text: This velocity () is closely related to the orbital velocity of a body in a circular orbit of the radius equal to the radial position of orbiting body on the parabolic trajectory:
  where:
  is orbital velocity of a body in circular orbit.
  Equation of motion
  For a body moving along this kind of trajectory the orbital equation is:
  where:
  is the radial distance of the orbiting body from the central body,
  is the specific angular momentum of the orbiting body,
  is the true anomaly of the orbiting body,
  is the standard gravitational parameter.
  Energy
  Under standard assumptions, the specific orbital energy () of a parabolic trajectory is zero, so the orbital energy conservation equation for this trajectory takes the form:
  where:
  is the orbital velocity of the orbiting body,
  is the radial distance of the orbiting body from the central body,
  is the standard gravitational parameter.
  This is entirely equivalent to the characteristic energy (square of the speed at infinity) being 0:
  Barker's equation
  Barker's equation relates the time of flight  to the true anomaly  of a parabolic trajectory:
  where:
  is an auxiliary variable
  is the time of periapsis passage
  is the standard gravitational parameter
  is the semi-latus rectum of the trajectory ( )
  More generally, the time between any two points on an orbit is