Not Spaghetti

It's been over a month since I completed most of the following analysis, which I've been planning to write up more concretely. This post is intended as a summary of the basic questions I've been trying to address, although there are some mathematical issues I've worked out that I won't cover here. First, a few basic facts and some terminology regarding Earth's atmosphere. If you're already familiar with lapse rate discussions you can skip the next few paragraphs.