The paper discusses the possibility of realizing a spacecraft-tether mission to study the surface of Phobos within the framework of the planar elliptic restricted three-body problem taking into account the topography of Phobos. The tether system is a weightless and inextensible tether with an instrument unit attached to it to study the surface of Phobos. Control laws of the tether length during deployment, the envelopment of the lunar surface by the instrument unit, and the retraction of the tether system into the spacecraft are considered. The spacecraft is located in a low quasi-satellite orbit of Phobos. Four different altitude quasi-satellite orbits are analyzed with respect to the possibility to study the Phobos topography by means of the tether system. Numerical modeling confirms the effectiveness of the chosen nonlinear control laws of the tether system at all stages of motion.
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