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Prospects of a tether system deployed at the L1 libration point


The paper focuses on the study and development of a mission to use the L1 libration point for deployment of a tether system in the direction of a moon in the planar elliptic restricted three-body problem on the example of the Mars-Phobos system. An orbiting spacecraft, which deploys the tether system, is located at the L1 libration point and is held at this point by the low thrust of its engines. The classical equations in the Nechville variables are converted into equations in polar coordinates. For the particular case when the tether is inextensible and two primaries moving in circular orbits about their mass center, these equations are integrated in quadrature, and the equilibrium positions and the oscillation period of the tether are found. As a result of eccentricity, the primaries move on ellipses around the barycenter, which rotates with angular velocity equal to that of the primaries, the position of the two-body pulsates along the axis connecting them. A new mission architecture is proposed, which includes three successive stages: initial deployment to the upper pulsation point (perigee), angular stabilization of the tether relative to the lower stable position, and maintaining a constant distance to a moon’s surface. An end mass with measuring equipment of this tether system can be set directly on the moon’s surface. Numerical simulations have shown the effectiveness of the proposed control laws of the tether system at all stages of the mission for the Mars-Phobos system, in which the L1 libration point is located quite close to the Phobos’ surface (~ 3.4 km). This paper is the first effort, using to justify publicly the possibility of implementing a mission with a tether system “attached” at L1 libration point to study surface of moons based on the proposed control laws and the sequence of their application. The results of this study can be used to enable many future missions throughout the solar system. If in the future similar missions will be approved, then undoubtedly more advanced control methods of this kind of systems will be developed.

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Data availability statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.


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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. Prospects of a tether system deployed at the L1 libration point. Nonlinear Dyn 106, 2021–2033 (2021).

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  • L1 libration point
  • Tether system
  • Stability and instability
  • Exact solutions
  • Control laws