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Measuring the lack of integrabiity of the J_{2} problem for earth's satellites
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We consider the motion around an oblate primary, keeping only the J2 term in the
expansion of the potential in spherical harmonics. The problem has cylindrical symmetry. It has
been suspected for a long time, due to numerical evidences, that the problem is non integrable.
This has been proved recently [4]. However, even if the system is non integrable, the size of the
stochastic zones can be so small that they can be neglected for all practica! purposes. This is what
we study here, and we show that for the case of the Earth and considering possible real orbits, i.e.,
non colliding with the Earth, the effect of the non integrability can be completely neglected.
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Preprint enviat per a la seva publicació en una revista científica: Predictability, Stability, and Chaos in N-Body Dynamical Systems , vol 272. pp 305-309. [https://doi.org/10.1007/978-1-4684-5997-5_26]
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SIMÓ, Carles. Measuring the lack of integrabiity of the J_{2} problem for earth's satellites. [consulted: 12 of August of 2026]. Available at: https://hdl.handle.net/2445/151959