Celestial Mechanics and Dynamical Astronomy

, Volume 109, Issue 1, pp 13–26 | Cite as

On the stability of artificial equilibrium points in the circular restricted three-body problem

  • Claudio BombardelliEmail author
  • Jesus Peláez
Original Article


The article analyses the stability properties of minimum-control artificial equilibrium points in the planar circular restricted three-body problem. It is seen that when the masses of the two primaries are of different orders of magnitude, minimum-control equilibrium is obtained when the spacecraft is almost coorbiting with the second primary as long as their mutual distance is not too small. In addition, stability is found when the distance from the second primary exceeds a minimum value which is a simple function of the mass ratio of the two primaries and their separation. Lyapunov stability under non-resonant conditions is demonstrated using Arnold’s theorem. Among the most promising applications of the concept we find solar-sail-stabilized observatories coorbiting with the Earth, Mars, and Venus.


Three-body problem Artficial equilibrium points Stability Solar sails 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.ETSI AeronauticosUniversidad Politecnica de MadridMadridSpain

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