Stability of planetary systems within the S-star cluster: the Solar
  system analogues
  A dynamically relaxed dense cluster comprised of about 40 stars (the
so-called S-stars) inhabits the central region of the Galaxy. Their stars
revolve around the Sgr A$^*$ massive object. To understand the dynamical
evolution of planetary systems in a particular environment like that around Sgr
A$^*$, we carry out direct N--body simulations of planetary systems embedded in
the S--star cluster. In this work, we investigate the short-term stability of
the planets orbiting around S-stars after their close interactions with the
central massive black hole of our galaxy. We find that planetary systems go
through encounters with the SMBH and the nearby stars. We determine the
frequency and the strength of planetary systems' encounters with the nearby
stars as these encounters remarkably increase for systems assigned to S-stars
closer to the SMBH. The SMBH severely destabilizes the planetary systems,
though we noted that the small oscillations in the mutual eccentricity and
inclination of the planetary system could be caused by the planet--planet
coupling and the near-resonance effect between the two planets. We obtain
estimates of the fraction of survivor planets ($\sim 51\%$), and find that
planets stripped from their hosting star are generally captured on close orbits
around Sgr A$^*$. We notify while gas giants are tidally disrupted, terrestrial
planets do not. We estimate that Sgr A$^*$ flares can be due to the tidal
disruption events of \textit{starless} giant planets.
