Dynamics and stability of the two body problem with Yukawa correction

We explore the dynamics and stability of the two-body problem by modifying the Newtonian potential with the Yukawa potential. This model may be considered a theory of modified gravity; where the interaction is not simply the Kepler solution for large distance. We investigate stability by deriving the Jacobian of the linearized matrix equation and evaluating the eigenvalues of the various equilibrium points calculated during the analysis. The subcases of a purely Yukawa and purely Newtonian potential are also explored.