Stability of the Euler resting N-body relative equilibria

  • D. J. Scheeres
Original Article
Part of the following topical collections:
  1. Recent advances in the study of the dynamics of N-body problem


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.


Full body problem Resting relative equilibria Rubble pile asteroids 



This research was supported by NASA grant NNX14AL16G.

Compliance with ethical standards

Conflict of interest

The author declares no conflict of interest.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Smead Department of Aerospace Engineering SciencesThe University of Colorado BoulderBoulderUSA

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