Propulsion system for an aircraft, having: - a propeller P with propeller blades, - an electric motor E, - a transmission system for the mechanical transmission of a positive torque T + from the electric motor E so as to drive the propeller P, and for the transmission of a negative torque T_ from the propeller P in a windmilling braking state so as to drive the electric motor E, - a first input interface for the input of an input IN1, - a first unit for the control of a torque T acting on the electric motor E, where: T ε {T_, 0, T +} and T_ ≤ 0 and T + ≥ 0, - a second unit for the detection of a rotational speed RPM E of the electric motor E, - a selection unit, by means of which an active mode AM is selected from a propulsion mode PM and a recuperation mode RM, where AM ε {PM, RM}, wherein in the recuperation mode RM the electric motor E generates recuperative electrical energy E recup, and - an energy management system, by means of which an energy flow in an electrical system of the aircraft, comprising the electric motor E, is controlled as a function of the active mode AM, wherein - the selection unit is designed and set up such that the active mode AM is selected as a function of an input IN1 into the first input interface, as a function of the rotational speed RPM E of the electric motor E, and as a function of a predetermined envelope, wherein the envelope specifies a maximum positive torque Max (T +) and a minimum negative torque Min (T_ (RPM E)) dependent on a rotational speed RPM E of the electric motor E, or values dependent thereon in each case, wherein the following applies to the torque T acting on the electric motor E: T = T (RPM E) ε [Min (T_(RPM E)),..., Max (T +)]. - a propeller P with propeller blades, - an electric motor E, - a transmission system for the mechanical transmission of a positive torque T + from the electric motor E so as to drive the propeller P, and for the transmission of a negative torque T_ from the propeller P in a windmilling braking state so as to drive the electric motor E, - a first input interface for the input of an input IN1, - a first unit for the control of a torque T acting on the electric motor E, where: T ε {T_, 0, T +} and T_ ≤ 0 and T + ≥ 0, - a second unit for the detection of a rotational speed RPM E of the electric motor E, - a selection unit, by means of which an active mode AM is selected from a propulsion mode PM and a recuperation mode RM, where AM ε {PM, RM}, wherein in the recuperation mode RM the electric motor E generates recuperative electrical energy E recup, and - an energy management system, by means of which an energy flow in an electrical system of the aircraft, comprising the electric motor E, is controlled as a function of the active mode AM, - the selection unit is designed and set up such that the active mode AM is selected as a function of an input IN1 into the first input interface, as a function of the rotational speed RPM E of the electric motor E, and as a function of a predetermined envelope, wherein the envelope specifies a maximum positive torque Max (T +) and a minimum negative torque Min (T_ (RPM E)) dependent on a rotational speed RPM E of the electric motor E, or values dependent thereon in each case, wherein the following applies to the torque T acting on the electric motor E: T = T (RPM E) ε [Min (T_(RPM E)),..., Max (T +)].