Hyperbolic motion
= Hyperbolic motion
{title2=$x^2-c^2t^2=c^2t_0^2$}
Hyperbolic motion in <special relativity> is rectilinear motion with constant <proper acceleration>. A representative positive-$x$ <world line> is $x=ct_0\cosh(\tau/t_0)$, $t=t_0\sinh(\tau/t_0)$, with proper acceleration $c/t_0$. This describes a hyperbola in spacetime, not a <hyperbolic Kepler orbit>.