On the Two-body Problem with Slowly Decreasing Mass

We intend to present two approximate analytic solutions of the two-body problem with slowly decreasing mass which are obtained through the integration of the Hamilton equations. The law of mass variation used was m = -αn on the first case, and mi = αimin(i); i = 1,2 on the second which gives rise to a perturbed Keplerian problem dependent on one and two small parameters respectively. Practical applications are included. This revised version was published online in August 2006 with corrections to the Cover Date.