Nekhoroshev estimates for the orbital stability of Earth’s satellites
نویسندگان
چکیده
Abstract We provide stability estimates, obtained by implementing the Nekhoroshev theorem, in reference to orbital motion of a small body (satellite or space debris) around Earth. consider Hamiltonian model, averaged over fast angles, including $$J_2$$ J 2 geopotential term as well third-body perturbations due Sun and Moon. discuss how bring into form suitable for implementation theorem version given Pöschel, (Math Z 213(1):187–216, 1993) ‘non-resonant’ regime. The manipulation includes (i) averaging (ii) expansion values orbit’s eccentricity inclination, (iii) preliminary normalization allowing eliminate particular terms whose existence is nonzero inclination invariant plane secular motions known ‘Laplace plane’. After bringing form, we examine domain applicability action space, translating result physical elements. find that necessary conditions hold are fulfilled some measure domains ( e , i ) body’s altitude (semimajor axis) up about 20 000 km. For altitudes 11 km, obtain times order several thousands years covering nearly all eccentricities inclinations interest applications satellite problem, except narrow zones so-called inclination-dependent resonances. On other hand, recovered present method shrink size semimajor axis increases (and corresponding reduce hundreds years), while practically vanish $$a>20{\,}000$$ a > 20 000 finally effect on adding more $$J_3$$ 3 $$J_4$$ 4 second-order Hamiltonian. these have only minimal moderate times.
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ژورنال
عنوان ژورنال: Celestial Mechanics and Dynamical Astronomy
سال: 2023
ISSN: ['1572-9478', '0923-2958']
DOI: https://doi.org/10.1007/s10569-023-10124-9