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In this study, a new expansion of planetary disturbing function is developedfor describing the resonant dynamics of minor bodies with arbitraryinclinations and semimajor axis ratios. In practice, the disturbing function isexpanded around circular orbits in the first step and then, in the second step,the resulting mutual interaction between circular orbits is expanded around areference point. As usual, the resulting expansion is presented in the Fourierseries form, where the force amplitudes are dependent on the semimajor axis,eccentricity and inclination and the harmonic arguments are linear combinationsof the mean longitude, longitude of pericenter and longitude of ascending nodeof each mass. The resulting new expansion is valid for arbitrary inclinationsand semimajor axis ratios. In the case of mean motion resonant configuration,the disturbing function can be easily averaged to produce the analyticalexpansion of resonant disturbing function. Based on the analytical expansion,the Hamiltonian model of mean motion resonances is formulated, and theresulting analytical developments are applied to Jupiter's inner and co-orbitalresonances and Neptune's exterior resonances. Analytical expansion is validatedby comparing the analytical results with the associated numerical outcomes.

A new expansion of planetary disturbing function and applications to interior, co-orbital and exterior resonances with planets