I totally agree with you and the other commenters that the total area of the spherical shell is only increasing by a few %, but I still think for the purposes o

I totally agree with you and the other commenters that the total area of the spherical shell is only increasing by a few %, but I still think for the purposes of "escaping earth" as the top level comment was talking about, all that matters is how spread out things are directly above you. When talking about the area of the spherical shells, it conflates what is above me as equally relevant to things that are on the other side of the planet from me. That is, satellite X and Y may be over me at 500km and 1000km distance, respectively. Later, they may be directly through the earth from me at distance 13200km and 13700km distance. In the first case, if I shine a laser straight up, my probability of hitting X is 4 times higher than my probability of hitting Y. In the second case, (if I could somehow shine a laser straight through the earth), the probabilities are nearly equal. But my intuition is that for the purpose of escaping earth, this second case does not matter, because we are just dealing with what is above us, not the entire spherical shell.