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We present a new method to fit the variations of both coordinates of a VLBIcomponent as a function of time, assuming that the nucleus of the radio sourcecontains a binary black hole system (BBH system). The presence of a BBH systemproduces 2 perturbations of the trajectory of the ejected VLBI components. Byusing only the VLBI coordinates, the problem we have to solve reduces to anastrometric problem. Knowledge of the variations of the VLBI coordinates as afunction of time contains the kinematical information, thus we are able todeduce the inclination angle of the source and the bulk Lorentz factor of theejected component. Generally, there is a family of the BBH system producing thesame fit to our data. To illustrate this method, we apply it to the source1807+784. We find that the inclination of the source is i = 5.8+-1.8 degreesand the VLBI component is ejected with a bulk Lorentz factor of 3.7+-0.3. Wedetermine the family of the BBH system which provides the best fit, assuming atfirst that the masses of the 2 black holes are equal and then that the massesare different. Each family of BBH systems is characterized by Tp/Tb~1.967,where Tp and Tb are the precession period of the accretion disk of the blackhole ejecting the VLBI component and the orbiting period of the BBH system.

Modeling nuclei of radio galaxies from VLBI radio observations. Application to the BL Lac Object S5 1803+784