Cooling of Kilrah

Astro commander

2nd Lieutenant
Ok, so I wanted to do a crude calculation for the fun of it. Im sure correct answer is orders of magnitude off, but still, orders of magnitude for astrophysics is accurate in many subfields.

In another thread it was questioned if Kilrah would still be so glowing hot if it exploded. This was brought up based on a painted planet I did which had a glowing core.
I showed the planet to my wife and she said it should be brighter at the core, more white, but I argued it exploded and was cooling so a nice yellow should be hot enough (blackbody yelloow is around 4000K depending on your eye's interpretation of blackbody spectra charts) But she countered that it exploded, which is absurd, but accepting that the core had to have gotten really hot and so thats a lot of thermal energy to dissapate. Then in this thread, it was questioned again.
So first to a chat on this topic

Yet I wanted to play and do a back of the napkin calc however woefully inadequat it would be.

If we assume
Mass Kilrah = mass earth = 6x10^24 Kg
Core is iron
Mass iron 55.8g/mol
heat capacity is 25.1J/mol*k or 450J/kg*K
Thermal mass of kilrah is 2.68 10^27 J/K
Area earth=area Kilrah = 5 10^8 km^2
boiling point of iron is 3134K so we assume that is the hottest Kilrah could be after it exploded.
Then we calcuate the energy necessary to chagne 1 degree kelvin

Q(J)=C(3x10^27 J/K)*DeltaT(1degree K)
Q=3 10^27 J to cool 1 deg Kelvin

Then using stefan-boltzman we calculate power radiated at a given temprature say T=3000K due to some explosive cooling, this is below the boiling point and we will assume no boiling or other mechanism for cooling, also ignore the suns minimal heating.

Power(W)=sigma(5.67 x10^-8 W/m2 K4) *T^4 *Area

Power(W)~8 x 10^17 Watts or J/s

Then 3x10^27 J / (8 10^17 J/s) = 3.7billion seconds or => 118 years to cool 1 degree Kelvin.

If I made a math error in there please correct.
But yea Billions of years to cool seems reasonable.
And yes there are lots of caveats as the link above points out since they look at a lot more factors. But basic blackbody suggests this will take a long time to cool in vacuum. That was fun, I hope it isnt too innacurate.
 

ChrisReid

Super Soaker Collector / Administrator
That's amazing, and I have no idea what it means, but like you said, even if you're off a couple orders of magnitude, you would still expect to see the glowy pieces in Prophecy.
 

Wedge009

Rogue Leader
Wow. I know of black body radiation and that sort of thing, but I never studied physics (not enough subjects slots left in secondary school), so most of that is beyond me.

I suppose if Kilrah remained mostly a single object, then I suppose it may be able to retain most of its heat internally. If it completely shattered into asteroid-sized pieces (for example, like Alderaan in A New Hope), then I'm sure it would take substantially less time to cool because of the greater surface area to mass ratios.

Finally, I really love that you and your wife had an intelligent discussion (note, not argument) on the colour of your Kilrah model relating to this topic.

PS Thanks for making another thread for this discussion. It really wasn't my intention to hijack your model creation thread with this topic.
 

Chernikov

Spaceman
Interesting!

Couple suggestions:

Area earth=area Kilrah = 5 10^8 km^2
Revise this way upwards? This oops this implies that large chunks of the crust are floating free with a section of mantle, effectively doubling or more the radiative surface.

The starting temperature of Kilrah may be lower than that of Earth (violent tectonics caused by thicker crust/grinds more? I could be wrong with this.) and it looks like large sections of the globe never fully liquefied. How much would this impact the rate of cooling, if at all?

Would an adjustment for the lower boiling point in a vacuum be relevant for the first few thousand years?

Possible adjustment for a large %age of other elements in the upper mantle or crust? http://hyperphysics.phy-astr.gsu.edu/hbase/tables/elabund.html

[bunch of math I don't understand at 4AM] = wow

Even if that cuts the time to cool into a third, that's still over 100k years until it's cooled, and likely usable as a glowing navigation beacon/nightlight/backdrop of impending doom for the foreseeable future.
 
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Astro commander

2nd Lieutenant
I showed her the calculation and she said while innacurate its a good first step.
She pointed out some flaws, similar to Chernikov's post

While the core of the earth may be mostly Iron, the surface is mostly silicate. Effectively a precipitate or separation of lighter and heavier elements. This among many other things changes the calculations since the silicates would radiate slightly differently and act as an insulator at the surface. But I dont feel like becoming an expert in geo-thermal physics so Ill leave it at that and say The planet exploded! If i can accept that absurdity then I can accept the rest of this with artistic liscence.

As for Hoth It takes a lot of energy to explode a planet. far less to just glass it and far less to just make it uninhabitable. Ahh sciFi. No half measures.

Thanks guys for the suggestions.

If anyone is or feels like becoming an expert please post more appropriate calculations and citations.

BTW: this is why I married my wife, our first real conversation was about the nuances of transporter technology and its application to removing annoying drivers from the road and planting their vehical halfway into the ground where they can nolonger be a nuisance. She was arguing relative inertial issues with teleportation which won me over.
 

Wedge009

Rogue Leader
I think the implication is that the Temblor bomb shattered the planet apart, disintegrating it. If, however, the pieces were in close enough proximity as to allow gravity to pull Kilrah back together, I suppose it's possible. It certainly wouldn't have any chance of sustaining life again within the current generation, though. Any atmosphere would have been lost in the initial explosion.

Although, given my track record with physics in this thread, real-world or otherwise, I'm sure someone will come along and say something that completely destroys my theories.
 

-danr-

Vice Admiral
Thanks for the thread, and also to Wedge009 for the link - in a way it's nice that mankind could set off all of his nuclear weapons at once and Earth's structure would remain intact and in orbit of the sun... The article sort of casts the Behemoth method into doubt, but I work in genetics and know basically next to nothing about the concepts of the physics in the article (or above)...

For a bonus point, can anybody remember the power output of Behemoth's big gun as decribed by Tolwyn? I've no idea without looking.
 

ChrisReid

Super Soaker Collector / Administrator
I think the implication is that the Temblor bomb shattered the planet apart, disintegrating it. If, however, the pieces were in close enough proximity as to allow gravity to pull Kilrah back together, I suppose it's possible.

I don't think disintegration is the right word. That implies a lot more matter to energy type explosion. amd the Temblor was more on the order of shaking the pieces apart. Perhaps the "explosion" is still happening when we see the planet in Prophecy, but it's so much of a planet-sized ball of mass that I don't know why the planet wouldn't reform.

The Kilrah System is full of asteroids, but the orbit that Kilrah itself had was obviously good for planet formation, so when you stick that much rocky stuff in that orbit, glopping back together into a planet is just what rocks do. https://cdn.wcnews.com/newestshots/full/kilrah.gif
 
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-danr-

Vice Admiral
The Kilrah System is full of asteroids, but the orbit that Kilrah itself had was obviously good for planet formation, so when you stick that much rocky stuff in that orbit, glopping back together into a planet is just what rocks do. https://cdn.wcnews.com/newestshots/full/kilrah.gif

Again, I'm no physicist, but that seems like sound science - given that every object has a gravitational pull proportional to its mass (as per Newton's theory)...I guess by 2681, big parts of Kilrah were amassed, held together in the void in a planet-shaped arrangement.

It's cool that Kilrah appears in Prophecy, a view '12 years on' but I can remember being unhappy when I first saw it because in WC3, the T-bomb explosion appeared to have almost vaporized the entire core, at least from the cut scene (can't remember how the novel describes the destruction taking place, will have a check later to see what it says.) Obviously the concept of shaking apart, and the above is a much better scientific version of events.
 
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Wedge009

Rogue Leader
I don't think disintegration is the right word.... when you stick that much rocky stuff in that orbit, glopping back together into a planet is just what rocks do.
You're right, disintegration perhaps isn't quite what I was meaning, though as danr mentioned, the WC3 video appears to show Kilrah completely disappearing (although one could argue that this was just for simplicity of the animation).

Also, the image you showed still has the hot core of Kilrah exposed, which, as the original topic of this thread is about, would imply that this interpretation of Kilrah never split apart into such small pieces - otherwise those individual pieces would have cooled down much faster than a planet-sized chunk of rock would. For Kilrah to still be glowing with heat in this scene, a very large portion of it would need to have remained without being broken up.
 

Mancubus

Rear Admiral
It's also possible that Kilrath is not cooling AT ALL - instead it keeps temperature or is getting even hotter, because small bits of platnet, that were blown away by T-bomb, are still falling back on it - constantly, with each impact generating extra heat. Also it seems that Kilrath was never truly destroyed - in the sense it never really siezed being a planet - tectonic forces released with the temblor detonation shatered the crust and sent lots of bits into space, but probably never really dameged the core itself
 

-danr-

Vice Admiral
the WC3 video appears to show Kilrah completely disappearing

We should also take into account the animation of Kilrah's destruction as seen in Armada, where it appears to come apart into several large pieces - Armada alone however doesn't specify if it was destroyed via the T-Bomb.

but probably never really dameged the core itself

That seems to be the implication from Prophecy, unless you count the molten stuff oozing outwards from the center. I really must get 'Heart Of The Tiger' from the shelf now and take a look.
 

-danr-

Vice Admiral
*Sorry to hijack thread* The novelisation is very brief about Kilrah coming apart:

From "Heart Of The Tiger" - William R. Forstchen.

Blair did not see the effects of the bomb. It took time for the 1st quakes to trigger subsidiery effects, radiating outward through all the inter-connected fault lines. The Excalibur had already reached orbit by the time the quakes became planetwide, collapsing Kilrathi made buildings and structures within the major quake zones.


Blair managed to steer clear of the largest of the debris... but his Excalibur was battered by smaller fragments. As Kilrah came apart, spreading out into a cloud of drifting asteroids... the fighters engines finally failed. He was drifting free now... trapped in the doomed system.
 
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