Admissible regions for too short arcs : nodal distances and oppositions

When a non identified object is observed, the first reaction of the scientific community is to try to determine its orbit. Unfortunately, for the observations collected on very short periods of time, the arc of observation is not long enough to give any estimation of the curvature and the determination of the orbit is impossible. However, in many cases, the right ascension, the declination and their instantaneous time derivatives are measurable. The idea of Milani and collaborators (see Milani et al 2004 and Gronchi et al 2004), is to draw an admissible region in the plane (r, dr/dt) compatible with the incomplete set of initial conditions. Each point of this region (called an attributable) corresponds to a virtual planet, compatible with the too short arc (TSA) data. Our purpose here is to refine this admissible region by different ways : we modify one of its boundaries, we plot the nodal distances coming from Opik's theory, we analyse the singularity in inclination, following the characteristics of the attributable, and we introduce the position of the conjonctions and oppositions on the graphics. The analysis of the results is double : either we try to reduce as much as possible the admissible regions to obtain a credible orbit for the observed candidate, or we use a maximum of data to determine whether this candidate is dangerous or not, even without getting a completely determined orbit.