Constraining the range of Yukawa gravity interaction from S2 star orbits
  We consider possible signatures for Yukawa gravity within the Galactic
Central Parsec, based on our analysis of the S2 star orbital precession around
the massive compact dark object at the Galactic Centre, and on the comparisons
between the simulated orbits in Yukawa gravity and two independent sets of
observations. Our simulations resulted in strong constraints on the range of
Yukawa interaction $\Lambda$ and showed that its most probable value in the
case of S2 star is around 5000 - 7000 AU. At the same time, we were not able to
obtain reliable constrains on the universal constant $\delta$ of Yukawa
gravity, because the current observations of S2 star indicated that it may be
highly correlated with parameter $\Lambda$ in the range $(0 <\delta < 1)$. For
$\delta > 2$ they are not correlated. However, the same universal constant
which was successfully applied to clusters of galaxies and rotation curves of
spiral galaxies ($\delta=1/3$) also gives a satisfactory agreement with the
observed orbital precession of the S2 star, and in that case the most probable
value for the scale parameter is $\Lambda \approx 3000 \pm 1500$ AU. Also, the
Yukawa gravity potential induces precession of S2 star orbit in the same
direction as General Relativity for $\delta > 0$ and for $\delta < -1$, and in
the opposite direction for $-1 <\delta < 0$. The future observations with
advanced facilities, such as GRAVITY or/and European Extremely Large Telescope,
are needed in order to verify these claims.
