I was wondering what the minimum amount of mass was for an object to become spherical. I am assuming it is constant, since I doubt gravity changes from object to object. Can anyone help?

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It's gotten to the point where careful investigation is needed just to tell parody from reality. I think that means reality is broken.- Noclevername.

It depends on the stuff the object is made from, too, since warm ice will flow a bit better than cold ice, which flows better than rock. A big ball of water would become spherical very readily, for instance.

So Mimas, radius 196km, is pretty much spherical with some big relief. Mass, 3.6e19 kg.
Hyperion, with a mean radius of 150km is a big slab of a thing. Mass 1.1e19 kg. So for icy things at the temperatures around Saturn, the cut-off seems to be somewhere between those two.
But Proteus, radius over 200km, mass around 5e19 kg, is very lumpy, presumably because of its lower temperature out beside Neptune. (Or perhaps it's because Mimas has been warmed by tidal heating or the big Herschel impact.)

Vesta is also non-spherical with a radius of 210km, but it's made of basalt.

Grant Hutchison

Thank you. It looks like I need a favour. Given what you just said, how would you reword this statement (regardless of whether you think it is correct)?

"A planet is an object that orbits a star and is large enough to become spherical under its own gravity."

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Wikipedia: A MMORPG for self-denialists.

It's gotten to the point where careful investigation is needed just to tell parody from reality. I think that means reality is broken.- Noclevername.

I dunno. If sphericity is your qualifying feature for planethood, just leave it as it is.
But you'd need to qualify what deviation from the mean radius makes an object not spherical. (1%? 0.1%? Some fixed distance?)
You should also bear in mind that Jupiter and Saturn aren't remotely spherical. Objects settle into equipotential surfaces, not spheres - so if they're rotating, or in a tidal environment, they'll be ellipsoidal.

Grant Hutchison

If it's water, all you need is one drop (~50mg) - but then, that thas nothing to do with gravity, it's just the dipole-dipole attraction of the molecules.

Sphericity probably won't work well to define what is and isn't a planet. Really, really cold water ice is terribly strong stuff. Even with that, though, moderate sized moons in our solar system are pretty round. If most of the moons were off wandering around the sun with no parent planet, we still probably wouldn't want to call them planets.

Sphericity occurs when the gravitational force is able to create an internal pressure that can overpower the counter pressure created by atoms in a 'solid' lattice arrangement. Water molecules freeze to a certain configuration and strongly resist alterations. Apply enough pressure, though, and they will flex and shear. That's how glaciers flow down hill too. One way to answer this for water near freezing temperatures is to ask how tall a column of ice can be before the bottom begins to flex under the weight of the column.

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-al

I agree with the others before me. Even with a refined definition about getting to within 0.1% of the equipotential surface, you'd still be making a kind of arbitrary rule that could permit certain objects that melted (such as Ceres) as planets, and rejecting larger strange objects like the "cigar-shaped" giant KBO that was recently announced.

We will probably end up saying things like:
- Star xxxxxxxxxxxx is orbited by 4 objects with mass > 10^30 grams another 7 objects above 10^28 grams, and a 215 (discovered so far) above 10^24 grams. These objects have the following designations and orbital parameters...

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