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

作　　者：Han-Lun Lei 雷汉伦(School of Astronomy and Space Science,Nanjing University,Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education,Nanjing University,Nanjing 210023,China)

机构地区：[1]School of Astronomy and Space Science,Nanjing University,Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education,Nanjing University,Nanjing 210023,China

出　　处：《Research in Astronomy and Astrophysics》2021年第12期433-452,共20页天文和天体物理学研究（英文版）

基　　金：financial support of the National Natural Science Foundation of China (No. 12073011);the National Key R&D Program of China (No. 2019YFA0706601)。

摘　　要：In this study, a new expansion of planetary disturbing function is developed for describing the resonant dynamics of minor bodies with arbitrary inclinations and semimajor axis ratios. In practice, the disturbing function is expanded around circular orbits in the first step and then, in the second step, the resulting mutual interaction between circular orbits is expanded around a reference point. As usual, the resulting expansion is presented in the Fourier series form, where the force amplitudes are dependent on the semimajor axis, eccentricity and inclination, and the harmonic arguments are linear combinations of the mean longitude, longitude of pericenter and longitude of ascending node of each mass. The resulting new expansion is valid for arbitrary inclinations and semimajor axis ratios. In the case of mean motion resonant configuration, the disturbing function can be easily averaged to produce the analytical expansion of resonant disturbing function. Based on the analytical expansion, the Hamiltonian model of mean motion resonances is formulated, and the resulting analytical developments are applied to Jupiter's inner and coorbital resonances and Neptune's exterior resonances. Analytical expansion is validated by comparing the analytical results with the associated numerical outcomes.

关 键 词：celestial mechanics 

分 类 号：P133[天文地球—天体力学]