Abstract: We present $\texttt{jf1uids}$, a one-dimensional fluid solver that can, by virtue of a geometric formulation of the Euler equations, model radially symmetric fluid problems in a conservative manner, i.e., without losing mass or energy. For spherical problems, such as ideal supernova explosions or stellar wind-blown bubble expansions, simulating only along a radial dimension drastically reduces compute and memory demands compared to a full three-dimensional method. This simplification also alleviates constraints on backpropagation through the solver. Written in $\texttt{JAX}$, $\texttt{jf1uids}$ is a GPU-compatible and fully differentiable simulator. We demonstrate the advantages of this differentiable physics simulator by retrieving the wind's parameters for an adiabatic stellar wind expansion from the final fluid state using gradient descent. As part of a larger "stellar winds, cosmic rays and machine learning" research track, $\texttt{jf1uids}$ serves as a solid foundation to be extended with additional physics modules, foremostcosmic rays and a neural-net powered gas-cooling surrogate and improved by higher order and more accurate numerical schemes. All code is available under https://anonymous.4open.science/r/jf1uids/.