Optimal Earth's reentry disposal of the Galileo constellation

Abstract Nowadays there is international consensus that space activities must be managed to minimize debris generation and risk. The paper presents a method for the end-of-life (EoL) disposal of spacecraft in Medium Earth Orbit (MEO). The problem is formulated as a multiobjective optimisation one, which is solved with an evolutionary algorithm. An impulsive manoeuvre is optimised to reenter the spacecraft in Earth’s atmosphere within 100 years. Pareto optimal solutions are obtained using the manoeuvre Δ v and the time-to-reentry as objective functions to be minimised. To explore at the best the search space a semi-analytical orbit propagator, which can propagate an orbit for 100 years in few seconds, is adopted. An in-depth analysis of the results is carried out to understand the conditions leading to a fast reentry with minimum propellant. For this aim a new way of representing the disposal solutions is introduced. With a single 2D plot we are able to fully describe the time evolution of all the relevant orbital parameters as well as identify the conditions that enables the eccentricity build-up. The EoL disposal of the Galileo constellation is used as test case.

[1]  Carmen Pardini,et al.  Post-disposal orbital evolution of satellites and upper stages used by the GPS and GLONASS navigation constellations: The long-term impact on the Medium Earth Orbit environment , 2012 .

[2]  Alan B. Jenkin,et al.  Collision Risk Posed to the Global Positioning System by Disposal Orbit Instability , 2002 .

[3]  N. K. Pavlis,et al.  The development and evaluation of the Earth Gravitational Model 2008 (EGM2008) , 2012 .

[4]  Tadashi Yokoyama,et al.  Some Initial Conditions for Disposed Satellites of the Systems GPS and Galileo Constellations , 2009 .

[5]  Paul J. Cefola,et al.  On the third-body perturbations of high-altitude orbits , 2012 .

[6]  Jonas Radtke,et al.  Impact of eccentricity build-up and graveyard disposal Strategies on MEO navigation constellations , 2014 .

[7]  Alessandro Rossi,et al.  Chaos in navigation satellite orbits caused by the perturbed motion of the Moon , 2015, 1503.02581.

[8]  Alessandro Rossi,et al.  Semi-analytical investigations of the long term evolution of the eccentricity of Galileo and GPS-like orbits , 2011 .

[9]  Alessandro Rossi,et al.  A numerical investigation on the eccentricity growth of GNSS disposal orbits , 2016 .

[10]  Sławomir Breiter,et al.  Lunisolar Resonances Revisited , 2001 .

[11]  J. Chapront,et al.  The lunar theory ELP revisited. Introduction of new planetary perturbations , 2003 .

[12]  J. Chapront,et al.  ELP 2000-85: a semi-analytical lunar ephemeris adequate for historical times , 1988 .

[13]  Hugh G. Lewis,et al.  Disposal Orbit Characteristics for Galileo Including Orbit Propagation Techniques , 2005 .

[14]  Giuseppe Pucacco,et al.  Bifurcation of Lunisolar Secular Resonances for Space Debris Orbits , 2015, SIAM J. Appl. Dyn. Syst..

[15]  S. Hughes,et al.  Earth satellite orbits with resonant lunisolar perturbations I. Resonances dependent only on inclination , 1980, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[16]  Romeli Barbosa,et al.  Optimal Sizing of a Photovoltaic-Hydrogen Power System for HALE Aircraft by means of Particle Swarm Optimization , 2015 .

[17]  S. Hughes,et al.  Earth satellite orbits with resonant lunisolar perturbations - II. Some resonances dependent on the semi-major axis, eccentricity and inclination , 1981, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[18]  Roberto Armellin,et al.  End-of-life disposal of high elliptical orbit missions: The case of INTEGRAL , 2015 .

[19]  Alessandra Celletti,et al.  A Study of the Lunisolar Secular Resonance 2ω˙+Ω˙=0 , 2016, Front. Astron. Space Sci..

[20]  André Deprit,et al.  Canonical transformations depending on a small parameter , 1969 .

[21]  A. B. Jenkin,et al.  Dilution of Disposal Orbit Collision Risk for the Medium Earth Orbit Constellations , 2005 .

[22]  Gilles Metris,et al.  Solar gravitational perturbations on the dynamics of MEO: Increase of the eccentricity due to resonances , 2015 .

[23]  Massimiliano Vasile,et al.  Effectiveness of GNSS disposal strategies , 2014 .

[24]  Alessandro Rossi,et al.  Galileo disposal strategy: stability, chaos and predictability , 2015, 1512.05822.

[25]  Paul J. Cefola,et al.  Long-term evolution of Galileo operational orbits by canonical perturbation theory , 2014 .

[26]  Tadashi Yokoyama,et al.  Study of Some Strategies for Disposal of the GNSS Satellites , 2015 .

[27]  G. E. Cook Luni-Solar Perturbations of the Orbit of an Earth Satellite , 1961 .

[28]  Aaron J. Rosengren,et al.  FROM ORDER TO CHAOS IN EARTH SATELLITE ORBITS , 2016, 1606.04180.

[29]  Juan Morales-Sánchez,et al.  Fractional Regularization Term for Variational Image Registration , 2009 .

[30]  Alessandro Rossi,et al.  Resonant dynamics of Medium Earth Orbits: space debris issues , 2008 .

[31]  C.A. Coello Coello,et al.  MOPSO: a proposal for multiple objective particle swarm optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[32]  Felix R. Hoots,et al.  Models for Propagation of NORAD Element Sets , 1980 .

[33]  Alessandro Rossi,et al.  The dynamical structure of the MEO region: long-term stability, chaos, and transport , 2015, 1507.06170.

[34]  D. Drob,et al.  Nrlmsise-00 Empirical Model of the Atmosphere: Statistical Comparisons and Scientific Issues , 2002 .

[35]  A. Morselli,et al.  A high order method for orbital conjunctions analysis: Sensitivity to initial uncertainties , 2014 .

[36]  Florent Deleflie,et al.  Long term evolution of the Galileo constellation due to gravitational forces , 2005 .

[37]  R. A. Gick,et al.  Long-term evolution of navigation satellite orbits: GPS/GLONASS/GALILEO , 2004 .