Long-term evolution of orbital inclination due to third-body inclination

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.