The use of innovative technologies in space missions has evolved considerably in the last decade. The use of large cables in space structures to connect spacecrafts and satellites with the goal to minimize cost of missions created a new field to be explored. A brief explanation will be considered about papers related to the equilibrium and stability of the movement of space systems connected by cables, known as Tether Systems. It will be presented the mathematical formulation for the system formed by two point masses connected by a tether in the central force field, in a Keplerian movement. The Lagrangian formulation was used to describe the rotational movement of the dumbbell-like system. Results of system behavior, tension and kinetic energy will be presented for two different situations, considering equal masses and different masses.