1:1 Ground-track resonance in a uniformly rotating 4th degree and order gravitational field

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• 作者：Jinglang Feng ; Ron Noomen ; Xiyun Hou…
• 关键词：Asteroid ; Resonance width ; Stability ; Chaos ; Poincaré sections ; Equilibrium Points (EPs) ; Vesta ; Betulia ; 1996 HW1
• 刊名：Celestial Mechanics and Dynamical Astronomy
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：127
• 期：1
• 页码：67-93
• 全文大小：8184KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Astrophysics and Astroparticles; Dynamical Systems and Ergodic Theory; Aerospace Technology and Astronautics; Geophysics/Geodesy; Classical Mechanics;
• 出版者：Springer Netherlands
• ISSN：1572-9478
• 卷排序：127

文摘

Using a gravitational field truncated at the 4th degree and order, the 1:1 ground-track resonance is studied. To address the main properties of this resonance, a 1-degree of freedom (1-DOF) system is firstly studied. Equilibrium points (EPs), stability and resonance width are obtained. Different from previous studies, the inclusion of non-spherical terms higher than degree and order 2 introduces new phenomena. For a further study about this resonance, a 2-DOF model which includes a main resonance term (the 1-DOF system) and a perturbing resonance term is studied. With the aid of Poincaré sections, the generation of chaos in the phase space is studied in detail by addressing the overlap process of these two resonances with arbitrary combinations of eccentricity (e) and inclination (i). Retrograde orbits, near circular orbits and near polar orbits are found to have better stability against the perturbation of the second resonance. The situations of complete chaos are estimated in the \(e-i\) plane. By applying the maximum Lyapunov Characteristic Exponent (LCE), chaos is characterized quantitatively and similar conclusions can be achieved. This study is applied to three asteroids 1996 HW1, Vesta and Betulia, but the conclusions are not restricted to them.