A planetary gear mechanism has a rotatable planet carrier, a device for conducting oil, and a housing-fixed oil collecting duct. The oil collecting duct surrounds an area of the planet carrier in the circumferential direction. Oil centrifuged off by the planet carrier is collected in the oil collecting duct. In the installation position of the oil collecting duct, the oil is conducted by a gravitational force in the direction of a lower collection area formed with an outlet through which oil can be discharged. A further outlet, through which oil can be conducted, is provided in front of the collection area with respect to the rotational direction of the planet carrier between an upper area of the oil collecting duct, as it appears in the installation position of the oil collecting duct, and the outlet. Also, an aircraft gas turbine with the planetary gear mechanism.