# If the Earth was a giant metal cube. . .

1. Jun 14, 2004

### smithpa9

A 43-year-old collegue of mine asked a childlike, yet intriguing question today. Perhaps someone could help answer it:

If (somehow) a giant metal cube the size of the Earth appeared out of nowhere, what would happen? Would it:

a) stay basically that way
b) immediately get crushed under it's own weight down to a spherical shape
c) something in between

Would it's center eventually turn to liquid under the heat caused by gravitational pressure?

2. Jun 14, 2004

### marcus

just for definiteness, did your colleague specify the initial conditions?

maybe gravity is turned off and
the cube is room temperature
when it initially appears and then
gravity is suddenly turned on

dont mean to be picky but I want to think
of the cube as having some initial temp
such as 2.7 kelvin (temp in open space)
or room or whatever

if it starts at room temp and the cube is mercury
then I picture it flinging globs of itself into space
because of all the gravitational energy released
The collapse of the liquid cube would set up huge waves
as it tried to assume spherical shape but kept sloshing

if the cube were sodium I would expect geysers to erupt of
liquid and gaseous sodium----blowing holes in the solid sodium crust
the final landscape might be dominated by dead volcanoes

if the cube were tungsten it might retain traces of the original cubic shape

but if it were made of gold the Klingons would steal it, so this
would not be a good idea

3. Jun 14, 2004

### smithpa9

Thanks Marcus. Your initial conditions sound reasonable. Let's say it's made of a less exotic metal, like iron. And ignore any malicious intent of our would-be cosmic neighbors :-)

do we stay cubic, or become a big cue ball?

4. Jun 14, 2004

### marcus

so out in the middle of nowhere there is this iron planet with
eight big mountains

the (inscribed sphere) radius is, say, 6000 kilometers
and the height of the each mountain is

$$\sqrt{3} - 1$$

times 6000 kilometers

so each one is around 4400 kilometers high

we want to know how geologically stable these eight mountains are

the planet starts out room temperature through and through

at the moment gravity is turned on there is a kind of huge boing
and the planet shrinks slightly and some gravitational energy
is released
we want to figure out where that energy goes

Jim Graber would know immediately and he was around here this
morning. Several other PF people would know. I will be quiet and listen.
It is a nice problem. Tell your friend.

Last edited: Jun 14, 2004
5. Jun 18, 2004

### Andre

That might be a bit more. The normal density of iron is 7870 kg/m3 at standard atmospheric pressure. The assumed iron core of the Earth has a density of about 11,000 kg/m3 (outer core) and 12,400 kg/m3 (inner core).

Hence perhaps quite a bit of compression/shrinking

6. Jun 18, 2004

### Phobos

Staff Emeritus
I suppose we should specify timeframes too. e.g., a few years vs. a few hundred million years (you'll get some significant cratering in that timeframe)

7. Jun 18, 2004

### shrumeo

i remember a friend of mine calculating (under the influence of sheer boredome) that an aluminum cube could be no more than (IIRC) something like 3-4 miles wide or it would crack apart under it's own weight (here on earth) , too bad i can' remember the math he used ( i think he just calculated the weight of a column of aluminum and compared it to it's tensile strength.)

but I think if a metal has any amount of maleability, that eventually it would become spherical, if it was only under the influence of it's own gravity. And if it was the size of the earth, and iron, then the core should be molten and rotating and it should have the biggest baddest magnetic field around.

I think we could calculate it. Figure out what the gavity would be for that much mass of whatever metal, then find out where the stresses would exceed the strengths in the cube and see if the points of the cube would deform.

8. Jun 18, 2004

### Nereid

Staff Emeritus
At least one quite critical initial condition was left out: rotation. Can we assume that our iron cube starts off rotating about an axis through the centre of a pair of opposite faces, with a period of 24 hours?

No, make that two: the Moon; does our iron cube have a ~spherical satellite (whose mass and density are the same as our Moon's, and whose distance - Cog to Cog - is the same too)?

We can quickly calculate an OOM pressure at the 'base' of one of the eight 'iron mountains', and compare it with the tensile strength of room temperature iron; my guess is the 'mountains' would be essentially in free fall, the forces will differ by at least 2 OOM. Among other things, this will result in pretty strong 'ironquakes'

There's also no doubt that there will be some shrinkage; as Andre said, the density of the core will rise considerably (same as for iron mountains, but not so many OOM out of balance; equilibrium (pressure, density, temperature) will be established (enter: thermodynamic equations of state)). How long will this take? I've no idea, except that it won't be hours or tens of millions of years :yuck:

So, the core will melt (gravitational potential energy), the temperature gradients will result in convection currents, and we'll quickly get the "biggest baddest magnetic field around", as shrumeo said. How plastic is iron? How similar to mantle currents will the 'mantle iron' become? But these are longer term effects; the collapsing iron mountains will generate enough heat, quickly, likely to melt the 'crust' to a depth of several hundred km.

Whew! And all this without even the tiniest envelope.

9. Jun 21, 2004

### TeV

This is about model I had in my mind (didn't noticed that part in first thread reading).Form of gravitational "collapse" will be going on,realising the energy and raising the temperature in various regions of the system under various pressures.
But ,without dissipation to the surrounding ambient the system (geometry)
will be unsteady in this case:shrinking and expanding..