  Fermat's principle applied to a flat metric in the plane yields the phase of
a Bessel function in the periodic domain for a constant index of refraction.
Gravitational forces cause the index of refraction to vary and lead to a
modified phase of the Bessel function. A distinction is made between the forces
that cause acceleration: the gravitational force affects the optical properties
of the medium whereas the centrifugal force does not, the latter being built
into the phase of oscillations of the Bessel function. The time delay in radar
echoes from planets is determined from Fermat's principle where the velocity of
light is the phase velocity and the index of refraction varies on account of
the gravitational potential. The deflection of light by a massive body is shown
to be produced by a quadrupole interaction, and the perihelion shift requires
both the gravitational potential, producing a closed orbit, and the quadrupole,
causing the perihelion to rotate.
