Abstract
We consider the motion of a massless particle around an oblate planet, keeping only in the expression of the perturbing potential the second degree zonal harmonic. We prove the analytical non integrability of this problem, by using Ziglin's theorem and the Yoshida criterion for homogeneous potentials.
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Irigoyen, M., Simó, C. Non integrability of theJ 2 problem. Celestial Mech Dyn Astr 55, 281–287 (1993). https://doi.org/10.1007/BF00692515
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DOI: https://doi.org/10.1007/BF00692515