We numerically investigate the features of typical orbits occurring in the Oort cloud ( r ≈ 50 -150 kAU) in the low-acceleration regime of the MOdified Newtonian Dynamics (MOND). We fully 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 ≈ 10¯10 m s ¯2 . We use three different forms of the MOND interpolating function µ(x) , two different values for the Galactic field at the Sun's location and different initial conditions corresponding to plausible Keplerian ellipses in the Oort cloud. 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. These facts may have consequences on the composition and the dynamical history of the Oort cloud which are difficult to predict in detail; certainly, the MOND picture of the Oort region is quite different from the Newtonian one exhibiting no regularities.
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