text: Alternately, the equation can be expressed in terms of periapsis distance, in a parabolic orbit :
  Unlike Kepler's equation, which is used to solve for true anomalies in elliptical and hyperbolic trajectories, the true anomaly in Barker's equation can be solved directly for . If the following substitutions are made
  then
  With hyperbolic functions the solution can be also expressed as:
  where
  Radial parabolic trajectory
  A radial parabolic trajectory is a non-periodic trajectory on a straight line where the relative velocity of the two objects is always the escape velocity. There are two cases: the bodies move away from each other or towards each other.
  There is a rather simple expression for the position as function of time:
  where
  μ is the standard gravitational parameter
  corresponds to the extrapolated time of the fictitious starting or ending at the center of the central body.
  At any time the average speed from  is 1.5 times the current speed, i.e. 1.5 times the local escape velocity.
  To have  at the surface, apply a time shift; for the Earth (and any other spherically symmetric body with the same average density) as central body this time shift is 6 minutes and 20 seconds; seven of these periods later the height above the surface is three times the radius, etc.