Two mathematical models of three bodies of variable masses are used to obtain a qualitative description of two interacting galaxies with mass exchange and mass loss. The reference system is centred on the largest body (the most massive galaxy), and the other two bodies are allowed to move around this one under the laws of gravity. The third body, which simulated the mass lost by the second galaxy in the form of a tail, increases its mass due to the mass lost by the second body and follows its trajectory. We are interested in knowing the time evolution of the separation of the two bulges of the interacting galaxies, and the parameters for the analytical models are obtained by running simulations with the GADGET-2 N-body code. The resulting behavior of this distance in our mathematical models is qualitatively in good agreement with that obtained by this code.

We study the classical dynamics of a binary stars when there is an interchange of mass between them. Assuming that one of the star is more massive than the other, the dynamics of the lighter one is analyzed as a function of its time depending mass variation. Within our approximations and models for mass transference, we obtain a general result which establishes that if the lightest star looses mass, its period increases. If the lightest star win mass, its period decreases.

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