Thursday, July 4, 2013

Irregularity of Asteroids by Mass

The very fact that an asteroid is non-spherical proves conclusively that it has some material strength.  It would then be tempting to use its material to hold in an atmosphere, literally with no processing at all.  This would be cheap, but it would also be potentially dangerous as well as unnecessary.  The reason lies in a mass-scale argument.

Looking at what we know about asteroids, we can find that the size cutoff at which most bodies appear highly spherical is fairly close to the point where their internal pressure approaches 1 Earth atmosphere.  Because of this, it would be tempting to imagine that an asteroid's material strength may be nearly sufficient to maintain an atmosphere.  There are a few hazards with that argument, but the main takeaway is that it's not necessary.  Basically, self-gravitation is more useful than tensile strength because we have no reason to believe that an asteroid's natural tensile strength is reliable.  There are more complicated arguments involving the role of compressive strength, but I'll get into those with a later post.

Abundance of Irregular Asteroids by Pictures

Here are a few examples of asteroids at different scales that we have pictures of.  There is a combined imgage out there which preserves the length scale, although this isn't as useful as just looking at the images side-by-side, since I'm interested in their degree of irregularity.

PictureNameM (kg)Center Pressure
due to self-gravity
(in Earth atmospheres)

1 Ceres9.4 x 1020221spherical

4 Vesta2.6 x 1020185borderline

21 Lutetia1.7 x 10186.3irregular

253 Mathilde1 x 10170.27somewhat

243 Ida4.0 x 10160.36irregular

951 Gaspra2.0 x 10160.24irregular

433 Eros7.0 x 10150.12irregular

2867 Steins1.0 x 10140.0032irregular

4179 Toutatis5.0 x 10130.0027somewhat

25143 Itokawa3.0 x 10102.0 x 10-5irregular

There is somewhat a deficit of information beyond this.  If you want to see more pictures of asteroids (like I do), you might be out of luck, because almost every one of the pictures above represents a major space exploration mission.  There's also a pronounced deficit of information for Earth-like center pressures, since the above tables skips over an order of magnitude between Mathilde and Lutetia.

Note that pressure doesn't follow directly from mass.  This is because the objects have different densities, and I used those when calculating the center pressure.  A lower density will result in a lower central pressure, even for the same total mass.  That is simply a quirk of self-gravitation.

Once we get to the extremely small bodies, they seem to commonly take on the shape of an prolate spheroid.  Beyond one Earth atmosphere, the bodies all seem to conform to a roughly spherical envelope, even though there are a lot of irregularities on the surface.

For those small bodies, it's interesting to note that the speed of rotation also puts a limit on the amount of material stress we could expect from them.  A list of fastest rotating objects shows that some have a rotation on the order of a minute, but these are all several meters in diameter.

Largest Bodies Identified Irregular

Another reference for this is the Wikipedia list of solar system objects by size.  I went through that table and grabbed the largest objects that were identified as irregular.  This is a good approach because it gives a mass figure below which irregular objects start to appear is large number.  However, its major shortcoming is that we have no idea how many corresponding regular bodies exist around their mass scale.

ObjectM (kg)Shape
Proteus (moon)5.0 x 1019 irregular
Nereid (moon)3.1 x 1019 irregular
52 Europa1.7 x 1019 irregular
Davida4.4 x 1019 irregular
Sylvia1.5 x 1019 irregular
Cybele1.8 x 1019 irregular

Reasonable accounting would put the limit for irregularity at somewhere between 1017 and 1019 kg.  However, the limit I've found for a habitable inner pressure is around 1016, and can even be lower than that.  Engineering limits are still more complicated.  Even though bodies in this size range are irregular, they're still roughly spherical in many cases, indicating that material strength doesn't hold up on the scale of self-gravitational forces.  Within the size range we're interested in, the bodies are showing that they withstand some deformation against the equipotential criteria, but exactly how much is unclear.

This evidence does give a clear message - that using an asteroid to hold breathable air would involve both self-gravitation forces, as well as some material pushback.

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