Preliminary limits on a logarithmic correction to the Newtonian gravitational potential in the solar system

Using the supplementary advances of the perihelia provided by INPOP10a (IMCCE, France) and EPM2011 (IAA RAS, Russia) ephemerides, we obtain preliminary limits on a logarithmic correction to the Newtonian gravitational potential in the solar system. This kind of correction may originate from fundamental frameworks, like string theories or effective models of gravity due to quantum effects and the non-local gravity scheme. We estimate upper limit of Tohline-Kuhn-Kruglyak parameter λ and lower bound of Fabris-Campos parameter α, which parametrize the correction and connect each other by αλ=−1. In our estimation, we take the Lense-Thirring effect due to the Sun’s angular momentum and the uncertainty of the Sun’s quadrupole moment into account. These two factors were usually absent in previous works. We find that INPOP10a yields the upper limit as α=−(0.66±5.82)×10−4 kpc−1 [or the lower limit as λ=(0.15±8.76)×105 kpc] while EPM2011 gives α=(0.52±1.74)×10−4 kpc−1 [or the lower limit as λ=−(0.19±3.29)×105 kpc]. The limits of |λ| are greater than the result based on the rotation curves of spiral galaxies by about 3 orders of magnitude, indicating its effects might be screened in high density regions.