Two body transient solution In the two body problem, if each body is given an initial condition as a momentum vector, what is the transient part of the solution as it settles into the steady state orbit?
Your question is very unclear.  As long as the orbit is bound (i.e. the total energy is negative), then there is a unique closed orbit solution (see Bertrand's theorem).  There will be no 'transient' part of the solution.