Why does the coldest layer of the atmosphere burn up meteors?

Answer 1

Friction.

Let's talk about "coldest layer" for a minute.

The temperature profile of the atmosphere drops pretty sharply from the surface up to about 10km, stays more or less constant up to 20km, then starts gradually increasing again to a peak (still lower than surface temperature) around 50km, drops gradually to a minimum around 90km, then increases very sharply again above that, reaching surface temperatures again around 110km and continuing to increase beyond that.

So the coldest layer is that from around 80-100 km.

To meteors, the actual temperature of the atmosphere doesn't matter all that much. Even at the surface (which is considerably warmer than the region they mostly burn up in), the temperature is not high enough to burn up a meteor. Melt, maybe, if it were made of ice, but not much more than that.

What happens instead is that the fast-moving meteor compresses (and therefore heats ... Ideal Gas Law) the air in front of it by a lot. Also, the friction of the air rushing past the meteor heats both the air itself and the meteor. That's what makes them "burn up", not the temperature of the atmosphere itself.

(This does lead to the question of why they don't burn up even higher where the temperature is higher, and the reason for that is that temperature is a measure of the average kinetic energy of molecules. Molecules above 110 km have a lot of kinetic energy per molecule, but there aren't that many of them, so the overall energy is still low, and the meteor has little problem radiating away the small amount of energy it picks up from them.)