If, as a first approximation, one considers the solar system as isolated, and the Sun as a point mass, the MOND effect in the inner solar system appears as an anomalous acceleration field in addition to the Newtonian one. In units of , the amplitude of the anomalous acceleration is given by , which can be constrained from the motion of the inner planets, typically their perihelion precession and the (non)-variation of Kepler’s constant [293, 391, 417]. These constraints typically exclude the whole -family of interpolating functions (Eq. 46) that are natural for multi-field theories such as TeVeS (see Section 6.2 and Section 7) because they yield for while it must be smaller than 0.04 at the orbit of Mars 35. Of course, this does not mean that the -function cannot be represented by the -family in the intermediate gravity regime characterizing galaxies, but it must be modified in the strong gravity regime36. Another potential effect of MOND is anomalously strong tidal stresses in the vicinity of saddle points of the Newtonian potential, which might be tested with the LISA pathfinder [37, 49, 255, 464]. The MOND bubble can be quite big and clearly detectable, or the effect could be small and undetectable, depending on the interpolating function [255, 161].
The approximation of an isolated Solar system being incorrect, it is also important to add the effect of the external field from the galaxy. Its amplitude is typically on the order of . From there, Milgrom  has predicted (both analytically and numerically) a subtle anomaly in the form of a quadrupole field that may be detected in planetary and spacecraft motions (as subsequently confirmed by [62, 185]). This has been used to constrain the form of the interpolating function in the weak acceleration regime characteristic of the external field itself. Constraints have essentially been set on the -family of -functions from the perihelion precession of Saturn [63, 154], namely that one must have in order to fit these data37.
However, it should be noted that it is slightly inconsistant to compare the classical predictions of MOND with observational constraints obtained by a global fit of solar system orbits using a fully-relativistic first-post-Newtonian model. Although the above constraints on classical MOND models are useful guides, proper constraints can only truly be set on the various relativistic theories presented in Section 7, the first-order constraints on these theories coming from their own post-Newtonian parameters [65, 99, 173, 372, 391, 450]. What is more, and makes all these tests perhaps unnecessary, it has recently been shown that it was possible to cancel any deviation from general relativity at small distances in most of these relativistic theories, independently of the form of the -function .
Living Rev. Relativity 15, (2012), 10
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