To generate the impactors NEOs were randomly selected from
the Bottke NEO model and assigned random longitudes of ascending node and arguments of perihelion. Orbits with a MOID small
enough to permit an impact were saved as potential impactors
and then filtered according to their likelihood of impact to obtain
the final set of impactors. The likelihood is the fraction of time that
an object spends in close proximity to the Earth’s orbit.i.e. orbits
with a small velocity relative to the Earth tend to have shorter impact intervals and higher intrinsic impact probabilities. Higher
likelihoods received higher weighting in the selection. If an orbit
was chosen as an impactor then a year of impact was randomly selected between 2010 and 2110—the date of collision is already randomly fixed by the longitude of the node at impact. To this point,
the process assumed a two-body asteroid orbit with no planetary
perturbations. The final step was to ensure an impact under the
influence of all the perturbations in a complete Solar System
dynamical model. This was done by differentially adjusting the
two-body argument of perihelion (x) and orbital anomaly to reach
a randomly selected target plane coordinate on the figure of the
Earth. The final result is an osculating element set that leads to
an Earth impact when propagated with the full dynamical model.
The full set of impactors generate about three impacts per day uniformly distributed over the globe with an average separation of
about 70 km.
3
This technique preferentially selects objects on Earth-like orbits
out of the Bottke NEO model butBrasser and Wiegert (2008)show
that objects do not remain long in these types of orbits. This is not a
problem except in the sense addressed above—that the Bottke NEO
model is provided on a relatively coarse grid—because the NEO
model already accounts for NEO ‘residence times’ on all types of
NEO orbits. However, since we assume a flat distribution of NEO
orbit elements within the (a,e,i) bin corresponding to Earth-like orbits it is likely that we generate fractionally more of the extremely
Earth-like orbits than exist in reality