The effects of third-body perturbations on natural and artificial satellite orbits have been studied extensively. However, much less attention has been given to the case considering the orbital inclination of the third body. In this paper, it is shown that a perturbed orbit, even with a small initial inclination—much less than the critical Kozai inclination of 39.23 degrees—may significantly increase its inclination due to the inclination of the third-body’s orbit. To study this phenomenon, a new method for finding the inclination of the perturbed body is proposed based on a coordinate transformation. This enables the derivation of an analytical solution for the orbital inclination, predicting the long-term evolution thereof when the third body’s orbit is inclined. It is found that the amplitude of the inclination depends on the inclination of the third body, and on the relative angle between the orbital planes of the perturbed orbiter and the perturbing body. Numerical simulations illustrate the accuracy of the proposed methodology for predicting the long-term evolution of the orbital inclination.

中文翻译：

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由于第三天体倾角，轨道倾角的长期演变

已经广泛研究了第三体扰动对自然和人造卫星轨道的影响。然而，考虑到第三天体轨道倾角的情况，人们对这种情况的关注要少得多。本文表明，即使初始倾角很小——远小于 39.23 度的临界 Kozai 倾角——扰动轨道也可能由于第三体轨道的倾角而显着增加其倾角。为了研究这种现象，提出了一种基于坐标变换的扰动体倾角的新方法。这使得能够推导出轨道倾角的解析解，预测当第三天体的轨道倾斜时其长期演化。发现倾角的幅度取决于第三个天体的倾角，以及受扰轨道器和扰动体轨道平面之间的相对角度。数值模拟说明了所提出的用于预测轨道倾角长期演变的方法的准确性。