Mathematical simulation of a tethered satellite system motion with an inflatable spherical balloon during a spacecraft orbit injection

This paper deals with a problem of spacecraft delivery into orbit using a tethered satellite system. Tethered system consists of satellite, elastic tether, and docking module equipped with an inflatable balloon. Spacecraft placed in an orbit makes a soft docking. The balloon is inflated after docking and the system transfers into rotation mode due to aerodynamic forces. When a half-turn has been made, the spacecraft is separated from the docking module. The objective of this paper is to study an applicability of the orbital injection scheme described. The mathematical model is developed using Lagrange equations of the second kind. It takes into account the effect of aerodynamic forces on the inflatable balloon. The numerical simulation of the system motion is implemented. A comparison of mechanical system motion with and without inflatable balloon is performed. The spacecraft orbit parameters are evaluated for different balloon radius. The estimation of unspent jet propellant is exposed.