A geodesic positioning system determines the position of a target point. The system includes a range pole that can be oriented toward the target point. A tilt sensor is arranged on the range pole, detachably where applicable, for generating a tilt angle signal related to the tilt angle of the range pole. A positioning element, more particularly a reflector or a satellite signal antenna, is arranged on the range pole. Positioning means is able to capture the position of the positioning element as a function of the tilt angle signal. Triggering means is in signal communication with the tilt sensor and with the positioning means, and adapted so that a trigger signal issued to capture the current position of the positioning element is transmitted to the positioning means as soon as the tilt angle signal corresponds to a tilt angle situated within a given tilt angle range.