Physical properties of liquid Fe-S alloys (from 10 to 50 at%S) under high pressure were investigated by in situ X-ray diffraction (up to 5 GPa and 1900 K) and by ab initio calculations. The local structure of Fe-S liquid alloys clearly shows how S modifies the local arrangement of the Fe atoms. Density has been extracted from the diffuse scattering by minimization of the oscillation in the short distance of the radial distribution function g(r). Two different formalisms for the P-V-T-X equation of state are presented to model density and sound velocity as a function of pressure, temperature, and sulfur content. Based on these results, Moon's core composition is discussed. This coherent data set will serve as a thermodynamically consistent ground for modeling the core of small telluric planets and large icy satellites.