Dynamical taxonomy of the coupled solar radiation pressure and oblateness problem and analytical deorbiting configuratio
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Dynamical taxonomy of the coupled solar radiation pressure and oblateness problem and analytical deorbiting configurations Ioannis Gkolias1,4 · Elisa Maria Alessi2,3
· Camilla Colombo1
Received: 9 July 2020 / Revised: 24 October 2020 / Accepted: 3 November 2020 / Published online: 27 November 2020 © The Author(s) 2020
Abstract Recent works demonstrated that the dynamics caused by the planetary oblateness coupled with the solar radiation pressure can be described through a model based on singly averaged equations of motion. The coupled perturbations affect the evolution of the eccentricity, inclination and orientation of the orbit with respect to the Sun–Earth line. Resonant interactions lead to non-trivial orbital evolution that can be exploited in mission design. Moreover, the dynamics in the vicinity of each resonance can be analytically described by a resonant model that provides the location of the central and hyperbolic invariant manifolds which drive the phase space evolution. The classical tools of the dynamical systems theory can be applied to perform a preliminary mission analysis for practical applications. On this basis, in this work we provide a detailed derivation of the resonant dynamics, also in non-singular variables, and discuss its properties, by studying the main bifurcation phenomena associated with each resonance. Last, the analytical model will provide a simple analytical expression to obtain the area-to-mass ratio required for a satellite to deorbit from a given altitude in a feasible timescale. Keywords Solar radiation pressure · Oblateness · Averaged dynamics · Equilibrium points · Bifurcation diagrams · Deorbiting
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Elisa Maria Alessi [email protected] Ioannis Gkolias [email protected] Camilla Colombo [email protected] https://www.compass.polimi.it
1
Department of Aerospace Science and Technology, Politecnico di Milano, Via la Masa 34, 20156 Milan, Italy
2
Istituto di Matematica Applicata e Tecnologie Informatiche “Enrico Magenes”, Consiglio Nazionale delle Ricerche, Via Alfonso Corti 12, 20133 Milan, Italy
3
Istituto di Fisica Applicata “Nello Carrara”, Consiglio Nazionale delle Ricerche, Via Madonna del Piano 10, 50019 Sesto Fiorentino (FI), Italy
4
Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
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1 Introduction The effect of the solar radiation pressure (SRP) on Earth satellites was recognised since the first space flights. The orbital evolution of Vanguard I (Musen et al. 1960) and the Echo balloons (Shapiro and Jones 1960) was found to be significantly influenced by SRP, and singly averaged equations were used to study the motion (Musen 1960). Treated as a perturbation problem, the singly averaged contribution of SRP is integrable and analytical solutions can be obtained (Mignard and Henon 1984; Oyama et al. 2008; Scheeres 2012). Nevertheless, when coupled with the effect of Earth’s oblateness J2 the system becomes a 2.5 degrees of freedom (DoF). An analytical insight
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