MOND effects in the inner solar system

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.