn't particularly useful for describing anything. Area is useful here on earth because we live in a world where verticality is only occasionally important -- things like land, floor space, and shelf space are measured in square units because height isn't usually relevant for purposes of comparison.</p>
<p>In space, we usually need to talk about volumes, which is to say <em>cubic</em> light years or cubic parsecs or whatever. And we do, when discussing things like star cluster density. (I don't think I've ever run across a cubic AU, but in theory it could be used for talking about stuff like the Oort cloud.)</p>

CC BY-SA 4.0
2024-11-21T08:32:11.680Z
"... usually only in terms of portions of the sky as seen from a viewpoint." -- which sounds like an awful lot of observational astronomy. And you're ignoring all surface-brightness measurements (mag/arcsec^2, MJy/sr, etc.).
Peter Erwin
CC BY-SA 4.0
2024-11-21T12:55:44.777Z
I'm not trying to downplay the usefulness of angular areas, it's just not what the OP was asking about (but I suspect it's what we do use for the kinds of things they're thinking of using square-lightyears for).
Darth Pseudonym
CC BY-SA 4.0
2024-11-21T15:57:41.347Z
You could describe the size of a galaxy or solar system by its area, but in practice we just use its diameter, as they're isomorphic.
Barmar
CC BY-SA 4.0
2024-11-25T10:05:22.147Z
Regarding the Oort cloud; it starts at 20,000 au and goes out to around 50,000 au. So its volume is about 5e14 au^3 - that's 2.5 cubic light years!
Oscar Bravo
CC BY-SA 4.0
2024-11-21T05:18:10.820Z
2024-11-21T12:56:45.817Z
2024-11-21T12:56:45.817Z
Darth Pseudonym
<p>Why aren't square units of measurements used in astronomy? Wouldn't it be useful to some degree, for example for finding the average amount of galaxies in x amounts of square AUs?</p>

CC BY-SA 4.0
2024-11-20T19:13:21.243Z
There are. Surface brightness is usually in units of magnitude per square arcsec, column densities are usually number of particles per square cm along some line of sight, and surface densities for galaxies are often in units of mass per square parsec (or square kiloparsec).
Peter Erwin
CC BY-SA 4.0
2024-11-21T00:19:01.820Z
There is no real use for **square** units for astronomical units or light years, but there are indeed **cubic** light years and cubic parsecs…
Pierre Paquette
CC BY-SA 4.0
2024-11-21T02:10:02.243Z
"the average amount of galaxies in x amounts of square au's": square AUs of what surface?
Christopher James Huff
CC BY-SA 4.0
2024-11-21T08:07:08.550Z
@PierrePaquette what about the Schmidt-Kennicutt law or the physics of accretion discs?
ProfRob
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2024-11-21T17:11:07.297Z
-1 How exactly would you find "amount of galaxies in x amounts of square AUs"?
Mithoron
CC BY-SA 4.0
2024-11-21T18:57:00.237Z
You *could* do the calculations for Kepler's second law ("a planet covers the same area of space in the same amount of time no matter where it is in its orbit"—[Orbits and Kepler’s Laws](https://science.nasa.gov/resource/orbits-and-keplers-laws/)), but you'd end up with messy conversion factors.
Andrew Morton
CC BY-SA 4.0
2024-11-21T23:53:16.243Z
@ProfRob: Never heard of it, but I suppose there are exceptions to what I said.
Pierre Paquette
CC BY-SA 4.0
2024-11-22T06:07:28.500Z
*Cubic* light years are not uncommon ("[The true stellar density near the Sun is estimated as 0.004 stars per cubic light year"](https://en.wikipedia.org/wiki/Stellar_density)); I suppose they are more common because, well, space and stuff.
Peter - Reinstate Monica
CC BY-SA 4.0
2024-11-22T20:12:10.993Z
@RabbiKaii Fun fact: the fractal dimension of the universe is actually rather close to 2.
Acccumulation
CC BY-SA 4.0
2024-11-24T13:41:48.317Z
@Acccumulation fun fact? More like fun FRACT. I'll show myself out
Rabbi Kaii
<observational-astronomy>
Why aren't there square astronomical units or square light years?
Modern inc.
# Why aren't there square astronomical units or square light years?

(Asked by: username_0 on 2024-11-20)

Why aren't square units of measurements used in astronomy? Wouldn't it be useful to some degree, for example for finding the average amount of galaxies in x amounts of square AUs?

**Tags:** observational-astronomy

> **Comments:**
> **username_1**: There are. Surface brightness is usually in units of magnitude per square arcsec, column densities are usually number of particles per square cm along some line of sight, and surface densities for galaxies are often in units of mass per square parsec (or square kiloparsec).  
> **username_2**: There is no real use for **square** units for astronomical units or light years, but there are indeed **cubic** light years and cubic parsecs…  
> **username_3**: "the average amount of galaxies in x amounts of square au's": square AUs of what surface?  
> **username_4**: @PierrePaquette what about the Schmidt-Kennicutt law or the physics of accretion discs?  
> **username_5**: -1 How exactly would you find "amount of galaxies in x amounts of square AUs"?  
> **username_6**: You *could* do the calculations for Kepler's second law ("a planet covers the same area of space in the same amount of time no matter where it is in its orbit"—[Orbits and Kepler’s Laws](https://science.nasa.gov/resource/orbits-and-keplers-laws/)), but you'd end up with messy conversion factors.  
> **username_2**: @username_4: Never heard of it, but I suppose there are exceptions to what I said.  
> **username_7**: *Cubic* light years are not uncommon ("[The true stellar density near the Sun is estimated as 0.004 stars per cubic light year"](https://en.wikipedia.org/wiki/Stellar_density)); I suppose they are more common because, well, space and stuff.  
> **username_8**: @RabbiKaii Fun fact: the fractal dimension of the universe is actually rather close to 2.  
> **username_9**: @username_8 fun fact? More like fun FRACT. I'll show myself out  

---

## 2 answers

### Answer by username_4 on 2024-11-21. Score: 21

Such units of area, or something similar, *are* used.

In particular, they crop up in observations, and the astrophysics of discs, which are essentially 2D objects, where a key observational or physical property would be the luminosity or mass per unit area.

The unit per square au would be approriately used for protoplanetary discs, whereas per square light year (or the somewhat bigger per square parsec) would be used for galactic discs.

References to come, but you could look at the [Kennicutt-Schmidt law](https://en.wikipedia.org/wiki/Kennicutt%E2%80%93Schmidt_law), which is the power law proportionality between star formation rate and mass of gas *per unit area* in a galactic disc. Usually expressed in units of pc$^{-2}$, (or kpc$^{-2}$) but that's only because
astrophysicists use parsecs rather than light years.

Some other random examples:

[Kuijken & Gilmore (1989)](https://ui.adsabs.harvard.edu/abs/1989MNRAS.239..571K/abstract) - a well-cited paper in the field. "The mass distribution in the galactic disc. I - A technique to determine the integral surface mass density of the disc near the sun."

> The results show a total surface mass density of the galactic disk of $46\pm 9$ solar masses/sq pc.

Having a bit more trouble finding reference using au$^2$ - actually, protoplanetary surface mass densities are more often expressed in SI or cgs units (g cm$^{-2}$), but I did find that disc angular momentum (SI unit kg m$^2$ s$^{-1}$) is sometimes conveniently expressed as $M\_\odot$ au$^2$ yr$^{-1}$. For example, in [Davis (2005)](https://ui.adsabs.harvard.edu/abs/2005ApJ...627L.153D/abstract) "The Surface Density Distribution in the Solar Nebula"

> The augmented system possesses an angular momentum of $5.349\times 10^{51}$ g cm$^2$ s$^{-1}$ ($0.379\ M\_\odot$ AU$^2$ yr$^{-1}$).


---

### Answer by username_10 on 2024-11-21. Score: 11

Area shows up in astronomy, but usually only in terms of portions of the sky as seen from a viewpoint. For example, discussions about telescopes and other detection equipment will often talk about how much of the sky it can observe at the same time, which is described in terms of square degrees (or more likely much smaller fractions thereof, like square arcminutes). The ESA's Euclid Telescope has a wide-angle camera that can look at a relatively enormous 0.5 degrees^2, just to mention a recent one. Technically that's really describing an angular area projected through space, but it's about as close as we get.

A concrete area measure like a square lightyear can theoretically exist, it just isn't all that useful astronomically because space is three-dimensional, and a flat plane in space isn't particularly useful for describing anything. Area is useful here on earth because we live in a world where verticality is only occasionally important -- things like land, floor space, and shelf space are measured in square units because height isn't usually relevant for purposes of comparison.

In space, we usually need to talk about volumes, which is to say *cubic* light years or cubic parsecs or whatever. And we do, when discussing things like star cluster density. (I don't think I've ever run across a cubic AU, but in theory it could be used for talking about stuff like the Oort cloud.)

> **Comments:**
> **username_1**: "... usually only in terms of portions of the sky as seen from a viewpoint." -- which sounds like an awful lot of observational astronomy. And you're ignoring all surface-brightness measurements (mag/arcsec^2, MJy/sr, etc.).  
> **username_10**: I'm not trying to downplay the usefulness of angular areas, it's just not what the OP was asking about (but I suspect it's what we do use for the kinds of things they're thinking of using square-lightyears for).  
> **username_11**: You could describe the size of a galaxy or solar system by its area, but in practice we just use its diameter, as they're isomorphic.  
> **username_12**: Regarding the Oort cloud; it starts at 20,000 au and goes out to around 50,000 au. So its volume is about 5e14 au^3 - that's 2.5 cubic light years!  

---

