A tether system at the L1, L2 collinear libration points of the mars-phobos system


DOI: 10.34759/trd-2022-122-02

Аuthors

Aslanov V. S.*, Neryadovskaya D. V.**

Samara National Research University named after Academician S.P. Korolev, 34, Moskovskoye shosse, Samara, 443086, Russia

*e-mail: aslanov_vs@mail.ru
**e-mail: neryadovskayadv@yandex.ru

Abstract

The article considers one of the L1 or L2 collinear libration points application for a tether system deployment in the direction of Phobos in a plane circular restricted three-body problem in the Mars-Phobos system. An orbital spacecraft by which one of the tether ends is being fixed is located in L1 or L2 collinear libration points and is being held in one of these unstable points by the low thrust of its engines. The equation of the tether system motion in the polar coordinates system was obtained for the tether of constant length, the equilibrium positions were found, and the dependence of the vibrations period on the tether length was determined. Comparison of approximate solution for the small angles of the tether deviation from the local vertical with the numerical one was performed. The article demonstrates that the system “fixed” either in both the L1 point and L2 has potential wells in cases when the tether is being directed towards the Phobos side. It was revealed that the dependencies of the vibrations period on the tether length for the L1 and L2 points were fundamentally different. Comparison for both L1 and L2 of approximate and numerical solutions revealed herewith that the vibrations amplitude remained constant in contrast to the frequency. The results of this study may be employed for the future space missions provision. Thus, for example, a space lift may be arranged in the Mars-Phobos system, which tether will pass through the L1 or L2 libraion point. Besides, such lift may serve as an intermediate station for conducting studies associated with the space exploration around it, as well as a platform for the interplanetary flights. “Fixing” the tether system in the L1 or L2collinear libration point of the Mars-Phobos system will allow conducting remote studies of Phobos employing a vehicle with sensors, which will hover above its surface.

Keywords:

tether system, libration point, state of equilibrium, phase plane, analytic solution, elliptic function

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