[cubic_earth]

Simplifying assumptions are allowed when reasoning about physics. What you are saying is interesting, but I think you might be misapplying it. For small heights differences, the difference in gravitation approaches 0. A ball raised .0002 mm off the ground has twice the potential energy of one raised only .0001 mm. But that is never true for speed. An object moving 0.0002 MPH does have 4x the kinetic energy of an object moving 0.0001 MPH.

So yeah, I am zooming in on an exponential and calling it linear, but that doesn't work for speed. And doubling of velocity gives 4x the energy regardless of how tiny the step.