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 a(0): 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)(a)(u) = -q(ij)(a)u(j), with q(ij)(a) diagonal, axisymmetric and traceless: -2q(xx)(a) = -2q(yy)(a) = q(zz)(a) = q(eta)(a(0)/R(M)), where R(M) = (M(circle dot)G/a(0))(1/2) approximate to 8 x 10(3) au is the MOND transition radius of the Sun. The anomaly is described and analysed as the Newtonian field of the fictitious cloud of 'phantorn 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) less than or similar to -q less than or similar to 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 front Solar system measurements. There might thus exist favourable prospects for either measuring the effect or constraining the theory and relevant parameters. Probing this anomaly may also help distinguish between modified-inertia and modified-gravity formulations of MOND. I also discuss briefly an anomaly that is generic to MOND in all its formulations, and competes with the quadrupole anomaly in the special case that 1 - mu(x) vanishes as x(-3/2) as x -> infinity.