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By using the most recently published Doppler tomography measurements andaccurate theoretical modeling of the oblateness-driven orbital precessions, wetightly constrain some of the physical and orbital parameters of the planetarysystem hosted by the fast rotating star WASP-33. In particular, themeasurements of the orbital inclination $i_{\rm p}$ to the plane of the sky andof the sky-projected spin-orbit misalignment $\lambda$ at two epochs about sixyears apart allowed for the determination of the longitude of the ascendingnode $\Omega$ and of the orbital inclination $I$ to the apparent equatorialplane at the same epochs. As a consequence, average rates of change$\dot\Omega_{\rm exp},~\dot I_{\rm exp}$ of this two orbital elements, accurateto a $\approx 10^{-2}~{\rm deg}~{\rm yr}^{-1}$ level, were calculated as well.By comparing them to general theoretical expressions $\dot\Omega_{J_2},~\dotI_{J_2}$ for their precessions induced by an oblate star whose symmetry axis isarbitrarily oriented, we were able to determine the angle $i^{\star}$ betweenthe line of sight the star's spin $S^{\star}$ and its first even zonal harmonic$J_2^{\star}$ obtaining $i^{\star} = 142^{+10}_{-11}~{\rm deg},~J_2^{\star} =(2.1^{+0.8}_{-0.5})\times 10^{-4}.$ As a by-product, the angle between$S^{\star}$ and the orbital angular momentum $L$ is as large as about $\psi\approx 100$ deg $(\psi^{2008} = 99^{+5}_{-4}~{\rm deg},~\psi^{2014} =103^{+5}_{-4}~{\rm deg})$, and changes at a rate $\dot\psi =0.7^{+1.5}_{-1.6}~{\rm deg}~{\rm yr}^{-1}$. The predicted general relativisticLense-Thirring precessions, or the order of $\approx 10^{-3}~{\rm deg}~{\rmyr}^{-1}$, are, at present, about one order of magnitude below themeasurability threshold.

Accurate characterization of the stellar and orbital parameters of the exoplanetary system WASP-33 b from orbital dynamics