  Based on the works of Gordon ([4]) and Zhang-Zhou([8])) on the variational
minimizing properties for Keplerian orbits and Lagrangian solutions of
Newtonian 2-body and 3-body problems, we use the constrained variational
principle of Ambrosetti-Coti Zelati ([1]) to compute the Lagrangian actions on
Keplerian and Lagrangian elliptical solutions with fixed energies, we also find
an interesting relationship between period and energy for Lagrangian elliptical
solutions with Newtonian potentials.
