Approximate solutions to equations that embody the dominant characteristics of the orbital motion of a two-satellite tethered system are investigated. Orbital motion of a tethered satellite system is considered as perturbed two-body motion and a "restricted problem" of tethered satellite system is obtained by neglecting librational motion. An exact solution to the restricted problem in terms of elliptic functions is presented. An approximate solution to the restricted problem obtained by applying the method of averaging is also provided. An approximate solution for small amplitude librational motion is based on the use of methods for solving equations with variable coefficinets. The analytical solutions are good approximations to the orbital motion of the tether-perturbed satellite and the libration of the perturbing satellite.
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