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Dynamical lifetime survey of geostationary transfer orbits

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Abstract

In this paper, we study the long-term dynamical evolution of highly elliptical orbits in the medium-Earth orbit region around the Earth. The real population consists primarily of Geosynchronous Transfer Orbits (GTOs), launched at specific inclinations, Molniya-type satellites and related debris. We performed a suite of long-term numerical integrations (up to 200 years) within a realistic dynamical model, aimed primarily at recording the dynamical lifetime of such orbits (defined as the time needed for atmospheric reentry) and understanding its dependence on initial conditions and other parameters, such as the area-to-mass ratio (A / m). Our results are presented in the form of 2-D lifetime maps, for different values of inclination, A / m, and drag coefficient. We find that the majority of small debris (\(>70\%\), depending on the inclination) can naturally reenter within 25–90 years, but these numbers are significantly less optimistic for large debris (e.g., upper stages), with the notable exception of those launched from high latitude (Baikonur). We estimate the reentry probability and mean dynamical lifetime for different classes of GTOs and we find that both quantities depend primarily and strongly on initial perigee altitude. Atmospheric drag and higher A / m values extend the reentry zones, especially at low inclinations. For high inclinations, this dependence is weakened, as the primary mechanisms leading to reentry are overlapping lunisolar resonances. This study forms part of the EC-funded (H2020) “ReDSHIFT” project.

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Notes

  1. www.space-track.org. Assessed in 25 Oct. 2016.

  2. See Tables 8–4 in Vallado (2013).

  3. Note that the satellite’s initial node and perigee angles were taken relative to the ecliptic lunar values at each epoch.

  4. Resonances are of the form \(\dot{\psi }=j\dot{\omega }\,{+}\,k\dot{\varOmega }\,{+}\,l\dot{\varOmega }_{M} = 0\). Lines crossing through the point \(\left( a,e\right) =\left( 0.518,0.5\right) \) correspond to \(\left[ j,k,l\right] =\left[ 0,1,-2\right] ,\left[ 2,1,-2\right] ,\left[ 2,-1,2\right] \). Lines passing through \(\left( a,e\right) =\left( 0.632,0.5\right) \) correspond to \(\left[ j,k,l\right] =\left[ 0,1,-1\right] ,\left[ 2,2,-2\right] ,\left[ 2,1,-1\right] ,\left[ 2,-1,1\right] ,\left[ 2,-2,2\right] \)

  5. For \(i_{0}=5.2^\circ \) and \(i_{0} = 28.5^\circ \), we only take into account the population with \(q_{0}\le 800\) km, since, according to the dynamical maps presented in section 3.1, very few reentry solutions exist for higher altitudes.

  6. One might be tempted to interpret these few particles as long-lived remnants of an initially larger population.

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Acknowledgements

This research was funded by the European Commissions Horizon 2020, Framework Program for Research and Innovation (2014–2020), under Grant Agreement 687500 (Project ReDSHIFT; http://redshift-h2020.eu/). The work of DKS is funded by the General Secretariat for Research and Technology (GSRT) and the Hellenic Foundation for Research and Innovation (HFRI). Results presented in this work have been produced using the AUTH Compute Infrastructure and Resources and the authors would like to acknowledge the support provided by the Scientific Computing Office throughout the progress of this research work. DKS wishes to acknowledge Davide Amato for supplying a prototype routine for atmospheric drag and for providing independent validation of our code.

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Authors and Affiliations

  1. Department of Physics, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    Despoina K. Skoulidou, Kleomenis Tsiganis & George Voyatzis

  2. Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ, 85721, USA

    Aaron J. Rosengren

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  1. Despoina K. Skoulidou
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  2. Aaron J. Rosengren
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  3. Kleomenis Tsiganis
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Correspondence to Despoina K. Skoulidou.

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This article is part of the topical collection on Innovative methods for space threats: from their dynamics to interplanetary missions.

Guest Editors: Giovanni Federico Gronchi, Ugo Locatelli, Giuseppe Pucacco and Alessandra Celletti.

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Skoulidou, D.K., Rosengren, A.J., Tsiganis, K. et al. Dynamical lifetime survey of geostationary transfer orbits. Celest Mech Dyn Astr 130, 77 (2018). https://doi.org/10.1007/s10569-018-9865-1

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