Description:
<jats:title>Abstract</jats:title><jats:p>This study is based on the definition of the admissible region introduced by Milani <jats:italic>et al</jats:italic>.(2004); in the search for potential Earth impactors, this theory allows to take into account the partial data of the TSA (<jats:italic>Too Short Arcs</jats:italic>) from which it is impossible to deduce a full orbit. Only a set of 4 variables (two angles and their instantaneous time derivatives), called an <jats:italic>attributable</jats:italic>, is known; a few suitable boundary conditions allow to restrict the motions to a specific bounded 2-dimensional region. In this work, a new inner boundary of this region is introduced, based on the geocentric hyperbolic motion of the immediate impactors; the nodal distances (crossings of the virtual asteroidal orbits with the Earth's orbit) are drawn for two different test attributables, associated with a determination of circular and linear orbits. This could reduce the search for impactors (by propagation of the orbits) to a one-dimensional set. A few comments about elongations and complementary curves complete this paper.</jats:p>