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

Jinglang Feng*, Ron Noomen, Xiyun Hou, Pieter Visser, Jianping Yuan

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
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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.

Original languageEnglish
Pages (from-to)67-93
Number of pages27
JournalCelestial Mechanics and Dynamical Astronomy: an international journal of space dynamics
Issue number1
Publication statusPublished - 1 Jan 2017


  • 1996 HW1
  • Asteroid
  • Betulia
  • Chaos
  • Equilibrium Points (EPs)
  • Poincaré sections
  • Resonance width
  • Stability
  • Vesta


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