New physics beyond the standard model of particles might cause deviation from the inverse-square law of gravity. In many theoretical models of modified gravity, it is parameterized by the Yukawa correction to the Newtonian gravitational force in terms of two parameters α and λ. Here α is a dimensionless strength parameter and λ is a length scale. Using the supplementary advances in perihelia provided by INPOP10a and EPM2011 ephemerides, we obtain new upper limits on the deviation from the inverse-square law when the uncertainty of the Sun's quadrupole moment is taken into account. We find that INPOP10a yields the upper limits as α = 3.1 × 10 −11 and λ = 0.15 au, and EPM2011 gives α = 5.2 × 10 −11 and λ = 0.21 au. In both of them, α is at least 10 times less than the previous results.

We obtain preliminary limits on a logarithmic correction to the Newtonian gravitational potential by using five binary pulsars: PSR J0737-3039, PSR B1534+12, PSR J1756-2251, PSR B1913+16 and PSR B2127+11C. This kind of correction may originate from fundamental frameworks, like string theories, effective models of gravity due to quantum effects and the non-local gravity scheme. We estimate the upper limit of the Tohline-Kuhn-Kruglyak parameter λ and the lower limit of the Fabris-Campos parameter α, which parameterize the correction and are connected to each other by αλ = −1. By analyzing the advances of periastron of these binary pulsars, we find that the preliminary upper limit of α is 0.19 ± 0.14 kpc −1 and the preliminary lower limit of λ is −5.2 ± 3.8 kpc. They are compatible with the bounds based on dynamics of spiral galaxies but quite different from those given by solar system dynamics. These results indicate that this logarithmic correction might be more observable in current timings of binary pulsars than in motions of the solar system.