# Rendezvous the space debris and the space tug using tether

### Аuthors

Aslanov V. S.*, Pikalov R. S.**

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

*e-mail: aslanov_vs@mail.ru
**e-mail: pickalovrs@gmail.com

### Abstract

The problem of space debris it is one of the most important problems of modern astronautics. According to the forecast made by Donald J. Kessler, the space debris can put an end to further space exploration. One of the solution its problem are so-called the active debris removal systems. The essence of this concept is the use of the special space tugs, which carry out the capture of the large space debris objects and their leading away from the orbit. This work focuses on the stage of pulling the space debris by the tug. The main particularity of this paper is to that the rendezvous of the tug and the space debris is done by controlling the length of the tether according to a prescribed law.

A mathematical model describing the spatial motion of the tug — space debris system was developed. The tug and the space debris are considered as material points, which connected by a viscoelastic tether. Internal interaction of the tug and the space debris is determined by the viscoelastic force of the tether. The tug is under constant thrust. Motion occurs in the gravitational field of the Earth. The linearized equations of motion was derived. The tether length control law for the rendezvous of the space debris and the tug by means of the viscoelastic tether is proposed. An analytic expression for the frequency oscillations of the tether was obtained.

A series of numerical simulations was performed to study the dynamics of the system at the time of the maneuver rendezvous. The simulations are run for 50 seconds with the tug thrust constantly on and without any active control system. The initial altitude is set to be 800 km and the initial velocities of the spacecraft are equal and in accordance to a circular orbit. The Runge-Kutta method is used to propagate the differential equations. Results show that at the end of the maneuver rendezvous in the tether, there are high-frequency oscillations and their frequency increases. That confirmed our analytical expression for the frequency of oscillations of the tether. Influence of the viscoelastic properties of the tether on the dynamics of the system was studied. It is shown that higher stiffness for the tether is better for implementation safety rendezvous of the tug and the space debris.

The results of the calculations show that the practical implementation of the rendezvous of the tug and the space debris is possible, but requires additional measures to damping of the oscillations. The obtained results can be applied to study the properties and possible configurations of the active debris removal system, as well as applications for the tasks of implement rendezvous of two bodies using tether.

In future research on the subject we should find ways to reduce the oscillation of the tether and verify the dynamics with regard to the consideration of the tug and the space debris as solids bodies.

### Keywords:

spacecraft rendezvous, active space debris removal, tethered system, space tug, tethered control

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