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In the previous paper, we have constructed two $f(T)$ models with nonminimaltorsion-matter coupling extension, which are successful in describing theevolution history of the Universe including the radiation-dominated era, thematter-dominated era, and the present accelerating expansion. Meantime, thesignificant advantage of these models is that they could avoid the cosmologicalconstant problem of $\Lambda$CDM. However, the nonminimal coupling betweenmatter and torsion will affect the tests of Solar system. In this paper, westudy the effects of Solar system in these models, including the gravitationredshift, geodetic effect and perihelion preccesion. We find that Model I canpass all three of the Solar system tests. For Model II, the parameter isconstrained by the measure of the perihelion precession of Mercury.

Solar system tests for realistic $f(T)$ models with nonminimal torsion-matter coupling