The dynamics of non-spherical systems described by MOND theories arising from generalizations of the Poisson equation is affected by an extra MONDian quadrupolar potential \phi _ { Q } even if they are isolated ( no EFE effect ) and if they are in deep Newtonian regime .
In general MOND theories quickly approaching Newtonian dynamics for accelerations beyond A _ { 0 } , \phi _ { Q } is proportional to a coefficient \alpha \sim 1 , while in MOND models becoming Newtonian beyond \kappa A _ { 0 } , \kappa \gg 1 , it is enhanced by \kappa ^ { 2 } .
We analytically work out some orbital effects due to \phi _ { Q } in the framework of QUMOND , and compare them with the latest observational determinations of Solar System ’ s planetary dynamics , exoplanets , double lined spectroscopic binary stars and binary radio pulsars .
The current admissible range for the anomalous perihelion precession of Saturn -0.5 milliarcseconds per century \leq \Delta \dot { \varpi } \leq 0.8 milliarcseconds per century yields | \kappa| \leq { \color { black } 3 } .5 \times 10 ^ { { \color { black } 3 } } , while the radial velocity of \alpha Cen AB allows to infer | \kappa| \leq 6.2 \times 10 ^ { 4 } ( { A } ) and | \kappa| \leq 4.2 \times 10 ^ { 4 } ( { B } ) .