MOND effects in the inner Solar system
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} = ηa_{0}: a byproduct of the MOND externalfield 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^{a}_{i}(u) = q^{a}_{ij}u^{j}, with q^{a}_{ij} diagonal, axisymmetric and traceless: 2q^{a}_{xx} = 2q^{a}_{yy} = q^{a}_{zz} = q(η)(a_{0}/R_{M}), where R_{M} = (M_{solar}G/a_{0})^{1/2} ~ 8 × 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 `phantom matter' that hovers around the Sun. I find, for the relevant range of η values and for a range of interpolating functions, μ(x), values of 10^{2} <~ q <~ 0.3, which turn out to be sensitive to the form of μ(x) around the MONDtoNewtonian transition. This range verges on the present bounds from 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 modifiedinertia and modifiedgravity 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  μ(x) vanishes as x^{3/2} as x > ∞.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 October 2009
 DOI:
 10.1111/j.13652966.2009.15302.x
 arXiv:
 arXiv:0906.4817
 Bibcode:
 2009MNRAS.399..474M
 Keywords:

 Solar system: general;
 galaxies: kinematics and dynamics;
 cosmology: theory;
 dark matter;
 Astrophysics  Cosmology and Extragalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 31 pages