  Non-spherical systems described by MOND theories of modified gravity arising
from generalizations of the Poisson equations are affected by a MONDian
extra-quadrupolar potential \phi_M even if they are isolated and they are in
deep Newtonian regime. In general MOND theories quickly approaching Newtonian
dynamics for accelerations beyond A_0, \phi_M is proportional to a
multiplicative scaling coefficient \alpha \sim 1, while in MOND models becoming
Newtonian beyond \kappa A_0, \kappa >> 1, it is enhanced by \kappa^2. We
analytically work out some orbital effects due to \phi_M in the framework of
QUMOND, and compare them with the latest observational determinations of Solar
System's planetary dynamics, exoplanets and double lined spectroscopic binary
stars. The current admissible range for the anomalous perihelion precession of
Saturn yields |\kappa| <= 3.5 x 10^3, while the radial velocity of \alpha Cen
AB allows to infer |\kappa|<= 6.2 x 10^4 (A) and |\kappa|<= 4.2 x 10^4 (B). In
evaluating such preliminary constraints it must be recalled that QUMOND is not
the nonrelativistic limit of TeVeS.

General Relativity and Quantum Cosmology;Earth and Planetary Astrophysics;Space Physics