We present a new method to fit the variations of both coordinates of a VLBI component as a function of time, assuming that the nucleus of the radio source contains a binary black hole system (BBH system). The presence of a BBH system produces 2 perturbations of the trajectory of the ejected VLBI components. By using only the VLBI coordinates, the problem we have to solve reduces to an astrometric problem. Knowledge of the variations of the VLBI coordinates as a function of time contains the kinematical information, thus we are able to deduce the inclination angle of the source and the bulk Lorentz factor of the ejected component. Generally, there is a family of the BBH system producing the same fit to our data. To illustrate this method, we apply it to the source 1807+784. We find that the inclination of the source is i = 5.8+-1.8 degrees and the VLBI component is ejected with a bulk Lorentz factor of 3.7+-0.3. We determine the family of the BBH system which provides the best fit, assuming at first that the masses of the 2 black holes are equal and then that the masses are 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 black hole ejecting the VLBI component and the orbiting period of the BBH system.
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