  In this paper we show the existence of syzygies for all periodic orbits
inside the bounded Hill's region of the planer circular restricted three-body
problem with energy below the second critical value. The proof will follow some
ideas of Birkhoff to compute the roots of partial derivatives of the effective
potential. Birkhoff's methods are extended to higher energies and a new base
case is created and shown to fulfil the requirements. An other step from
Birkhoff is scrutinized to continue the statement to all mass ratios. The final
step is achieved by integrating over periodic orbits. Applying the same methods
to Hill's lunar problem delivers similar results in that setting as well.
