Special relativity relates measurements in a ‘‘moving’’ frame to measurements in a ‘‘rest’’ frame. Navigation, as it is performed in practice, uses neither pure a ‘‘rest’’ nor pure a ‘‘moving’’ frame, but instead measures distance in the fixed, Earth, frame and time in the moving, ship, frame. Brehme diagrams arise naturally when relative motion is considered using navigational coordinates. In navigational coordinates the Lorentz transformation is expressible as an ordinary orthogonal transformation.