That's incredibly idiotic, and I may be no expert so if I am totally off base I will eat my words.
Get ready with the ketchup!
First off, our core is not radioactive namely because it is made up of one of the more stable elements.
Raptortail is correct.
80-90% of the heat inside the earth is thought to be due to the radioactive decay of isotopes like Uraniums 235 and 238, Potassium 40, Thorium 232 etc that are contained within the mantle. As these isotopes shed their excess energy they radiate heat - keeping the core liquid.
Gravitational forces are thought to account for 5-10% of the core's heat, and heat left over from the formation of the earth also is thought to be around 5-10%. But by far the majority is from radioactive decay. The percentage contributions differ widely depending on who you talk to, but it is widely accepted that radioactivity is the main contributor.
You have to bear in mind that most of the Earth's crust contains radioactive material, with each kg of surface rock giving off heat through radioactive decay equivalent to 10^-9 Watts or so.
The energy radiated by the sun over one acre on average over the period of the day is equivalent to a very small nuclear detonation.
The surface of the earth - i.e. the outer layer on which we live - heats up very fast and cools very quickly... irrespective of what the inside of the earth is doing. The surface is extremely well insulated from the heat of the core - so is hardly affected by the core temperature, and almost entirely driven by the sun. With no sun the equilibrium temp at the surface would be about -400F.
the final evidence is antarctica. It has areas frozen all year round. Now, since the earth is a globe or a sphere, that means that every spot recieves the same amount of energy on average. If we the internal heat or "radiation" as you call it is enough to keep the earth thawed and warm than explain than how antarctica is frozen. Surely if the internal heat can keep the entire crust thawed than antarctica should be entirely melted especially because of the sun being there to help for a large part of the year.
He never said that the core would maintain the temperature on the surface "thawed and warm" - but that the planet (i.e. the internal core) would not "Freeze Solid", as the temp and activity in the core is driven mainly by the radioactive decay of the various isotopes. And this will take billions of years to run down such that the earth's core solidifies.
It also doesn't have much bearing on the surface temperature... and vice versa.
The Earth will therefore NOT drop to the ambient temperature of space (about 4-Kelvin, I think)... but (and I'm still trying to find the source!) to about -400F (-240C, or about 33K).
Assuming your theory is right on the fact that there is radiation that would prevent the earth from -400 degrees it would still leave it at around -130 degrees because that is the coldest that Antarctica gets.
You misunderstood both him and me: he never said the radiation would prevent the earth reaching -400F, and I said that the
surface would reach an equilibrium of about -400F... i.e. the surface of the earth would reach -400F while the core would remain at around 10,000F for a few billion years or so.
The -400F on the surface is the equilibrium temp: i.e. at which the heat energy reaching the surface from the core matches the heat energy radiating out from the surface into space.
And the reason the temp of Antarctica (and the night side of our planet, for that matter) doesn't drop to -400F is because of the atmosphere keeping things warmer than would otherwise be the case - not because of the core temp.
So - feel free to chow down on those words.
