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As an extension of a previous work in which perihelion advances areconsidered only and as an attempt to find more stringent constraints on itsparameters, we investigate effects on astronomical observation and experimentsconducted in the Solar System due to the $f(T)$ gravity which contains aquadratic correction of $\alpha T^2$ ($\alpha$ is a model parameter) and thecosmological constant $\Lambda$. Using a spherical solution describing theSun's gravitational field, the resulting secular evolution of planetary orbitalmotions, light deflection, gravitational time delay and frequency shift arecalculated up to the leading contribution. Among them, we find qualitativelythat the light deflection holds a unique bound on $\alpha$, without dependenceon $\Lambda$, and the time delay experiments during inferior conjunction imposea clean constraint on $\Lambda$, regardless of $\alpha$. Based on observationand experiments, especially the supplementary advances in the periheliaprovided by the INPOP10a ephemeris, we obtain the upper-bounds quantitatively:$|\alpha| \le 1.2 \times 10^{2}$ m${}^2$ and $ |\Lambda| \le 1.8 \times10^{-43}$ m${}^{-2}$, at least 10 times tighter than the previous result.

$f(T)$ gravity: effects on astronomical observation and Solar System experiments and upper-bounds