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which we have considered wide variations of all the relevant parameters
(sidereal period, axial ratios, pole coordinates, initial rotational phase of
the object). The tests have been performed so far using different simulators
of Gaia photometric data developed independently by different teams in
the Gaia Solar System Working Group. Most tests have been carried out so
far by simulating Gaia photometric observations of asteroids, both in the
main belt and belonging to the near-Earth population, having ideal triax-
ial ellipsoid shapes. In these cases, the inversion algorithm is able to find
the “true” solution (spin period, pole coordinates, and axial ratios) with
an excellent accuracy. Preliminary tests are encouraging, however, even
in cases of simulated objects having more complicated shapes. Moreover,
a few preliminary tests concerning real asteroids previously observed by
the Hipparcos satellite are also encouraging. For instance, the correct spin
period, and a reasonable general shape have been obtained in the case of
asteroid 216 Kleopatra, in spite of a small number of available Hipparcos
measurements (of the order of 20). In this respect, the simulations carried
out so far allow us to derive an estimate of the performances of the inver-
sion algorithm as a function of the number of available observations for a
given object, and as a function of the photometric accuracy of the observa-
tions. In particular, it turns out that excellent inversions of triaxial objects
can be obtained for data-sets of about 30 measurements, characterized by
Gaussian observational errors having a
σ
of 0.02 mag. This is significantly
larger than the expected Gaia photometric error bars for objects fainter
than
V
=18
.
5, to be pessimistic. Moreover, we have also checked that the
inversion algorithm is able to determine the right sense of rotation of the
objects, as theoretically expected.
We note that another fully independent approach, adopted by other col-
leagues from Helsinki is also being applied for the treatment of simulated
Gaia photometric data. The method is based on a different approach.
4
According to simulations, also this technique seems to be extremely
effective.
It should be stressed that the data-set of sparse Gaia photometric detec-
tions will be qualitatively similar to what we can expect to come in the
future from ground-based asteroid surveys like Pan-STARRS or the Large-
Aperture Synoptic Survey Telescope. This means that the same techniques
of photometric inversion that are being developed for Gaia will be also use-
ful for the above-mentioned surveys. The main difference, however, is that
Gaia will be able to sample the possible range of ecliptic longitudes (hence,
aspect angles) of the objects at a much faster pace than ground-based
