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

TL;DR

This paper demonstrates that a Darboux transformation of the gravitational field can cause a body with an atmosphere to exhibit rising motion under quadratic resistance, highlighting the influence of time-dependent gravity.

Contribution

It introduces a novel application of Darboux transformations to model how time-dependent gravity can induce atmospheric bodies to rise instead of fall.

Findings

Darboux-transformed gravity leads to rising atmospheric motion

Time dependence of gravity affects free fall dynamics

Mathematical physics methods explain unusual gravitational effects

Abstract

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