Doppler effect in a moving medium (Q1267377)

A theory of the Doppler effect in a moving and dispersive medium is developed in terms of the Lagrangean, or ray derivative of the optical path. The relativistic Hamiltonian theory of geometrical optics is first presented. Then, a general perturbation theorem, which allows a rigorous theory of the Doppler effect in terms of the Lagrangean derivative of an integral over the unperturbed ray, is proven. Relativistic corrections due to retardation are obtained. It is shown that in solar corona experiments these corrections are larger than the current accuracy and must be taken into account.