A drilling apparatus includes an upper drill string, a lower drill string including a rotary drilling motor, an orientable rotatable connection between the drill strings, a reactive torque control device associated with the orientable rotatable connection, an orientation sensing device for providing a sensed actual orientation of the lower drill string, and a feedback control system configured to actuate the control device in response to the sensed actual orientation to achieve a target orientation of the lower drill string. A drilling method includes actuating the control device to prevent relative rotation of the drill strings, providing a sensed actual orientation of the lower drill string, comparing the sensed actual orientation with a target orientation of the lower drill string, actuating the control device to allow the lower drill string to rotate to provide the target orientation, and actuating the control device to prevent relative rotation of the drill strings.