or hyperbolic orbits, it is possible to solve Barker's equation and find a closed-form expression for the position as a function of time.

When , the orbit is circular. Increasing causes the circle to become elliptical. When , there are four possibilities:
* a parabolic trajectory,
* a trajectory that goes back and forth along a line segment from the centre of attraction to a point at some distance away,
* a trajectory going in or out along an infinite ray emanating from the