The Modified Newtonian Dynamics (MOND) paradigm generically predicts that the
external gravitational field in which a system is embedded can produce effects
on its internal dynamics. In this communication, we first show that this
External Field Effect can significantly improve some galactic rotation curves
fits by decreasing the predicted velocities of the external part of the
rotation curves. In modified gravity versions of MOND, this External Field
Effect also appears in the Solar System and leads to a very good way to
constrain the transition function of the theory. A combined analysis of the
galactic rotation curves and Solar System constraints (provided by the Cassini
spacecraft) rules out several classes of popular MOND transition functions, but
leaves others viable. Moreover, we show that LISA Pathfinder will not be able
to improve the current constraints on these still viable transition functions.Comment: 13 pages, 7 figures, accepted for publication in MNRA
