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## 1.1 Virtual asteroids and lost asteroids

When an asteroid is discovered, we do not know anything like ``the orbit'' of the real object. There is a range of possible orbits, all compatible with the observations, forming a region of confidence in orbital element space. We can describe this by thinking of a swarm of virtual asteroids, with slightly different orbits all compatible with the observations. The reality of the asteroid is shared among the virtual ones, in the sense that only one of them is real, but we do not know which one. To make things simple, we can think that all the virtual objects are equally likely to be the real one; a more complicated probability law could be used, changing the exact values of the estimated probabilities but not the qualitative picture. Since the confidence region contains a continuum of orbits, each virtual asteroid is in turn representative of a small region, that is its orbit is also uncertain, but to a much smaller degree 1. Note that the so called ``nominal'' orbit is just one of the virtual asteroids, without any special significance.

What does it mean that an asteroid is lost? The virtual asteroids, as seen in the sky, are initially very close together, within the range of possible errors in the observations; as time goes by, they gradually separate, mostly because of small differences in the semimajor axis; they thus become like a string of pearls, ``the wampum of the night.'' When the length of the string, as seen in the sky, is too long to be contained in a reasonable number of fields of view of a typical telescope, the real asteroid cannot be recovered by using the ephemerides, that is a single prediction of the position based upon the nominal orbit. It could be recovered by taking many frames, but to discuss this we need to introduce the notion of negative observation: one telescope frame needs to be scanned to ascertain that the asteroid is not there, that is, that some virtual asteroids do not exist, before going to scan another frame. When the number of required frames is very large, the observational expense of the recovery may not be warranted, and the asteroid is considered lost.

What should be done to recover an asteroid when it is indeed lost, but is of special significance? The observational scanning of many frames where different virtual asteroids could be found needs not to be done with the same telescope, and not in the same night. For each virtual asteroid there are better times for observation, as an example when it is bright enough 2. For each of these recovery opportunities the negative observations need to be recorded, and some coordinating center needs to assemble the negative observations to make sure that all virtual asteroids have been searched for (``to see that none is due'') until the real one is found. It is important that the sampling of the confidence region by virtual asteroids be dense enough to ensure that the real asteroid does not slip through a gap in observation coverage. This idea was discussed by [Bowell et al. 1993], who attempted to recover the historically important asteroid (719) Albert, which is desperately lost.

Next: 1.2 Virtual impactors Up: 1. The problem Previous: 1. The problem
Andrea Milani
2000-06-21