Recently developed Probabilistic Evolution Theory (PREVTH) aims to get a linear but denumerable infinite dimensional theory of ODEs. This has been accomplished by using Kronecker power series and space extension variaties, and, squarification of Telescopic matrices. In this work, we apply Probabilistic Evolution Theory (PREVTH) to a two particles celestial mechanical system. This can be realised directly or indirectly. In the latter case, before everything, the number of the unknowns and ODEs on them are reduced to a level as small as possible. We prefer this case and use the separation of center of mass unknowns and relative unknowns. The use of geometrical reduction possibility together with the circular (polar) coordinates and the angular momentum conservation facilitate the application of PREVTH. This is a conceptual paper and basic goal is to show how PREVTH can be applied to these kinds of systems. We do not present numerical implementations here. They are given under a different title in this conference papers.