The programming system ERA (Ephemeris Research in Astronomy) has been developed in IAA RAS to support scientific research in ephemeris and dynamical astronomy as well as for aims of astronomical education. The main feature of the system is its versatility: user not limited by a predefined set of ephemeris tasks but easily develops his/ her applications practically in any branch of positional astronomy. In the frame of the ERA system, a user has easy access to an embedded universal package to process high precision observations of Solar System bodies, including those that are hazardous for humanity, such as NEAs and comets. In the present paper the databases for both observations and elements of asteroids and comets in the ERA system are described, as well as examples of the orbit determination and the processing of observations for these objects. The peculiarities of computations are described and examles of usage of the ERA system for orbit determination are presented.