  This work presents a new parametrisation suitable for parameter-space studies
of heliocentric Earth-impacting orbits. Originally motivated by the issue of
potentially hazardous asteroids (PHAs) and the mitigation of such a risk, we
show that the simultaneous analysis of all the conceivable impacting elliptical
orbits is greatly facilitated by the use of a parametrisation that involves
only the true anomaly at impact, the eccentricity and the inclination.
  While the new parametrisation is presented from an explicit planetary-defence
perspective, it is general enough to be useful in analogous studies.
