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Stability of the Euler resting N-body relative equilibria

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A Correction to this article was published on 20 August 2018

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Abstract

The stability of a system of N equal-sized mutually gravitating spheres resting on each other in a straight line and rotating in inertial space is considered. This is a generalization of the “Euler Resting” configurations previously analyzed in the finite density 3 and 4 body problems. Specific questions for the general case are how rapidly the system must spin for the configuration to stabilize, how rapidly it can spin before the components separate from each other, and how these results change as a function of N. This paper shows that the Euler Resting configuration can only be stable for up to 5 bodies and that for 6 or more bodies the configuration can never be stable. This places an ideal limit of 5:1 on the aspect ratio of a rubble pile body’s shape.

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Change history

  • 20 August 2018

    Due to an error in a supporting algorithm used in writing the paper there was an incorrect conclusion given which is corrected here.

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Acknowledgements

This research was supported by NASA grant NNX14AL16G.

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Authors and Affiliations

  1. Smead Department of Aerospace Engineering Sciences, The University of Colorado Boulder, 429 UCB, Boulder, CO, USA

    D. J. Scheeres

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  1. D. J. Scheeres
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Correspondence to D. J. Scheeres.

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This article is part of the topical collection on Close Approaches and Collisions in Planetary Systems.

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

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Scheeres, D.J. Stability of the Euler resting N-body relative equilibria. Celest Mech Dyn Astr 130, 26 (2018). https://doi.org/10.1007/s10569-018-9819-7

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  • DOI: https://doi.org/10.1007/s10569-018-9819-7

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