In a classical two body problem,when we superpose our origin of co-ordinates on any one of the two particles,the other particle(now we see it to have reduced mass [mM/(m+M)],moves w.r.t. me... I saw in a book #Central Force Motion, that the particle is treated by 2nd law of motion... i.e. [mM/(m+M)]*a=F where a and F are accelen. and force term. My question is how do we know that this is indeed an inertial frame?After all the two particles are interacting among themselves and there may well be a radial accelen.(Like in the case of Binary stars). Another point is that we invoke the concept of centrifugal energy... (=L^2/(2*mu*r^2)) where mu denotes the reduced mass. Atam P Arya says that here we are working from a rotating frame as a penalty of eliminating theta from the equations...i.e. we are being bound to put this centrifugal force term(and hence a centrifugal energy) as we are working from a rotating frame... I am having the fragrance...But cannot see the reality... Please highlight on this topic.