A method of motion reconstruction of an isotropic compact source in the vicinity of a Schwarzschild black hole is described. The method is based on the analysis of the redshift and the luminous intensity of several images of the source and is most effective for the source located at the distance of several Schwarzschild radii to the black hole. The cases of three and two observed images are considered. The uniqueness of motion reconstruction is investigated for each case. The results are illustrated by an example of direct and inverse problem solution. An observational scenario that allows to obtain the information necessary for motion reconstruction is suggested.

• Received 6 February 2010

DOI:https://doi.org/10.1103/PhysRevD.81.123005