External field effect of modified Newtonian dynamics in the Solar system
  The Modified Newtonian Dynamics (MOND) has been formulated as a modification
of the Poisson equation for the Newtonian gravitational field. This theory
generically predicts a violation of the strong version of the equivalence
principle, and as a result the gravitational dynamics of a system depends on
the external gravitational field in which the system is embedded. This
so-called external field effect has been recently shown to imply the existence
of an anomalous quadrupolar correction, along the direction of the external
Galactic field, in the gravitational potential felt by planets in the Solar
System. In this paper we confirm the existence of this effect by a numerical
integration of the MOND equation in the presence of an external field, and
compute the secular precession of the perihelion of planets induced by this
effect. We find that the precession effect is rather large for outer gaseous
planets, and in the case of Saturn is comparable to published residuals of
precession obtained by Saturn range tracking data. The effect is much smaller
for inner planets, but in the case of the Earth it appears to be in conflict
for most of the MOND functions $\mu(y)$ with the very good constraint on the
perihelion precession obtained from Jupiter VLBI data. The MOND functions that
are compatible with this constraint appear to have a very rapid transition from
the MONDian regime to the Newtonian one.
