[nickjarboe]

The Earth part was just shorthand for the fact that the atmosphere and gravity of Earth add about 1.3–1.8 km/s of delta v to achieving the pure kinetic delta v of 7.8 km/s needed to achieve LEO [1]. The first stage adds almost all of this "extra" delta v.

I was mostly just correcting your "one-sixteenth of the energy required for orbit" statement. I agree that reentering at 7.8 km/s is much more difficult than 2.0 km/s, but the second stage is smaller and more spherical than the first stage. That might make reentering it a bit easier than if it had the shape of the first stage.

[1] https://en.wikipedia.org/wiki/Low_Earth_orbit

[stcredzero]

A better approximation to the 2nd stage's shape would be that of a cow.

(If that made no sense, it's a variation on an old freshman physics joke.)