a fuel circuit including a pressurization valve at an outlet of the fuel circuit, a return valve, a servo valve, and a flow rate sensor having an input and an output, the output of the flow rate sensor connected in fluid communication with the return valve and the pressurization valve, wherein the servo valve is arranged to control operation of the pressurization valve;

a pump arranged to send fuel into the fuel circuit at a fuel flow rate, the fuel flow rate an increasing function of a rotational speed of a shaft of the pump, wherein the fuel is supplied to the flow rate sensor from an outlet of the pump,

the flow rate sensor comprising a sliding drawer, a return spring and a sensor for detecting a position of the sliding drawer, the position of the sliding drawer being controlled by a pressure difference across the flow rate sensor which is shaped to compensate for a force applied by the return spring to the sliding drawer, wherein the position of the sliding drawer indicates the flow rate passing through the flow rate sensor,

wherein the fuel supply system further includes an epicyclic gear arrangement arranged to drive the pump with a controllable rotational speed, and a control that controls the epicyclic gear arrangement based on a measurement provided by the flow rate sensor, wherein the rotational speed of the shaft of the pump adapts to a flow rate setpoint value at the outlet of the fuel circuit,

wherein the epicyclic gear arrangement drives the pump from a drive shaft of the turbomachine and is arranged to vary a ratio between the rotational speed of the shaft of the pump and a rotational speed of the drive shaft,

wherein the epicyclic gear arrangement comprises an epicyclic gear reducer comprising three elements, a central sun gear, an outer ring gear, and a planet carrier, whose planets mesh with the central sun gear and the outer ring gear, a first of the three elements being connected to the drive shaft and a second of the three elements being coupled to the shaft of the pump, wherein the three elements are movable in rotation about an axis of the epicyclic gear reducer, wherein the epicyclic gear arrangement further comprises at least a first electrical motor arranged to rotatably drive a third of the three elements of the epicyclic gear reducer, to modify a rotational speed ratio between the first of the three elements and second of the three elements, and

wherein the epicyclic gear arrangement comprises a second electrical motor coupled to the first of the three elements or the second of the three elements of the epicyclic gear reducer, the first electrical motor and second electrical motor being configured to transfer electrical power reversibly from one to the other.