A system and method are disclosed for computing a vehicle's motion in four dimensions (e.g., three spatial dimensions and time) and reliably predicting the vehicle's arrival time at a predetermined location, by providing a graphical display to an operator of the vehicle's progress that enables the operator to adjust the vehicle's movement and achieve the desired arrival time. Specifically, a system and method are disclosed for computing the movement of an aircraft in four dimensions, predicting its arrival time at a predetermined waypoint, and displaying (in a highly intuitive format) the aircraft's progress in achieving that desired arrival time. The pilot can then adjust the movement (e.g., speed) of the aircraft in accordance with the parameter(s) displayed, in order to achieve the desired arrival time. Thus, for example, numerous aircraft could be scheduled to arrive at a specific final approach waypoint at a predetermined rate (e.g., one aircraft per minute), which would enable the traffic controllers to optimize runway traffic without having to stack the aircraft in holding patterns and thereby waste fuel. Notably, although an example of an aircraft navigation and control system and method is disclosed, the system and method can be implemented for any type of vehicle (e.g., aircraft, spacecraft, ship, submarine, bus, train, automobile, etc.) whose operator desires to reach a particular location at a specified time.