用于改进GARATÉA-L轨道设计的半解析理论
A Semi-Analytical Theory for Improved Orbit Design of the GARATÉA-L
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中文总结 AI 辅助
针对GARATÉA-L月球任务，提出半解析理论改进轨道设计，通过参数研究识别低漂移状态，得到的新轨道可避免碰撞，保障轨道安全。
中文摘要 AI 辅助
本研究提出一种用于改进巴西GARATÉA-L月球任务轨道设计的半解析理论。该动力学模型纳入了月球引力场直至12阶3次调和项，以及考虑地球相对于月球轨道的偏心率和倾角的第三体摄动模型。通过Hori方法，从哈密顿函数中消除短周期和中周期项，以推导基于平均轨道要素的一阶理论。研究表明，在简化的第三体运动圆轨道和赤道假设下设计的标称冻结轨道，在该更真实的动力学环境中无法维持，会导致偏心率显著增长，可能引发探测器与月球表面碰撞。第三体的倾角和偏心率的引入破坏了系统的轴向对称性，将升交点经度引入双平均变分方程，使稳定冻结轨道实际上难以实现。因此，通过围绕简化模型冻结条件的参数研究来解决该问题，以识别偏心率变化大幅降低的“低漂移”状态。本研究为GARATÉA-L提出了一种新的标称轨道，针对高保真传播和JPL星历的数值验证证实，该新构型在整个任务期间保持“低漂移”行为，确保轨道安全，避免了简化模型预测的碰撞。
英文摘要
This work proposes a semi-analytical theory for improving orbit design of the GARATÉA-L Brazilian lunar mission. The dynamical model incorporates the lunar gravitational potential up to degree 12 and order 3 harmonics and a third-body perturbation model accounting for the eccentricity and inclination of the Earth's orbit with respect to the Moon. Through Hori's method, short- and medium-period terms are eliminated from the Hamiltonian to derive a first-order theory in mean orbital elements. It is demonstrated that nominal frozen orbits designed under simplified circular and equatorial assumptions for the motion of the third body are not maintained in this more realistic dynamical environment, leading to significant eccentricity growth and potential collisions of the probe with the lunar surface. The inclusion of the third body's inclination and eccentricity breaks the system's axial symmetry, introducing the longitude of the ascending node into the double-averaged variational equations and rendering stationary frozen orbits practically unattainable. Consequently, the problem is addressed through a parametric study around the simplified model's frozen conditions to identify ``low-drift" states where eccentricity variations are highly decreased. A new nominal orbit is proposed for GARATÉA-L. Numerical validation against high-fidelity propagation and JPL ephemeris confirms that this new configuration maintains the ``low-drift" behaviour throughout the mission, ensuring orbital safety and avoiding the collision predicted by simpler models.
