  The Planet Nine hypothesis has now enough constraints to deserve further
attention in the form of detailed numerical experiments. The results of such
studies can help us improve our understanding of the dynamical effects of such
a hypothetical object on the extreme trans-Neptunian objects or ETNOs and
perhaps provide additional constraints on the orbit of Planet Nine itself.
Here, we present the results of direct N-body calculations including the latest
data available on the Planet Nine conjecture. The present-day orbits of the six
ETNOs originally linked to the hypothesis are evolved backwards in time and
into the future under some plausible incarnations of the hypothesis to
investigate if the values of several orbital elements, including the argument
of perihelion, remain confined to relatively narrow ranges. We find that a
nominal Planet Nine can keep the orbits of (90377) Sedna and 2012 VP113
relatively well confined in orbital parameter space for hundreds of Myr, but it
may make the orbits of 2004 VN112, 2007 TG422 and 2013 RF98 very unstable on
time-scales of dozens of Myr, turning them retrograde and eventually triggering
their ejection from the Solar system. Far more stable orbital evolution is
found with slightly modified orbits for Planet Nine.
