2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167467We solve the brachistochrone problem for a particle travelling through a spherical mass distribution of uniform density. We examine the connection between this problem and the popular "gravity elevator" result. The solution is compared to the well known brachistochrone problem of a particle in a uniform gravitational field.3 pages, 1 figureMathematical Physics49S05text