\label{superfast}A spacetime diagram is shown for the journeys taken by the superluminal ships described in the text. Time is plotted against distance traveled, both measured in the frame of the Earth. Earth remains at \((0,0)\). The world line of the planet continually receding from the Earth at \(v_{p}=0.1c\), in the Earth frame, is depicted by the dark dotted line on the right. A ship traveling out at \(v=c\) to the planet is shown by the solid line. Spaceships traveling out from the Earth at speeds of (\(v=5c\), \(10c\), \(30c\), and \(\infty\)) are depicted by the (dotted, dashed, dot-dashed, triple dot-dashed) world lines respectively. World lines of similar type that connect back to Earth at times other than \(t=0\) are formally described as returning to Earth at the designated speed in the frame of the planet. However, as detailed in the paper, world lines that “return” to Earth at \(t<0\) are actually time-reversed and described by the formalism as heading out from the Earth. Therefore, these world lines better describe the trip of a second ship that left Earth before the first ship, and arrived at the planet simultaneously with the first ship. All of these world lines depict actual spaceship positions and not the images of the ships as seen back on Earth.