In this talk, I will introduce a novel Riemannian geometric model for wave propagation in gas giant planets. Terrestrial planets and gas giants have one key difference: in gas, density goes to zero at the surface, and seismic waves come to a full stop. We model the sound speed in a planet by a Riemannian metric. Starting from a polytropic model for the planet, we derive that the vanishing of the density ammounts to a specific conformal-type singularity in the Riemannian metric. We will highlight the key differences between the arising geometry and its more studied relatives. We finish with an overview of inverse problems results in our new geometry. The talk is based on joint work with Maarten de Hoop (Rice University), Joonas Ilmavirta (University of Jyväskylä), and Rafe Mazzeo (Stanford University).