  We looked at the orbital motions of test particles according to the External
Field Effect (EFE) predicted by the MOdified Newtonian Dynamics (MOND) in the
Oort cloud which falls in the deep MONDian regime (r\approx 50-150 kAU).
Concerning the interpolating function \mu(x), we extensively used the forms
\mu_1=1/(1+x),\mu_2=x/(1+x^2)^1/2,\mu_3/2=x/(1+x^3/2)^2/3. We integrated both
the MOND and the Newtonian equations of motion in Cartesian coordinates sharing
the same initial conditions. We considered both ecliptic and nearly polar
trajectories, all with high eccentricities (e>0.1). In order to evaluate the
characteristic MOND parameters \mu_g and L_g entering the problem, we used two
different values (V=220 km s^-1 and V=254 km s^-1) of the circular speed of the
solar system's motion through the Galaxy; $V$ allows to evaluate the Milky
Way's gravitational field at the Sun's location. It turns out that EFE induces
strong distortions of the Newtonian ellipses, especially in the ecliptic plane
yielding more involved paths which span less extended spatial regions.
