In the method for propelling an aircraft, to obtain electric energy, a fuel is combusted, and an electric machine is used, wherein the fuel is used to cool at least one part of the electric machine and contains natural gas. The propulsion system is configured to propel an aircraft, in particular according to the above-mentioned method. The propulsion system has an electric machine configured to obtain electric energy by combusting a fuel. The propulsion system further includes a natural gas tank configured to supply the fuel formed with natural gas, and a cooling device configured to cool at least one part of the electric machine. The aircraft has such a propulsion system.