  Fireball networks establish the trajectories of meteoritic material passing
through Earth's atmosphere, from which they can derive pre-entry orbits.
Triangulated atmospheric trajectory data requires different orbit determination
methods to those applied to observational data beyond the Earth's
sphere-of-influence, such as telescopic observations of asteroids. Currently,
the vast majority of fireball networks determine and publish orbital data using
an analytical approach, with little flexibility to include orbital
perturbations. Here we present a novel numerical technique for determining
meteoroid orbits from fireball network data and compare it to previously
established methods. The re-entry of the Hayabusa spacecraft, with its known
pre-Earth orbit, provides a unique opportunity to perform this comparison as it
was observed by fireball network cameras. As initial sightings of the Hayabusa
spacecraft and capsule were made at different altitudes, we are able to
quantify the atmosphere's influence on the determined pre-Earth orbit.
Considering these trajectories independently, we found the orbits determined by
the novel numerical approach to align closer to JAXA's telemetry in both cases.
Comparing the orbits determined from the capsule's re-entry shows the need for
an atmospheric model, which the prevailing analytical approach lacks. Using
simulations, we determine the atmospheric perturbation to become significant at
~90 km; higher than the first observations of typical meteorite dropping
events. Using further simulations, we find the most substantial differences
between techniques to occur at both low entry velocities and Moon passing
trajectories. These regions of comparative divergence demonstrate the need for
perturbation inclusion within the chosen orbit determination algorithm.
