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Constructing ballistic capture orbits in the real Solar System model

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An Erratum to this article was published on 06 November 2014

Abstract

A method to design ballistic capture orbits in the real Solar System model is presented, so extending previous works using the planar restricted three-body problem. In this generalization a number of issues arise, which are treated in the present work. These involve reformulating the notion of stability in three-dimensions, managing a multi-dimensional space of initial conditions, and implementing a restricted \(n\)-body model with accurate planetary ephemerides. Initial conditions are categorized into four subsets according to the orbits they generate in forward and backward time. These are labelled weakly stable, unstable, crash, and acrobatic, and their manipulation allows us to derive orbits with prescribed behavior. A post-capture stability index is formulated to extract the ideal orbits, which are those of practical interest. Study cases analyze ballistic capture about Mercury, Europa, and the Earth. These simulations show the effectiveness of the developed method in finding solutions matching mission requirements.

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Notes

  1. The ephemerides are defined in the International Celestial Reference Frame (ICRF), which has an infinitesimal discrepancy with respect to the EME2000 (Archinal 2011).

  2. Data available at http://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/planets/de430.bsp, \(\sim \)/satellites/ jup310.bsp, \(\sim \)/sat360.bsp, \(\sim \)/ura111.bsp, \(\sim \)/nep081.bsp, and \(\sim \)/plu043.bsp [retrieved 5 May 2014].

  3. Data available at http://naif.jpl.nasa.gov/naif/toolkit.html [retrieved 5 May 2014].

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Acknowledgments

The first author acknowledges financial support from China Scholarship Council and the Innovation Fund of National University of Defense Technology under Grant No. B100101.

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Authors and Affiliations

  1. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, People’s Republic of China

    Z.-F. Luo & G.-J. Tang

  2. Department of Aerospace Science and Technology, Politecnico di Milano, Via La Masa, 34, 20156, Milan, Italy

    F. Topputo & F. Bernelli-Zazzera

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  1. Z.-F. Luo
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  2. F. Topputo
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  3. F. Bernelli-Zazzera
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  4. G.-J. Tang
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Correspondence to F. Topputo.

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Luo, ZF., Topputo, F., Bernelli-Zazzera, F. et al. Constructing ballistic capture orbits in the real Solar System model. Celest Mech Dyn Astr 120, 433–450 (2014). https://doi.org/10.1007/s10569-014-9580-5

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