The Impact Monitoring (IM) of Near Earth Objects (NEOs) is a fundamental part of the planetary defense strategy. Current NEO IM systems (Aegis, NEODyS and Sentry) scan the Confidence Region (CR) of each observed object looking for Virtual Impactors (VIs) with a time horizon of about 100 years. This procedure is performed regardless of the uncertainty with which the orbit of the object is known, and without considering whether a scattering encounter is present in the propagation time span. In view of the likely future increase of the IM workload due to higher future NEO discovery rates, it might be more reasonable to adapt the predictability horizon of the impacts to each object, taking into account the orbit uncertainty and the close encounters experienced. In this paper we discuss the problem of estimating a reasonable predictability horizon when multiple close encounters are present and start to address the problem proposing a formal mathematical definition of scattering encounter.

The future space debris environment will be dominated by the production of fragments coming from massive fragmentations. In order to identify the most relevant parameters influencing the long term evolution of the environment and to assess the criticality of selected space objects in different regions of the circumterrestrial space, a large parametric study was performed. In this framework some indicators were produced to quantify and rank the relevance of selected fragmentations on the long term evolution of the space debris population. Based on the results of the fragmentation studies, a novel analytic index, the Criticality of Spacecraft Index, aimed at ranking the environmental criticality of abandoned objects in LEO, has been devised and tested on a sample population of orbiting objects.

After the PR disaster of 1997 XF11 (March 1998), we started a crash research program on impact predictions. The difficulty was the chaotic motion of Earth-crossing asteroids (orbit uncertainty increases exponentially with time); it can be solved by replacing a real asteroid with a swarm of Virtual Asteroids. In 1999 we introduced Geometric Sampling to replace Monte-Carlo methods (see Milani, Chesley & Valsecchi, A&A 346, 1999). In November 1999 the first Impact Monitoring system CLOMON was operational. From 2002 the second generation systems CLOMON2 at Pisa and SENTRY at JPL are operational: critical cases are scanned for possible impacts in the next 90–100 years.

We have for this General Assembly 25 new applications for C20 membership, which represents about 10% increase with respect to the total number of members. We are very satisfied with the increase rate of our commission membership, which reflects the high degree of activity in our field. Nevertheless we note that there are not many people involved in the commission business.

The meeting was opened by Ted Bowell, president, at 11 am. The 2006 Division III meetings were reviewed by Guy Consolmagno, secretary; as the minutes of those meetings have already been published, they were assumed to be approved.

Commission 20 has been involved in the discussion on discovery credit rules of solar system objects (mainly concerned with asteroids) in particular with the role played by dynamicists in recovering objects by linking their orbits with previous apparitions. A working group was set up to discuss the issue that was integrated by professional astronomers as well as amateurs. There was some exchange of opinions and conflicting views, but the trend of the majority was to keep the discovery credit for the discoverer whose observations led to the object's principal designation, as expressed in the MPC existing rules (see <cfa-www.harvard.edu/iau/info/HowNamed.html>), considering only exceptionally credit for dynamicists when linkage of different apparitions led to the recovery of a lost object. The precise definition of non-trivial linkage should be worked out, and for the time being, the idea is to keep the existing MPC rules and, if necessary, to improve them, rather than starting a new set of rules.

Division III's activities focus on a broad range of astronomical research on bodies in the solar system (excluding the Sun), on extrasolar planets, and on the search for life in the Universe.

A total of 16 among the new IAU members have asked to join Commission 20; they are: Jerome Berthier, Nicholas J. Cooper, Marco Delbò, Romina P. Di Sisto, Michael W. Evans, Tetsuharu Fuse, Ludmila Hudkova, Yurij N. Krugly, Elena N. Polyakhova, Zhanna Pozhalova, Alessandro Rossi, Qi Rui, Jonathan D. Shanklin, Slawomira E. Szutowicz, Gino Tuccari and Hong-Suh Yim. Moreover, two requests to join the Commission have been received by astronomers that are already IAU members: Peter De Cat and Ricardo A. Gil-Hutton.

Some of the problems related to Near Earth Objects (NEOs), like orbit determination and ephemeris computation, are not new, and had to be dealt with since the beginning of NEO astronomy. The latter practically started with the discovery of Comet D/1770 L1 Lexell, that passed very close to the Earth in 1770; studies of the chaotic dynamics of this exceptional object continued well into the XIXth century. At the end of the XXth century there has been a renewal of interest in NEOs, as attested by IAU Symposium 236.

The Working Group was formed at the request of the Board of DivisionIII and approved by the IAU Executive committee in March 2004. This was in recognition of the fact that discoveries in the Trans Neptunian region were repeatedly raising the question of “what is a planet”. The task of the WG was to investigate the options available and give indications of the level of support and opposition for each if more than one option was emerging.

The past triennium has continued to see a huge influx of astrometric positions of small solar system bodies provided by near-Earth object (NEO) surveys. As a result, the size of the orbital databases of all populations of small solar system bodies continues to increase dramatically, and this in turn allows finer and finer analyses of the types of motion in various regions of the orbital elements space.

The uncertainty of the close approach distance of a Potentially Hazardous Object (PHO), either an asteroid or a comet, can be represented on the Modified Target Plane (MTP), a modification of the one used by Öpik. The MTP is orthogonal to the geocentric velocity at the closest approach along the nominal orbit, solution of the least square fit to the observations. The confidence regions of this solution in the 6-D space of orbital elements (for an epoch close to the observations) are well approximated by a family of concentric ellipsoids, if the observed arc is not too short. In the linear approximation these ellipsoids are mapped on the MTP into concentric ellipses, which can be computed by solving for the state transition matrix.

For a PHO observed at only one opposition, with a close approach expected after many revolutions, the ellipses on the MTP become extremely elongated and the linear approximation may fail. In this case the confidence boundaries on the MTP, i.e. the nonlinear images of the confidence ellipsoids, may not be well approximated by the ellipses. The Monte Carlo method (Muinonen and Bowell, 1993) can be used to find nonlinear confidence regions, but the computational load is very heavy: to estimate a low probability event the number of test cases must be larger than the inverse of the probability. We propose a new method to compute semilinear confidence boundaries on the MTP (Milani and Valsecchi, 1998), based on the theory developed to compute confidence boundaries for predicted observations (Milani, 1999). This method is a good compromise between reliability and computational load, and can be used for real time risk assessment.