Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nekhoroshev estimates for the orbital stability of Earth's satellites   We provide stability estimates, obtained by implementing the Nekhoroshev
theorem, in reference to the orbital motion of a small body (satellite or space
debris) around the Earth. We consider a Hamiltonian model, averaged over fast
angles, including the $J_2$ geopotential term as well as third-body
perturbations due to Sun and Moon. We discuss how to bring the Hamiltonian into
a form suitable for the implementation of the Nekhoroshev theorem in the
version given by P\"oschel(1993) for the `non-resonant' regime. The
manipulation of the Hamiltonian includes i) averaging over fast angles, ii) a
suitable expansion around reference values for the orbit's eccentricity and
inclination, and iii) a preliminary normalization allowing to eliminate
particular terms whose existence is due to the non-zero inclination of the
invariant plane of secular motions known as the `Laplace plane'. After bringing
the Hamiltonian to a suitable form, we examine the domain of applicability of
the theorem in the action space, translating the result in the space of
physical elements. We find that the necessary conditions for the theorem to
hold are fulfilled in some non-zero measure domains in the eccentricity and
inclination plane (e, i) for a body's orbital altitude (semi-major axis) up to
about 20000 km. For altitudes around 11000 km we obtain stability times of the
order of several thousands of years in domains covering nearly all
eccentricities and inclinations of interest in applications of the satellite
problem, except for narrow zones around some so-called `inclination-dependent'
resonances. On the other hand, the domains of Nekhoroshev stability recovered
by the present method shrink in size as the semi-major axis a increases (and
the corresponding Nekhoroshev times reduce to hundreds of years), while the
stability domains practically all vanish for a > 20000 km.

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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex