  We estimate the conjectured interaction between the Earth gravitational field
and a superconductor immersed in external, static electric and magnetic field.
The latter is close to the sample upper critical field and generates the
presence of a vortex lattice. The proposed interaction could lead to multiple,
measurable effects. First of all, a local affection of the gravitational field
inside the superconductor could take place. Second, a new component of a
generalized electric field parallel to the superconductor surface is generated
inside the sample. The analysis is performed by using the time-dependent
Ginzburg-Landau theory combined with the gravito-Maxwell formalism. This
approach leads us to analytic solutions of the problem, also providing the
average values of the generated fields and corrections inside the sample. We
will also study which are the physical parameters to optimize and, in turn, the
most suitable materials to maximize the effect.
