Spherically symmetric solutions for $f(T)$ gravity models are derived by the so-called Noether symmetry approach. First, we present a full set of Noether symmetries for some minisuperspace models. Then, we compute analytical solutions and find that spherically symmetric solutions in $f(T)$ gravity can be recast in terms of Schwarzschild-like solutions modified by a distortion function depending on a characteristic radius. The obtained solutions are more general than those obtained by the usual solution methods.

In this work, we show that it is possible to study the notion of a geodesic deviation equation in $f(T)$ gravity, in spite of the fact that in teleparallel gravity there is no notion of geodesics, and the torsion is responsible for the appearance of gravitational interaction. In this regard, we obtain the general relativity equivalent equations for $f(T)$ gravity, which are in the modified gravity form such as $f(R)$ gravity. Then, we obtain the geodesic deviation equation within the context of this modified gravity. In this way, the obtained geodesic deviation equation will correspond to the $f(T)$ gravity. Eventually, we extend the calculations to obtain the modification of the Mattig relation.