MOND orbits in the Oort cloud
  We numerically investigate the features of typical orbits occurring in the
Oort cloud (r\approx 50-150 kAU) in the low-acceleration regime of the MOdified
Newtonian Dynamics (MOND). We take into account the so-called External Field
Effect (EFE) because the solar system is embedded in the Milky Way. In the
framework of MOND this does matter since the gravitational acceleration of
Galactic origin felt by the solar system is of the same order of magnitude of
the characteristic MOND acceleration scale A_0\approx 10^-10 m s^-2. We use
three different forms of the MOND interpolating function \mu(x) and two
different values for the Galactic field at the Sun's location. We find that
MOND produces highly distorted trajectories with respect to the Newtonian case,
especially for very eccentric orbits. It turns out that the shape of the MOND
orbits strongly depend on the initial conditions. For particular initial state
vectors, the MOND paths in the ecliptic plane get shrunk extending over much
smaller spatial regions than in the Newtonian case, and experience high
frequency variations over one Keplerian orbital period. Ecliptic orbits with
different initial conditions and nearly polar orbits are quite different
getting distorted as well, but they occupy more extended spatial regions. This
facts may have consequences on the composition and the dynamical history of the
Oort cloud which are difficult to predict.
