论文标题
绘制关于二氧化钛的长期天然轨道，这是天王星的卫星
Mapping Long-Term Natural Orbits about Titania, a Satellite of Uranus
论文作者
论文摘要
近极和圆形轨道对自然卫星的探索引起了极大的兴趣。在文献中仍然没有研究围绕天王星卫星卫星的轨道的研究。在这项工作中，我们介绍了进行一组数值模拟的结果，以获取围绕二氧化钛探测的长效轨道。通过将重力电位扩展到二阶的扩展，由于二氧化烷的系数$ c_ {22} $，Zonal系数$ J_2 $以及天王星的重力扰动而引起的引力场的不对称性。使用多个回归模型研究了$ j_2 $和$ c_ {22} $的寿命灵敏度的分析。对不同的偏心率进行了模拟，并构建了寿命图。结果表明，由于天王星的干扰与二氧化钛的重力系数之间的平衡，低海拔和近圆形轨道具有更长的寿命。结果还表明，与$ω= 0^\ circ $相比，至关重要的是，围节点（$ω$）的非零值（$ω$）和上升节点的经度（$ω$）是必不可少的。我们还表明，具有偏心的轨道$ 10^{ - 3} $是受$ J_2 $和$ C_ {22} $的错误影响最大的轨道。
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 ($ω$) and longitude of the ascending node ($Ω$) are essential to increase the lifetime up to eight times compared to cases where $ω= Ω=0^\circ$. We also show that an orbit with eccentricity $10^{-3}$ is the most affected by errors in the values of $J_2$ and $C_{22}$.
