Mapping Long-Term Natural Orbits about Titania, a Satellite of Uranus

Abstract

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 C22, the zonal coefficient J2, and the gravitational perturbation of Uranus is considered. The analysis of lifetime sensitivity due to possible errors in the values of J2 and C22 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 (ω) and longitude of the ascending node (Ω) are essential to increase the lifetime up to eight times compared to cases where ω=Ω=0∘. We also show that an orbit with eccentricity 10−3 is the most affected by errors in the values of J2 and C22.

Mapping Natural Orbits around Io

“…Thus, the results show the importance of properly choosing the value of the argument of the pericenter and the longitude of the node, since a successful implementation can generate orbits within the desired appropriate orbital region. Similar behaviors for ω 0 and Ω 0 are also observed around other natural satellites, which can be seen in previous works ( [25,43,44].) 3.4.…”

“…These results are important, because previous works [43,44] reinforce the results regarding the dependence of lifetimes with the choice of the initial semi-major axis around other natural satellites. In the case of orbits around Io, our maps show several initial conditions with lifetimes greater than 180 days, so evidencing orbits with good times for carrying out possible missions.…”