These hyperbolic reformulations of the general relativistic equations of motion are useful when we wish to reckon time intervals in our own proper time (t) for certain computations rather than using rest-frame or Earth time (T). These equations are useful in designing software to compute or simulate the effects of long-term space travel, including the effects of space-time dilation.

  SI Units are assumed

  c = Speed of light = 299,792,458 m/s
  x = Distance accelerated during time interval (T or t)
  a = Acceleration rate experienced aboard spacecraft
  T = Time interval according to rest-frame (Earth)
  t = Time interval (proper time) according to spacecraft