Smallest "Spherical" Planetary Object / Moon

Kitsune · Post by **Kitsune** » 2008-09-23 02:24pm

I am curious if there is a certain size where objects (not including hyper dense stuff like Neutron Stars) in space which tend to become spherical just by their own gravity? Wondering what our observations seem to show the minimum being?

Feil · Post by **Feil** » 2008-09-23 03:35pm

Not unless you specify what it's made of.

Kitsune · Post by **Kitsune** » 2008-09-23 04:17pm

The Moon is a sphere, Ceres is a sphere, Charon is a sphere (We think).....
I am looking for what are the smallest planetoids / moon type objects that still appear to be more or less spherical

Solauren · Post by **Solauren** » 2008-09-23 04:26pm

How spheical an object in space is, is in direct perportion to how much damage it's taken over the years.

After all, a bowling ball is perfectly spherical to start, but after years of bombardment with debris in space, it could at best be called 'round'.

Now, are you talking planetary formation here, or just 'in general'

Kitsune · Post by **Kitsune** » 2008-09-23 04:29pm

Planetary formation?

Kanastrous · Post by **Kanastrous** » 2008-09-23 04:59pm

Knowing the volume of the body compacting to sphericality isn't enough. What's the density of the material from which it's made?

Kitsune · Post by **Kitsune** » 2008-09-23 05:02pm

Observed? Not looking for a formula but the name of an object and how small it is?

Kanastrous · Post by **Kanastrous** » 2008-09-23 05:06pm

I don't think this is the sort of thing an astronomer would look through observational data, to learn.

I think that the formulas exist, to generate an answer once you know the entire question.

Sriad · Post by **Sriad** » 2008-09-23 05:32pm

This is one of those pesky questions that is much easier to ask than to answer.

First you have to know what you're asking about:

-What is the composition of the body? You're looking at funky calculations relating to angle of repose, gravity, and plasticity.

-How spherical do you want it? IE what's the permissible eccentricity?

-What is the body's situation in its solar system? Comets and close-orbiting bodies will become spherical more easily than those far from their star.

This is pretty much a roundabout way of saying "I don't know, and figuring it out will be hard."

To be a bit more helpful though, Phobos and Deimos are useful as a lower boundary: at 6km and 11km average radius, they're about 50% non-spherical (ie their largest dimension is 50% larger than their smallest). If you want to continue in this vein, inductively rather than deductively, I'd suggest you study small named solar objects in the 10-100km range of sizes and see where you get.

Post by **Surlethe** » 2008-09-23 06:58pm

Qualitatively, in order for an object to prevent its gravity from collapsing into a sphere, it must be able to resist the stress gravity applies to it. I'm not sure how to determine the mass in terms of the shape for an irregular body, but you can probably consider a spherical body with a mountain and then ask how large the mountain can grow with respect to the radius of the body. If the maximum height of the mountain is significant compared to the radius, then you've found a situation where the body is probably not a sphere by its own gravity.

CaptainChewbacca · Post by **CaptainChewbacca** » 2008-09-23 07:26pm

From memory (and orbital mechanics was a while ago) a rocky body will collapse into a sphere if its more than about 30 miles across.

You could probably look up a more precise answer on the 'tubes, though.

Kuroneko · Post by **Kuroneko** » 2008-09-23 11:05pm

That depends on how precise you want the answer to be. A general situation has far too many variables, but we can concentrate on the most important factor in determining the shape of the object: whether or not the bulk of the material melted during formation. The thermal energy gained from gravitational collapse would be roughly the difference in gravitational binding energies of the two configurations (some of it would be lost to other mechanisms). An order-of-magnitude estimate for a particles falling from far from the center of gravity could be (f/2)kT ≅ GMm/r, m mass of molecule, so for a bulk density ρ, so that
[1] M ≅ [ 3(fkT/2)³/[(Gm)³(4πρ)] ]^{1/2} ≅ (1/5)[fkT/(Gm)]^{3/2} ρ^{-1/2}
The particular values depend on composition, and for a rough order-of-magnitude, both 1/5 and the number of degrees of freedom f can probably be ignored with impunity (worse hand-waving was involved in the gravitational potential estimate anyway). This seems to suggest a range of 1E20-1e22kg as a minimum for a most reasonable rocky compositions.

Grandmaster Jogurt · Post by **Grandmaster Jogurt** » 2008-09-24 11:50am

Kuroneko wrote:This seems to suggest a range of 1E20-1e22kg as a minimum for a most reasonable rocky compositions.

This fits with the asteroids of the belt, at least. Hygiea is ~8.6E19kg and is ellipsoid, Pallas is ~2.2kg and is almost spherical, Vesta is ~2.7E20kg and is assumed to have been roughly spherical before a large impact, and Ceres is ~9.4E20kg and is spherical enough that the dimensions are given in terms of radius rather than three different axes.