  We revisit the properties of the two-component Fermi gas with short-range
interactions in three dimensions, in the limit where the s-wave scattering
length diverges. Such a unitary Fermi gas possesses universal thermodynamic and
dynamical observables that are independent of any interaction length scale.
Focusing on trapped systems of N fermions, where N$\leq10$, we investigate how
well we can determine the zero-temperature behavior of the many-body system
from published few-body data on the ground-state energy and the contact. For
the unpolarized case, we find that the Bertsch parameters extracted from
trapped few-body systems all lie within 15% of the established value.
Furthermore, the few-body values for the contact are well within the range of
values determined in the literature for the many-body system. In the limit of
large spin polarization, we obtain a similar accuracy for the polaron energy,
and we estimate the polaron's effective mass from the dependence of its energy
on N. We also compute an upper bound for the squared wave-function overlap
between the unitary Fermi system and the non-interacting ground state, both for
the trapped and uniform cases. This allows us to prove that the trapped
unpolarised ground state at unitarity has zero overlap with its non-interacting
counterpart in the many-body limit N$\to \infty$.
