Semi-analytical orbital model around an oblate body with an inclined eccentric perturber

The semi-analytical model (based on the averaging technique) for long-term orbital evolution has proven to be useful in both astrophysical and astrodynamical contexts. In this secular approximation, orbits exhibit rich evolutionary behaviors under the effects of various perturbations. For example, in the hierarchical three-body systems, the Lidov-Kozai mechanism based on the quadrupole-level third-body perturbation model can produce large-amplitude oscillations of the eccentricity and inclination. In recent years, the octupole order has been found to induce dramatically new features when the perturbing body’s orbit is eccentric, including extremely high eccentricities and orbit flips between prograde and retrograde. Motivated by the striking effects of the octupole-order terms, we intend to derive a more general dynamical model by incorporating J₂ of the central body and the inclined eccentric third-body perturbation to the hexadecapole order with its non-spherical gravity also included. This issue can be relevant for astrophysical and astrodynamical systems such as planets in stellar binaries, irregular satellites in planetary systems, and artificial probes about binary asteroid systems. Applications to the binary asteroid system 4951 Iwamoto and a fictitious exoplanetary system are illustrated as examples to validate our secular model. From these numerical results, we show the high accuracy of our secular model. Also, we show the important role of these high-order terms and the effects of the third-body’s inclination and eccentricity. Besides, we have found several different secular effects that could drive large eccentricities.