The investigations of the influence of aerodynamics on the motion of an artificial two solid satellite-link a reconditioned by the expansion of their field of application to orbital large extension tether systems. Aerodynamic effects are quite significant for such large space systems. The paper considers the classification of cylindrical phase space limit cycles and also researches the form of the limit cycle for the equation of the relative motion of two bodies orbital link with the influence of the gravitational effect, aerodynamic pressure, aero-gradient and dissipative factors, depending on the eccentricity growth and aerodynamic parameter. We use the associated motion equations taking into account gravity gradient and aerodynamic factors. An assessment of the influence of eccentricity and aerodynamic parameter changes on the behavior of limit cycles is also given in the paper. The research applies well-known methods of nonlinear mechanics: Lagrange equations of the first kind, the phase plane method, a numerical implementation of the point mapping method and stability theory methods. *