After doing a little calculus, we find that the velocity and position of the ship are given by the above expressions. The equation for zh describes the asymptote to the position curve, which is the path of a light ray that intersects the t-axis at a time th. The velocity of the ship approaches c but never reaches it, since the mass, which is the resistance to acceleration, increases as the velocity increases. We also find that light emitted from too far behind us or too late will never reach the ship. More precisely, any light emitted from the region of spacetime lying to the right of the asymptote in the plot of position as a function of time cannot reach us. This means that part of the universe will never be able to communicate with the ship and is hidden from it, as long as we continue to operate our engines. The hidden region lasts only as long as we accelerate and is only hidden from us. Other observers in the universe can receive signals from the region and we will be able to also if we cut our engines and coast.

Interestingly, the time characterizing the hidden region th, which is the t-intercept for the asymptote, is the time it would take the ship to accelerate to the speed of light in Newtonian physics, which turns out to be almost a year for our particular craft.