Planetary g(t) for which resistive atmospheric falling is rising

A Darboux-transformed surface gravitational acceleration of the constant gravitational acceleration for a body endowed with an atmospheric layer is shown to turn the atmospheric free fall with quadratic resistance in the opposite motion, i.e., a free rising. Although the atmosphere of such a body may look completely normal, it is the time dependence of its gravitational field that produces this type of motion. The result is a consequence of general, one-parameter-dependent Darboux transformations in mathematical physics