Is there a particular size/mass limit where an object in the solar system would be have to be spherical in shape because of its size/mass? Similarly, is there minimum size/mass for an object to permanently keep a moon/moonlet in orbit?

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I don't know the answer to the first one, but I would say it's worth mentioning density in there, although of course it's implicit if you have both size and mass. But as far as the second one goes, not really, do a Google on "Ida" and "Dactyl" to see why. I suppose there would be a size at which perturbations would be enough to pull a moonlet away, but it's certainly a less meaningful limit than the first.

Added: Just to be clear, that's a single search for both the words "Ida" and "Dactyl" together.

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I would say it's around 250 miles +-50 miles because Ceres, Pallas, and Vesta are round, but the smaller asteroids aren't. It's just a guess though.

The largest irregular satellite observed is Hyperion:

http://www.solarviews.com/eng/hyperion.htm

I think the consensus is that any bodies significantly more massive than Hyperion (which is 205km along the long axis) would be spherical, but I would have thought that it also depends on density, so rocky bodies (i.e asteroids) should tend to spheres more readily than icy bodies like KBOs.

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Fin
Skep-ti-cult® member #488-28303-790

Are you sure about Vesta?

PS: And Pallas and Ceres are both listed here as having unequal diameters.

Vesta seems to be a spheroid, rather than a sphere:

http://neo.jpl.nasa.gov/images/vesta.html (Keck and Hubble images)

Actually that's interesting, because it's often suggested that Hyperion at 205km is just on the edge of going spherical (as I said above), yet Vesta is fully 525km across, which I would have thought should make it a bit more regular. For comparison, Saturn's satellite Tethys is of a similar diameter, yet almost perfectly spherical.

Could this be because Vesta is rocky and Tethys is icy?

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Fin
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In this article, Gabor Basri proposed the planetary cutoff at 700km diameter, which he says is the size necessary for an object to form into a sphere, though this does depend on the density of the object. It would seem to be a good start though.

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It also depends on the structural strength of the material. Solid rock is much stiffer than ice. Glaciers "flow" down the mountains under the pressure of their own weight. The mountains are essentially immobile under the same conditions.

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Why not use the average value of g on the 'planetary' surface as a cutoff? Then you account for density.

No matter what is chosen as the definition, there will always be bodies out there that ride the line. This is true in just about everything.

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1 m/sec**2 is a nice round figure. The disadvantage is that it makes it hard to tell whether an object is a planet unless it has a satellite.

By this criteria, Pluto is not a planet, although the Moon, Io, Europa, Ganymede, Callisto, and Titan would be if they were orbiting the sun.

Using instead 1 km/sec escape velocity, Pluto is back in as well as all the others and Triton.

Dr. Michael Brown (discoverer of Sedna) was on C2C tonight. He said that, although he did not consider Pluto to be a planet, it would probably be listed as one until we find something out there that is bigger.

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T. Anderson