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Author Topic: How massive would an asteroid need to be for gravity to make it spherical?  (Read 3931 times)

Offline thedoc

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Bullmusic  asked the Naked Scientists:
   
How massive would an asteroid need to be for gravity to make it spherical?

Kevin Bull

What do you think?
« Last Edit: 01/05/2013 19:30:59 by evan_au »


 

Offline syhprum

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Off the top of my head I would have one with the mass of Ceres an opinion supported by Wiki but of course it depends to some extent as to by what materiel it is composed.
The most spherical objects are or course neutron stars which are much smaller than Ceres but have a mass of at least 3*10^30 kg

"The asteroid Ceres appears to be the smallest spherical asteroid, with a mass of around 10^21 kg"
« Last Edit: 01/05/2013 14:33:54 by syhprum »
 

Offline Bored chemist

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Well, the earth isn't quite spherical, so the answer might depend on how fast the item is spinning.
Also, if it was a liquid it would be much easier for the lumps to get pulled in.
 

Offline David Cooper

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You'd need to have some kind of definition for spherical which allows a certain size of mountains relative to the size of the planet, but that's going to be arbitrary so I don't think there's going to be a satisfactory answer. If the object starts out hot and is mainly liquid, it will go roughly spherical, but that is no guide as to what shape it could have been if it had somehow been able to form as a cold solid.

If you imagine building something like that in space as an experiment, perhaps a giant cube made of smaller cubes of rock, all glued together (or melt-frozen together at the edges) so that they can't slide relative to each other without fracturing, it would be interesting to know how big that could become before the weight in the corners began to crack and distort the lower surface regions in between, but it would likely vary a lot depending on the type of rock used, and if you used iron instead of rock it would probably make a huge difference again.
 

Offline lightarrow

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But certainly, no matter which material it is, it would always collapse if the gravity is strong enough (of course, as you say, once we have fixed the maximum height of the roughness), the problem is I don't know the answer  :)
« Last Edit: 01/05/2013 19:28:28 by lightarrow »
 

Offline evan_au

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..and then there is the question about a small object which is spherical under its own gravity (perhaps because it started liquid and then solidified), but is then struck so that it shatters.

If it melted, it would reform as a distorted sphere like Saturn's moon Mimas
If it didn't melt significantly, it would have a very irregular shape.
 

Offline lightarrow

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Someone who has the will to look up in the net for physical data of the rocks, specifically the maximum load of compression per unit area (maximum pressure which it can sustain); then, fixed, let's say, one metre as the maximum height h of the asteroid's roughnesses and, let's say, 2000 kg/m3 as typical rock's density rho, we can equal that max pressure with rho*g*h to find the maximum gravity g.

Edit: then, assuming a uniform composition and density (of course it would be just a rough approximation) it could be used the equation: g = k*r where r is the radius of the spherical asteroid and k the appropriate constant.

Edit2: assuming, just to see what comes out, 1 GPa as the plastic deformation load of a rock, the asteroid's radius should be 1 billion kilometres  ::)
Clearly, its average density couldn't be that at all...
« Last Edit: 01/05/2013 20:16:14 by lightarrow »
 

Offline lightarrow

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..and then there is the question about a small object which is spherical under its own gravity (perhaps because it started liquid and then solidified), but is then struck so that it shatters.

If it melted, it would reform as a distorted sphere like Saturn's moon Mimas
If it didn't melt significantly, it would have a very irregular shape.
Certainly. But maybe the OP intended to ask: given enough time, how big should an asteroid be to collapse, as a solid material, by its own gravity?
But of course he only could say this.
 

Online yor_on

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I think I'll go with Bored Chemist here, also assuming a 'flat space' (as locally defined), I think?
Only one billion Lightarrow? Why, I've heard of billionaires having more?

I like this site, we do not hesitate to bring clarity. To most everything conceivable, and then some.
=

although if it is spinning then there would be frame dragging involved, which locally would make a space no 'flat' at all?
Da***n.

I don't know this one either ::))
« Last Edit: 02/05/2013 10:12:44 by yor_on »
 

Online yor_on

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Maybe one can reformulate it into. "What is the most spherical object know to physics, astronomically"? Which then should be something getting to become a black hole, presumably? That is, can one assume that it under its compression at some time forming a 'perfect sphere'? Myself I would guess no, at least if we're discussing the Black Holes we've inferred so far, as they all are spinning?
 

Offline lightarrow

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Only one billion Lightarrow? Why, I've heard of billionaires having more?
LOL  ;D
Quote
although if it is spinning then there would be frame dragging involved, which locally would make a space no 'flat' at all?
even without spinning, the space wouldn't be flat, with such a mass  :)
My model fails miserably...
« Last Edit: 02/05/2013 15:44:29 by lightarrow »
 

Online yor_on

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At least you tried, we others was just hand waving, well, I was :) at least..
 

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