The idea of nonlocal theories of gravity has been employed to extend Einstein's general relativity (GR). And a remarkable feature is that the nonlocal gravity can simulate the astrophysical dark matter. These corrections of the nonlocal gravity are characterized by two constant parameters: α and λ₀. α is a dimensionless strength parameter; λ₀ is the fundamental length scale of the nonlocal gravity. In the previous work, these two parameters were obtained by fitting the rotation curves of spiral galaxies. However, this results are not built on the newest and most accurate datesets of the solar system dynamics. 

  Inspired by the above idea, by using the supplementary advances in the perihelia provided by current INPOP10a and EPM2011 ephemerides, the authors find that INPOP10a yields the solar system’s bounds as α=(-0.6±12)×10^-12 and λ₀ =(0.2±2.1)×10⁵Kpc, while EPM2011 gives α=(0.3±3.2)×10^-12 and λ₀ =(-0.4±1.7)×10⁵Kpc (see the tables 2 and 3). Both of them are improved at least by about 5 times than previous results obtained by the rotation curves. As check of the estimation, the reducedχ_v² of several cases are listed in table 3. With the parameters fitted to INPOP10a, χ_v²=0.5, and , in the case of EPM2011, χ_v²=4.8. According to this research, in order to be compatible with the current solar system ephemerides as well as explaining the rotation curves, the nonlocal gravity needs to be screened in the solar system. 

   This work is published by the journal of Annals of Physics. And this research is supported by the National Nature Science Foundation of China and the National basic research program of China (Nos. 11473072, 1103085 and 11103010) and the Fundamental Research Program of Jiangsu Province of China (Nos. BK20131461 and BK2011553).  For more details, please see the following link: http://www.sciencedirect.com/science/article/pii/S0003491615002468