Semianalytical Study of Geosynchronous Orbits About a Precessing Oblate Earth Under Lunisolar Gravitation and Tesseral Resonance

Belyanin, Sofia; Gurfil, Pini

doi:10.1007/bf03321515

Cited by 14 publications

(5 citation statements)

References 19 publications

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“…So in this work we neglect the tesseral terms, and concentrate our attention to the behaviour of the inclination and of the eccentricity, due to the solar radiation pressure, the J 2 , the lunar and solar perturbations. The results obtained in this paper could be easily combined, if necessary, with resonant previous studies such as or Belyanin and Gurfil (2010).…”

Section: Introductionmentioning

confidence: 63%

Long-term evolution of space debris under the $$J_2$$ J 2 effect, the solar radiation pressure and the solar and lunar perturbations

Casanova

Petit

Lemaître

2015

Celest Mech Dyn Astr

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The aim of this paper is the development of a model to propagate space debris in the geostationary ring considering the J 2 effect due to the Earth oblateness, the Sun and Moon perturbations, and the solar radiation pressure. We justify the importance of considering the J 2 effect when propagating space debris independently of the ratio A/m for short and longterm propagation. We study the role of the Sun and the Moon in the period and amplitude of the inclination for different values of A/m. Thanks to the Hamiltonian formulation of the problem and the use of Poincaré's variables it is possible to express the evolution of the space debris through a simplified dynamical system. We test and validate our obtained analytical solutions with the numerical ones, computed with a powerful integrator named NIMASTEP. We analyse the improvements obtained when we include the J 2 effect and the third body perturbations by a rigorous comparison with a previous model, which only considers the solar radiation pressure. Finally, we study the effect of the area-to-mass ratio on short and long-term propagation.

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Section: Introductionmentioning

confidence: 63%

Long-term evolution of space debris under the $$J_2$$ J 2 effect, the solar radiation pressure and the solar and lunar perturbations

Casanova

Petit

Lemaître

2015

Celest Mech Dyn Astr

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“…In this work we concentrate on the effect of lunisolar perturbations ( [3,6,20]) and precisely on some secular resonances, which depend only on the inclination (see [29], compare also with [30]). With the terms of lunar and solar gravitational resonance we mean that there exists a commensurability relation of the type k 1ω + k 2Ω + k 3ωb + k 4Ωb = 0 (1.1) for some integers (k 1 , k 2 , k 3 , k 4 ), not all identically zero; in (1.1) the quantity ω denotes the argument of perigee of the debris and Ω is the longitude of the ascending node, while ω b and Ω b are, respectively, the argument of perigee and the longitude of the ascending node of the perturber.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation of Lunisolar Secular Resonances for Space Debris Orbits

Celletti¹,

Galeş²,

Pucacco³

2016

SIAM J. Appl. Dyn. Syst.

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Using bifurcation theory, we study the secular resonances induced by the Sun and Moon on space debris orbits around the Earth. In particular, we concentrate on a special class of secular resonances, which depend only on the debris' orbital inclination. This class is typically subdivided into three distinct types of secular resonances: those occurring at the critical inclination, those corresponding to polar orbits, and a third type resulting from a linear combination of the rates of variation of the argument of perigee and the longitude of the ascending node.The model describing the dynamics of space debris includes the effects of the geopotential, as well as the Sun's and Moon's attractions, and it is defined in terms of suitable action-angle variables. We consider the system averaged over both the mean anomaly of the debris and those of the Sun and Moon. Such multiply-averaged Hamiltonian is used to study the lunisolar resonances which depend just on the inclination.Borrowing the technique from the theory of bifurcations of Hamiltonian normal forms, we study the birth of periodic orbits and we determine the energy thresholds at which the bifurcations of lunisolar secular resonances take place. This approach gives us physically relevant information on the existence and location of the equilibria, which help us to identify stable and unstable regions in the phase space. Besides their physical interest, the study of inclination dependent resonances offers interesting insights from the dynamical point of view, since it sheds light on different phenomena related to bifurcation theory.2010 Mathematics Subject Classification. 37N05,37L10,70F15.

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“…The variations of semimajor axis and longitude drift rate of the GEO satellites during a long duration station change is essentially due to the Earth's triaxiality, especially the tesseral harmonics [28,29].…”

Section: The Variation In Semimajor and Longitude Induced By Earth's mentioning

confidence: 99%

Minimum-fuel station-change for geostationary satellites using low-thrust considering perturbations

Zhao

Zhang

2016

Acta Astronautica

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Semianalytical Study of Geosynchronous Orbits About a Precessing Oblate Earth Under Lunisolar Gravitation and Tesseral Resonance

Cited by 14 publications

References 19 publications

Long-term evolution of space debris under the $$J_2$$ J 2 effect, the solar radiation pressure and the solar and lunar perturbations

Long-term evolution of space debris under the $$J_2$$ J 2 effect, the solar radiation pressure and the solar and lunar perturbations

Bifurcation of Lunisolar Secular Resonances for Space Debris Orbits

Minimum-fuel station-change for geostationary satellites using low-thrust considering perturbations

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