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Magnetic flux trapped on the surface of superconducting rotors of the GravityProbe B (GP-B) experiment produces some signal in the SQUID readout. For theneeds of GP-B error analysis and simulation of data reduction, this signal iscalculated and analyzed in the paper. We first solve a magnetostatic problemfor a point source (fluxon) on the surface of a sphere, finding the closed formelementary expression for the corresponding Green's function. Second, wecalculate the flux through the pick-up loop as a function of the fluxonposition. Next, the time dependence of a fluxon position, caused by rotormotion according to a symmetric top model, and thus the time signature of theflux are determined, and the spectrum of the trapped flux signal is analyzed.Finally, a multi-purpose program of trapped flux signal generation based on theabove results is described, various examples of the signal obtained by means ofthis program are given, and their features are discussed.Comment: 14 pages, including 7 figures. Submitted to: "Journal of Applied  Physics

Explicit Green’s function of a boundary value problem for a sphere and trapped flux analysis in Gravity Probe B experiment