... Equations are obtained for the plane relative motion of the system on the taut thread (on the assumption that the centre of mass of the system moves along the Keplerian elliptic orbit). ... The torques of gravitational forces, aerodynamic pressure, aerodynamic friction and the aerogradient effect are taken into account. ... First, the problem is investigated in case of taut thread and Keplerian elliptic motion of the centre of mass. ... In a general case the free motion is bound to become connected....