Understanding the processes that led Venus to its current state and will drive its future evolution is one of the main challenges of the next generation of space missions. In this work we analyze the retrieval of the spin vector, the tidal response and the moment of inertia of Venus with VERITAS, a Discovery-class mission proposed to NASA. By simulating the joint analysis of Doppler tracking data and tie points provided by the onboard synthetic aperture radar, we show that VERITAS would provide strong constraints on the interior structure of the planet. In particular we show that VERITAS would provide accuracies in the estimates of the tidal Love number k2 to 3.9×10^-4, its tidal phase lag to 0.04^o, and the moment of inertia factor to 1.4×10^-3 (0.4% of the expected value).