Unveiling the nature of SgrA* with the geodesic motion of S-stars
  Despite the huge improvements guaranteed by future GRAVITY observations of
the S0-2 star, these will not be able to unveil the fundamental nature, whether
black hole or wormhole, of the central supermassive object. Nevertheless,
observing stars orbiting closer to the central gravitational source could allow
to distinguish between the black hole and wormhole nature of this object at
more than 5$\sigma$. Firstly, we have used publicly available astrometric and
spectroscopic measurements of the S0-2 star to constrain the metric around the
supermassive object without finding any evidence either favouring or ruling out
the wormhole nature. Secondly, we have designed a mock catalogue of future
observations of the S0-2 star mirroring the accuracy and precision of GRAVITY.
Afterwards, we firstly tested our methodology showing that our procedure
recovers the input model, and subsequently we demonstrated that the
constraining power of such a dataset is not enough to distinguish between black
hole and wormhole. Finally, we built some toy models representing stars
orbiting much closer the central object than S0-2. We used these toy models to
investigate which are the ideal orbital features and observational strategies
to achieve our aim of unveiling the fundamental nature of the central
supermassive object, demonstrating that a star with a period of the order of
$\sim 5$ years and a pericentre distance of $\sim 5$ AU could identify the
nature of the central object at almost 5$\sigma$ accuracy.
