  I pinpoint a previously unrecognized MOND effect that may act in the inner
solar system, and is due to the galactic acceleration, g_g=eta*a0: a byproduct
of the MOND external-field effect. Predictions of the effect are not generic to
the MOND paradigm, but depend on the particular MOND formulation at hand.
However, the modified-Poisson formulation, on which I concentrate, uniquely
predicts a subtle anomaly that may be detected in planetary and spacecraft
motions (and perhaps in other precision systems, such as binary pulsars),
despite their very high accelerations, and even if the MOND interpolating
function is arbitrarily close to unity at high accelerations. Near the sun,
this anomaly appears as a quadrupole field, with the acceleration at position u
from the sun being g_i(u)=-q_{ij}u^j, with q_{ij} diagonal, axisymmetric, and
traceless: -2q_{xx}=-2q_{yy}=q_{zz}=q(eta)*(a0/R_M), where
R_M=(MG/a0)^{1/2}=8*10^3 au is the MOND radius of the sun. The anomaly is
described and analyzed as the Newtonian field of the fictitious cloud of
``phantom matter'' that hovers around the sun. I find, for the relevant range
of eta values, and for a range of interpolating functions, mu(x), values of
10^{-2}<-q< 0.3, which turn out to be sensitive to the form of mu(x) around the
MOND-to-Newtonian transition. This range verges on the present bounds from
solar system measurements. There might thus exist favorable prospects for
either measuring the effect, or constraining the theory and the relevant
parameters.
