Measuring the radius and mass of Planet Nine

Batygin and Brown (2016) have suggested the existence of a new Solar System planet supposed to be responsible for the perturbation of eccentric orbits of small outer bodies. The main challenge is now to detect and characterize this putative body. Here we investigate the principles of the determination of its physical parameters, mainly its mass and radius. For that purpose we concentrate on two methods, stellar occultations and gravitational microlensing effects (amplification, deflection and time delay). We estimate the main characteristics of a possible occultation or gravitational effects: flux variation of a background star, duration and probability of occurence. We investigate also additional benefits of direct imaging and of an occultation.