MOND effects in the inner solar system

TL;DR

This paper identifies a subtle MOND-induced quadrupole anomaly in the inner solar system caused by galactic acceleration, which could be detectable through planetary or spacecraft motion measurements, providing a potential test for MOND theories.

Contribution

It predicts a specific, measurable MOND effect in the inner solar system based on the modified-Poisson formulation, linking galactic acceleration to local gravitational anomalies.

Findings

Predicted quadrupole anomaly magnitude ranges from 0.01 to 0.3

Anomaly depends on the MOND transition function mu(x)

Potential for detection or constraint with current solar system data

Abstract

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.