A frequency portrait of Low Earth Orbits

Schettino, Giulia; Alessi, Elisa Maria; Rossi, Alessandro; Valsecchi, G. B.

doi:10.1007/s10569-019-9912-6

Cited by 9 publications

(7 citation statements)

References 24 publications

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“…Besides providing a robust basis for the choice of the terms to consider in an analytical modeling, a possible application of the analysis is to explain observational data or to estimate the maximum eccentricity growth in the long term due to lunisolar perturbations, as done in [19,20] in the case of solar radiation pressure.…”

Section: Discussionmentioning

confidence: 99%

On the Dominant Lunisolar Perturbations for Long-Term Eccentricity Variation: The Case of Molniya Satellite Orbits

2021

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The aim of this work is to investigate the main dominant terms of lunisolar perturbations that affect the orbital eccentricity of a Molniya satellite in the long term. From a practical point of view, these variations are important in the context of space situational awareness—for instance, to model the long-term evolution of artificial debris in a highly elliptical orbit or to design a reentry end-of-life strategy for a satellite in a highly elliptical orbit. The study assumes a doubly averaged model including the Earth’s oblateness effect and the lunisolar perturbations up to the third-order expansion. The work presents three important novelties with respect to the literature. First, the perturbing terms are ranked according to their amplitudes and periods. Second, the perturbing bodies are not assumed to move on circular orbits. Third, the lunisolar effect on the precession of the argument of pericenter is analyzed and discussed. As an example of theoretical a application, we depict the phase space description associated with each dominant term, taken as isolated, and we show which terms can apply to the relevant dynamics in the same region.

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Section: Discussionmentioning

confidence: 99%

On the Dominant Lunisolar Perturbations for Long-Term Eccentricity Variation: The Case of Molniya Satellite Orbits

2021

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“…is the 'resonant module'. A normal form of the form (31) implies the existence of n − l max quasi-integrals of the form…”

Section: Normal Form and Remainder Consider A Hamiltonian Function Of...mentioning

confidence: 99%

“…where the vectors K i satisfy the equations K i • m l = 0 for all l with 1 ≤ l ≤ l max . The quantities I i are called the resonant integrals of the Hamiltonian (31).…”

Section: Normal Form and Remainder Consider A Hamiltonian Function Of...mentioning

confidence: 99%

“…The huge amount of objects (up to millions) in LEO, MEO, GEO needs a careful control of their orbits and the analysis of their dynamical stability ( [6,3,5,4,15,31]), also in view of devising appropriate mitigation measures (see, e.g., [17,27,9]). For objects in LEO, it is of crucial importance to evaluate the orbital lifetime, which is strongly affected by the atmospheric drag which provokes a decay of the orbits ( [19,22,24,32,34]).…”

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Semi-analytical estimates for the orbital stability of Earth's satellites

De Blasi,

Celletti,

Efthymiopoulos

2021

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Normal form stability estimates are a basic tool of Celestial Mechanics for characterizing the long-term stability of the orbits of natural and artificial bodies. Using high-order normal form constructions, we provide three different estimates for the orbital stability of point-mass satellites orbiting around the Earth. i) We demonstrate the long term stability of the semimajor axis within the framework of the J 2 problem, by a normal form construction eliminating the fast angle in the corresponding Hamiltonian and obtaining H J2 . ii) We demonstrate the stability of the eccentricity and inclination in a secular Hamiltonian model including lunisolar perturbations (the 'geolunisolar' Hamiltonian H gls ), after a suitable reduction of the Hamiltonian to the Laplace plane. iii) We numerically examine the convexity and steepness properties of the integrable part of the secular Hamiltonian in both the H J2 and H gls models, which reflect necessary conditions for the holding of Nekhoroshev's theorem on the exponential stability of the orbits. We find that the H J2 model is non-convex, but satisfies a 'three-jet' condition, while the H gls model restores quasi-convexity by adding lunisolar terms in the Hamiltonian's integrable part.

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“…The huge amount of objects (up to millions) in LEO, MEO, GEO needs a careful control of their orbits and the analysis of their dynamical stability (Celletti and Galeş 2014;Celletti and Galeş 2018;Celletti et al 2020;Gkolias and Colombo 2019;Schettino et al 2019), also in view of devising appropriate mitigation measures (see, e.g., Jenkin et al 2019;Park et al 2018;Choi et al 2015). For objects in LEO, it is of crucial importance to evaluate the orbital lifetime, which is strongly affected by the atmospheric drag which provokes a decay of the orbits (King-Hele and Walker 1988; Krag et al 2013;Liu and Wang 2000;Shute and Chiville 1966;Westerman 1963).…”

Section: Introductionmentioning

confidence: 99%

Semi-Analytical Estimates for the Orbital Stability of Earth’s Satellites

2021

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Normal form stability estimates are a basic tool of Celestial Mechanics for characterizing the long-term stability of the orbits of natural and artificial bodies. Using high-order normal form constructions, we provide three different estimates for the orbital stability of point-mass satellites orbiting around the Earth. (i) We demonstrate the long-term stability of the semimajor axis within the framework of the $$J_2$$ J 2 problem, by a normal form construction eliminating the fast angle in the corresponding Hamiltonian and obtaining $${\mathcal {H}}_{J_2}$$ H J 2 . (ii) We demonstrate the stability of the eccentricity and inclination in a secular Hamiltonian model including lunisolar perturbations (the ‘geolunisolar’ Hamiltonian $${\mathcal {H}}_\mathrm{gls}$$ H gls ), after a suitable reduction of the Hamiltonian to the Laplace plane. (iii) We numerically examine the convexity and steepness properties of the integrable part of the secular Hamiltonian in both the $${\mathcal {H}}_{J_2}$$ H J 2 and $${\mathcal {H}}_\mathrm{gls}$$ H gls models, which reflect necessary conditions for the holding of Nekhoroshev’s theorem on the exponential stability of the orbits. We find that the $${\mathcal {H}}_{J_2}$$ H J 2 model is non-convex, but satisfies a ‘three-jet’ condition, while the $${\mathcal {H}}_\mathrm{gls}$$ H gls model restores quasi-convexity by adding lunisolar terms in the Hamiltonian’s integrable part.

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A frequency portrait of Low Earth Orbits

Cited by 9 publications

References 24 publications

On the Dominant Lunisolar Perturbations for Long-Term Eccentricity Variation: The Case of Molniya Satellite Orbits

On the Dominant Lunisolar Perturbations for Long-Term Eccentricity Variation: The Case of Molniya Satellite Orbits

Semi-analytical estimates for the orbital stability of Earth's satellites

Semi-Analytical Estimates for the Orbital Stability of Earth’s Satellites

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