  The relative motion of stars and other celestial objects in very wide pairs,
separated by distances of the order of 1 pc, is strongly influenced by the
tidal gravitational potential of the Galaxy. The Coriolis component of the
horizontal tidal force in the rotating reference frame tends to disrupt such
marginally bound pairs. However, even extremely wide pairs of bodies can be
bound over intervals of time comparable to the Hubble time, under appropriate
initial conditions. Here we show that for arbitrary chosen initial coordinates
of a pair of stars, there exists a volume of the space of initial velocity
components where the orbits remain bound in the planar tidal field for longer
than 10 Gyr, even though the initial separation is well outside the Jacobi
radius. The boundary of this phase space of stable orbits is fractal, and the
motion at the boundary conditions is clearly chaotic. We found that the pairs
may remain confined for several Gyr, and then suddenly disintegrate due to a
particularly close rendezvous. By reversing such long-term stable orbits, we
find that entrapment of unrelated stars into wide pairs is possible, but should
be quite rare. Careful analysis of precision astrometry surveys revealed that
extremely wide pairs of stars are present in significant numbers in the Galaxy.
These results are expected to help discriminating the cases of genuine binarity
and chance entrapment, and to make inroads in testing the limits of Newtonian
gravitation.
