Applying the Ginzburg-Landau theory including frame dragging effects to the case of a rotating superconductor, we were able to express the absolute value of the gravitomagnetic field involved to explain the Cooper pair mass anomaly previously reported by Tate. Although our analysis predicts large gravitomagnetic fields originating from superconductive gyroscopes, those should not affect the measurement of the Earth gravitomagnetic field by the Gravity Probe-B satellite. However, the hypothesis might be well suited to explain a mechanical momentum exchange phenomena reported for superfluid helium and a dragging force present in a rotating superconductor experiment. (c) 2005 Elsevier B.V. All rights reserved.