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 [391]^{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
regime^{36}.
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 [314] 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
data^{37}.

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 [22].

Living Rev. Relativity 15, (2012), 10
http://www.livingreviews.org/lrr-2012-10 |
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