new features of the orbital motion of free test particles around SFNSs and SFBHs. First, for a given *positive* mass, there exists a continuum of SFNSs with asymptotic geometry of the Schwarzschild spacetime with the same mass; thus, in contrast to Schwarzschild naked singularities, SFNSs exhibit the attractive nature of gravitation.

Second, the radii of the event horizon and of the innermost stable circular orbit of a SFBH are normally much less than those of the Schwarzschild black hole with the same mass. A SFNS does not have an innermost stable circular orbit but has a stable, degenerated, static orbit on which a test particle, having zero angular momentum and the minimum of its energy, remains at rest as time passes. It is important that this phenomena cannot take place on the outside of the event horizon of a vacuum black hole or a SFBH. Moreover, in the theory of self-gravitating scalar fields with the positive kinetic term in the Lagrangian, among all configurations possessing a positive mass, naked singularities and only naked singularities have such an orbit. If a noninteracting test particle is initially has a sufficiently small specific angular momentum, it will permanently remain close to the static 