Analysis of the motion of a nanosatellite with an uninsulated conductive tether

The motion of an electrodynamic tether system consisting of a nanosatellite and an auxiliary body (electron emitter) is analyzed. The nanosatellite and the emitter are connected by an uninsulated conductive tether. The task is related to the urgent problem of removing exhausted nanosatellites or small spacecraft from space without using jet engines. The interaction of the conductive tether with the Earth's magnetic field leads to the appearance of an Ampere (Lorentz) force, which provides rapid braking of the tether system. To analyze the motion of the considered space system, a mathematical modeling method is used using equations of motion constructed using the Lagrange formalism. A feature of the mathematical model of the system motion is the consideration of the uneven current distribution along the bare conductive tether, which depends on the potential difference between the end bodies. The effect of electron concentration in the ionosphere and inclination on the current distribution along the tether and the change in the orbital parameters of the center of mass of the system is studied. It is established that for non-equatorial orbits, the motion of the tether system has a complex spatial character (it oscillates relative to the orbital plane). Numerical results are presented illustrating the effect of electron concentration and inclination on the increments of the parameters of the orbit of the center of mass of the tether system.