  Polar ring galaxies are ideal objects with which to study the
three-dimensional shapes of galactic gravitational potentials since two
rotation curves can be measured in two perpendicular planes. Observational
studies have uncovered systematically larger rotation velocities in the
extended polar rings than in the associated host galaxies. In the dark matter
context, this can only be explained through dark halos that are systematically
flattened along the polar rings. Here, we point out that these objects can also
be used as very effective tests of gravity theories, such as those based on
Milgromian dynamics (MOND). We run a set of polar ring models using both
Milgromian and Newtonian dynamics to predict the expected shapes of the
rotation curves in both planes, varying the total mass of the system, the mass
of the ring with respect to the host, as well as the size of the hole at the
center of the ring. We find that Milgromian dynamics not only naturally leads
to rotation velocities being typically higher in the extended polar rings than
in the hosts, as would be the case in Newtonian dynamics without dark matter,
but that it also gets the shape and amplitude of velocities correct. Milgromian
dynamics thus adequately explains this particular property of polar ring
galaxies.
