  We investigate the action spectrum of Hill's lunar problem by observing
inclusions between the Liouville domains enclosed by the regularized energy
hypersurfaces of the rotating Kepler problem and Hill's lunar problem. In this
paper, we reinterpret the spectral invariant corresponding to every nonzero
homology class $\alpha \in H_*(\Lambda N)$ in the loop homology as a symplectic
capacity $c_N(M, \alpha)$ for a fiberwise star-shaped domain $M$ in a cotangent
bundle with canonical symplectic structure $(T^*N, \omega_{can}=d
\lambda_{can})$. Also, we determine the action spectrum of the regularized
rotating Kepler problem. As a result, we obtain estimates of the action
spectrum of Hill's lunar problem. This will show that there exists a periodic
orbit of Hill's lunar problem whose action is less than $\pi$ for any energy
$-c < -{3^{4 \over 3} \over 2}$.
