Constraining f(T) gravity in the Solar System

In the framework of $f(T)$ theories of gravity, we solve the field equations for $f(T)=T+\alpha T^n$, in the weak-field approximation and for spherical symmetry spacetime. Since $f(T)=T$ corresponds to Teleparallel Gravity, which is equivalent to General Relativity, the non linearity of the Lagrangian are expected to produce perturbations of the general relativistic solutions, parameterized by $\alpha$. Hence, we use the $f(T)$ solutions to model the gravitational field of the Sun, and exploit data from accurate tracking of spacecrafts orbiting Mercury and Saturn to infer preliminary insights on what could be obtained about the model parameter $\alpha$ and the cosmological constant $\mathrm{\Lambda }$. It turns out that improvements of about one-three orders with respect to the present-day constraints in the literature of magnitude seem possible.