  It is common practice nowadays to derive spins and 3D shapes of asteroids
from the inversion of photometric light curves. However, this method requires a
good number of photometric points and dedicated observing sessions. On the
other hand, the photometric observations carried out by the Gaia mission will
be sparse and their number relatively small. For this reason, a
multi-parametric shape described by a large number of elementary facets cannot
probably be derived from Gaia data alone. Therefore, the Data Processing and
Analysis Consortium (DPAC), implemented a simpler solution as an unattended
data reduction pipeline which relies on three axial ellipsoids for the shape
representation. However, overall accuracy of such triaxial shape solutions has
to be assessed. How adequate is an ellipsoidal approximation to represent the
overall properties of an irregular body? Which error is made on the volume in
comparison a more accurate model with irregular shape? To answer these
questions, we have implemented numerical procedures for comparing ellipsoids to
more complex and irregular shapes, and we performed a full simulation of the
photometric signal from these objects, using both shape representations.
Implementing the same software algorithm that will be used for the analysis of
Gaia asteroid photometry, rotation period, spin axis orientation and
ellipsoidal shape were derived from simulated observations of selected Main
Belt asteroids assuming a geometric scattering model (work is in progress for
more complex scattering models). We found that the ellipsoids by photometry
inversion are closely similar to the best-fitting ellipsoids of the simulated
complex shapes and that the error on the asteroid volume (relative to a complex
shape) is generally low, usually around $10\%$.
