... 8, ``Celestial Mechanics'', 2002 Preliminary results of search studies of predicted hypothetical objects beyond the orbit of Jupiter B. R. Mushailov, A. A. Kaloshin Sternberg Astronomical Institute, Moscow, Russia In paper [1] on the basis of the external variant of the restricted circular three­ body problem we calculated the most probable orbits of hypothetical asteroids moving in orbital commensurabily with Jupiter. ... The upper estimate of the brightness of these objects has been found as well....