Two-body problem with slowly decreasing mass

Evolution of the orbital elements in the two-body problem with slowly decreasing mass is described by a non-linear, non-autonomous system of differential equations. It is shown that the system of differential equations can be replaced by an integral equation and that three domains of the phase plant can be distinguished where the behaviour of the solutions is entirely different. For each domain a number of approximate solutions have been constructed which are valid for a limited interval of time