eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2021-05-15 9 2 53 56 10.12691/ajams-9-2-3 AJAMS2021923 article Ilhan M. Izmirli iizmirl2@gmu.edu 1 George Mason University, United States In this paper, we obtain the solution of the two-body problem with variable masses by posing some assumptions on the classical equation and thereby reducing the solution of the problem to investigating the solutions of some Ricatti type differential equations. Along this process, we also give a simple proof of the well-known Mestscherskii Theorem and establish some related formal relations under these assumptions. http://pubs.sciepub.com/ajams/9/2/3/ajams-9-2-3.pdf two body problem with variable masses ricatti equation Mestscherskii's therem