JPL Horizons On-Line Ephemeris System

The real orbit (or the best approximation to such) considers perturbations by all planets, a few of the larger asteroids, a few other usually small physical forces, and requires numerical integration.

[2] Instead, JPL integrates the equations of motion in Cartesian coordinates (x,y,z), and adjusts the initial conditions in order to fit modern, highly accurate measurements of planetary positions.

Objects (such as C/1980 E1) on an outbound ejection trajectory will show an eccentricity greater than 1, an apoapsis distance of AD= 9.99E+99 and an orbit period of PR= 9.99E+99.

Due to the galactic tide and passing stars it is impossible to know if an object with a weak hyperbolic trajectory will truly be ejected or gently nudged back inward.

The galactic tide and passing stars can also cause objects inbound from the Oort cloud to have a weakly hyperbolic trajectory.