Solar system tests for realistic f (T) models with non-minimal torsion-matter coupling

In the previous paper, we have constructed two f(T) models with non-minimal torsion-matter coupling extension, which are successful in describing the evolution history of the Universe including the radiation-dominated era, the matter-dominated era, and the present accelerating expansion. Meantime, the significant advantage of these models is that they could avoid the cosmological constant problem of Lambda CDM. However, the non-minimal coupling between matter and torsion will affect the tests of the Solar system. In this paper, we study the effects of the Solar system in these models, including the gravitation redshift, geodetic effect and perihelion precession. We find that Model I can pass all three of the Solar system tests. For Model II, the parameter is constrained by the uncertainties of the planets' estimated perihelion precessions.