Let’s say I took a little trip to outer space – WAY outer, as in far enough from any stars to not be bothered by any gravitational fields of any consequence. I throw a special switch which turns off all gravity everywhere, and chuckle silently at the mayhem I’ve just caused on the Jersey Turnpike.
I then pull a 6 inch iron cube out of my backpack and set it in front of me. I then set a second cube six inches from the first one – that is, there is a six inch space between them. A third cube goes six inches from the second, and I continue in this way until I have made a line of cubes a million miles long.
Then I construct a second line six inches from the first, then a third line six inches from that, and continue until I have a million miles of rows. Then I continue with layers on top of that grid, so that I have a cube that’s a million miles in all dimensions.
I then sit back and throw that special switch that turns gravity back on everywhere. The results in Jersey must be particularly amusing – but what happens to my cube?
What if, instead of iron blocks, they’re made out of granite? Or ice?
The outward cubes would be drawn to the center of the cube. The combined mass of the cubes in the center would be significant (way more than the Earth). Eventually (and probably not all that long a time) all the cubes would be mushed into the center. I suspect the center would grow quite hot from the pressure and turn molten. In time you’d end up with an iron planet…a big one (note: fission cannot occur with iron so no star for this [at least at iron fission is a net loss in energy so will not self sustain itself]).
As for different materials gravity is based on mass. So, the more dense something is the more mass it has thus a greater gravitational pull. Granite or ice would still easily draw all the cubes to the center. Heck, a cube that big of styrofoam cubes would be a significant mass.
Your cubes would tuble together and form a big iron sphere. We’ve talked about the gravity of cube-shaped planets on this Board before. Bizarro World to the contrary wotwithstanding, the strength of material needed to keep the corners of a cube world from collapsing under their own weight would be monumental (in any reasonably-sized world). There’s a reason they build planets spherical.
If you could build a cubical planet and keep it that shape, you’d get interesting results. Oceans would form in the middles of faces. Gravity would point in unexpected directions, not always towards the geometric center of your cube. The corners would stick up above your atmosphere.
Hydrogen is best (so I suppose ice would be a good start for a solid since it has a lot of hydrogen). As you move up the periodic ladder in elements fusion (I know I said fission before…my bad :smack: although fission won’t work for it either) gets more difficult requiring greater pressure and temperature. Hydrogen, being at the bottom of that ladder is easiest to fuse. When star fuses its way to iron the fusion engine stops.
And yes, eventually the cube would become a sphere.
Given that amount of iron collapsing, wouldn’t it collapse into a black hole? At the least it would hit “maximum scrunch” and have a spectacular rebound.
I don’t think so. I did some quick back-of-the-envelope calculations and I think the whole cube only has a mass of about 20% of the mass of our sun. In order for gravitational collapse to form a black hole you need to start with a mass 3 to 4 times larger than our sun.
It certainly wouldn’t form anything solid though. The potential energy released by the collapse would vaporize the iron. What you’d wind up with is a big sphere of very, very hot iron atoms. Hmmm … now I’m wondering how hard it would be to calculate the color it would glow … .
A 6 X 6 X 6" iron cube (216 cubic inches) will mass 27.9 kg.
A row of such cubes, 1 a foot for a million miles, will contain 5,280,000,000 cubes and mass 147312000000 kg.
Cube that to get the mass of your construct: 3.2 X 10[sup]33[/sup] kg.
That’s about 1600 solar masses, so you’re going to end up up with a fair to middling size black hole when things settle down.
If the construct were made of ice, it’d mass about 200 suns, and might settle down to become a large star, before exhausting all its nuclear fuel and becoming a black hole.
You’re cubing the mass of a row, but you should just be cubing the number of cubes in a row.
Essentially your formula is:
(mass of a row) x (mass of a row) x (mass of a row)
When it should be:
(cubes in a row) x (cubes in a row) x (cubes in a row) x (mass of one cube)
If you use the latter formula you get a result that’s much smaller – about 20% of the mass of the sun. Which is the same result I got above. So no black hole!
True, but iron is much denser than mostly hydrogen and helium.
Probably not enough the make a difference…or is it ?
At the very least you’d probably have to wait a long time until that molten iron went from hot enough to be nearly gaseous to something a fair bit cooler.
It shouldn’t make any difference. Neutronium is far denser than iron, but neutron stars massing more than our sun still don’t collapse into black holes.
I was thinking all along that the core of this structure would come together first, with the outer pieces flying in last, and at high speed. But that’s not what would really happen, is it? Wouldn’t it first form an outer shell and still have a semi-hollow interior?
No, everything is going to be pulled toward the center of mass. There won’t be any hollow interior.
I did some more quick calculations and I think the outermost cubes will start falling inward with an acceleration of about 15,000 m/s^2, or about 1500 x the acceleration that objects experience under Earth gravity. The entire collapse should only take a few hours.
As the cubes on the interior start to heat up and vaporize, the pressure of the interior will increase, slowing the collapse. After the initial inward rush the superheated iron will stabilize as a gaseous sphere then slowly shrink over thousands of years as it gradually radiates its heat away.
I was thinking that since the outer pieces had more gravity acting on them, they’d accelerate faster – but instead of forming an outer shell, the whole structure would come together all at once, right? Every cube impacts every other cube at the same time?
That’s kind of weird to think about, a corner cube travelling so fast it could go from the Earth to the Moon in just a couple of hours – and yet taking just as long to close the six inch gap with its neighbor.
OK, iron has a density of about 7.8, and you’re starting off with a 1/8 filling factor, so the net density (at the start) will be right around 1 (that is, the density of water). A million-mile cube of water would have a mass of 4e30 kg (about twice the mass of the Sun), which would give it a Schwarzschild radius of [about 6 km]((1000000 miles)^3*(1 g/cc)2G/c^2) (much smaller than the size of this object, so it’s not going to immediately become a black hole). It will, however, collapse significantly further, and it’s above the Chandrasekhar limit, so it’ll probably end up as a neutron star. And it’s not quite clear whether a neutron star can be that big, either, so it just might still end up as a black hole anyway, and is certainly close to becoming one.
Whoops, you’re right. I dropped an order of magnitude somewhere. I was getting 0.2 of a solar mass instead of 2.0.
I just redid my calculations on a 500,000 mile cube of iron with a density of ~8 kg/m^3 and I get the correct result … about twice the mass of the sun. So, yes, it’s about the right size to potentially collapse into a black hole.
