  The Planck mission, originally devised for cosmological studies, offers the
opportunity to observe Solar System objects at millimetric and submillimetric
wavelengths. We concentrate in this paper on the asteroids of the Main Belt. We
intend to estimate the number of asteroids that can can be detected during the
mission and to evaluate the strength of their signal. We have rescaled the
instrument sensitivities, calculated by the LFI and HFI teams for sources fixed
in the sky, introducing some degradation factors to properly account for moving
objects. In this way a detection threshold is derived for asteroidal detection
that is related to the diameter of the asteroid and its geocentric distance. We
have developed a numerical code that models the detection of asteroids in the
LFI and HFI channels during the mission. This code perfoprms a detailed
integration of the orbits of the asteroids in the timespan of the mission and
identifies those bodies that fall in the beams of Planck and their signal
stenght. According to our simulations, a total of 397 objects will be observed
by Planck and an asteroidal body will be detected in some beam in 30% of the
total sky scan--circles. A significant fraction (in the range from ~50 to 100
objects) of the 397 asteroids will be observed with a high S/N ratio. Flux
measurements of a large sample of asteroids in the submillimeter and millimeter
range are relevant since they allow to analyze the thermal emission and its
relation to the surface and regolith properties. Furthermore, it will be
possible to check on a wider base the two standard thermal models, based on a
nonrotating or rapidly rotating sphere. Our method can also be used to separate
Solar System sources from cosmological sources in the survey. This work is
based on Planck LFI activities.
