  The planar circular restricted three body problem (PCRTBP) is symmetric with
respect to the line of masses and there is a corresponding anti-symplectic
involution on the cotangent bundle of the 2-sphere in the regularized PCRTBP.
Recently it was shown that each bounded component of an energy hypersurface
with low energy for the regularized PCRTBP is fiberwise starshaped. This enable
us to define a Lagrangian Rabinowitz Floer homology which is related to
periodic orbits symmetric for the anti-symplectic involution in the regularized
PCRTBP and hence to symmetric periodic orbits in the unregularized problem. In
this paper we compute of this homology and discuss about symmetric periodic
orbits.
