Next: 1. Introduction: the lost
THE ASTEROID IDENTIFICATION PROBLEM I:
RECOVERY OF LOST ASTEROIDS
Andrea Milani
Dipartimento di Matematica, Università di Pisa
Via Buonarroti 2
56127 PISA, ITALY
E-mail: milani@dm.unipi.it
Running title: Recovery of Lost Asteroids
Second revision, October 12, 1998
Manuscript pages: 39; Figures: 17.
Abstract:
When an asteroid is lost, the observers need to know the portion of
the celestial sphere where it could be recovered at a given time. This
region is an image of the region, in the space of orbital elements,
where the orbit is compatible with the previous observations. The map
between these two regions is nonlinear, therefore the classical linear
approximation can fail; indeed it fails by a large amount when both
these regions are large, that is precisely when an asteroid has been
observed only over a short arc and/or it has been lost for a long
time. The recovery, and identification, of asteroids long lost is very
difficult, if the only available prediction is a single point
corresponding to the least squares solution, which could be very far
from the real state; thus the availability of an efficient algorithm
to bound the recovery region is essential, also to decide if the
recovery is worth the effort. This paper proposes three new algorithms
to better approximate the recovery region, based upon approximations
going beyond linearisation. It gives the results of tests based upon
asteroids which have been recovered by chance, and could have been
found in the recovery region computed by the new algorithms. Free
software is available now, by means of which the new algorithms can be
tested, and eventually adopted, by the observers and by the
ephemerides computation centres.
Next: 1. Introduction: the lost
Andrea Milani
2000-06-21