A splitting of collinear libration points in circular restricted three-body problem by an artificial electrostatic field


This paper focuses on the study of a new type of a planar, circular restricted three-body problem with an attractive artificial electrostatic field (E-field) at collinear libration points. For instance, this attractive field can be generated by an orbiting spacecraft located at the Mars-Phobos L1 libration point and an electrostatic capsule launched from Phobos. The feasibility of the proposed retrieval system is discussed from the aspect of local space weather Debye length. The attractive E-field splits the collinear libration point into two new collinear points, and the greater the E-field potential and the Debye length the greater the distance between the new libration points and the “old” original libration point. The new equilibrium positions caused by the action of the E-field have been found, and an instability of these new libration points has been proven. A new Jacobi integral in analytical form is obtained and equations of motion are derived for the restricted problem of three bodies taking into account the E-field. A numerical simulation shows the impact of the E-field potential on capsule capture in the small vicinity of the Mars-Phobos L1 libration point. This work expands the classic three-body problem filling with new content. The obtained results can be applied, for example, to study an opportunity of delivering the Phobos samples using Coulomb interaction of bodies in space.

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This study was supported by the Russian Science Foundation (Project No. 19-19-00085).

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Correspondence to Vladimir S. Aslanov.

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Aslanov, V.S. A splitting of collinear libration points in circular restricted three-body problem by an artificial electrostatic field. Nonlinear Dyn 103, 2451–2460 (2021). https://doi.org/10.1007/s11071-021-06226-4

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  • Libration points
  • Electrostatic field
  • Stability and instability
  • Exact solutions
  • Jacobi integral