  We present variational characterizations of frozen planet orbits for the
helium atom in the Lagrangian and the Hamiltonian picture. They are based on a
Levi-Civita regularization with different time reparametrizations for the two
electrons and lead to nonlocal functionals. Within this variational setup, we
deform the helium problem to one where the two electrons interact only by their
mean values and use this to deduce the existence of frozen planet orbits.
