  Close polar and circular orbits are of great interest for the exploration of
natural satellites. There are still no studies in the literature investigating
orbits around Titania, the largest satellite of Uranus. In this work, we
present results of a set of numerical simulations carried out to obtain
long-duration orbits for a probe around Titania. Through an expansion of the
gravitational potential up to second order, the asymmetry of the gravitational
field due to Titania's coefficient $C_{22}$, the zonal coefficient $J_2$, and
the gravitational perturbation of Uranus is considered. The analysis of
lifetime sensitivity due to possible errors in the values of $J_2$ and $C_{22}$
is investigated using multiple regression models. Simulations were performed
for different eccentricity values, and lifetime maps were constructed. The
results show that low-altitude and near-circular orbits have longer lifetimes
due to the balance between the disturbance of Uranus and the gravitational
coefficients of Titania. The results also show that non-zero values of the
longitude of periapsis ($\omega$) and longitude of the ascending node
($\Omega$) are essential to increase the lifetime up to eight times compared to
cases where $\omega= \Omega=0^\circ$. We also show that an orbit with
eccentricity $10^{-3}$ is the most affected by errors in the values of $J_2$
and $C_{22}$.
