  We expose the phenomenology of the massless dilaton theory in the Solar
system for a non universal quadratic coupling between the scalar field which
represents the dilaton, and the matter. Modified post-Newtonian equations of
motion of an $N$-body system and the light time travel are derived from the
action of the theory. We use the physical properties of the main planets of the
Solar system to reduce the number of parameters to be tested to 3 in the linear
coupling case. In the linear case, we have an universal coupling constant
$\alpha_0$ and two coupling constants $\alpha_T$ and $\alpha_G$ related
respectively to the telluric bodies and to the gaseous bodies. We then use the
planetary ephemeris, INPOP19a, in order to constrain these constants. We
succeeded to constrain the linear coupling scenario and the constraints read
$\alpha_0=(1.01\pm23.7)\times 10^{-5}$, $\alpha_T=(0.00\pm24.5)\times 10^{-6}$,
$\alpha_G=(-1.46\pm12.0)\times 10^{-5}$, at the 99.5 \% C.L.
