Abstract
The recently discovered Kepler circumbinary systems and the circumbinary polar-ring debris disc in the 99 Herculis system call for the study of circumbinary orbits. As an approximation, it is advisable to investigate the problem with the assumption that the outer body is massless. In such a scheme, we briefly summarize the main characteristics of the evolution of the orbits and give the general solutions to some secular orbital elements under the quadrupole formalism and then, using the solution, explore the octupole Hamiltonian, which allows us to reveal the evolution of the eccentricity of the outer orbit. By doing so, we have discovered that the evolution of slightly inclined orbits does not deviate much from coplanar ones. For the near polar configurations, the inner binary can significantly excite the eccentricity of such orbits (in some cases to about 0.3); this may influence the stability of orbits near the binary.
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