A mechanical gearbox for aircraft includes a sun gear with an external toothing, a ring gear with an internal toothing, and planet gears which are meshed with the sun gear and the ring gear and which each have a first toothing of average diameter D32 meshed with the toothing of the sun gear, and a second toothing of average diameter D28, different from D32, meshed with the internal toothing of the ring gear. The planet gears are guided by hydrodynamic bearings which each include a first smooth guiding surface extending at least partly under the first toothing, and a second smooth guiding surface extending at least partly under the second toothing.