July 31, 2015 16:37 WSPC Proceedings - 9in x 6in DokuchaevEroshenko page 1 1 Precession of stars in the Galactic center and dark matter annihilation limits V. I. Dokuchaev 1,2 and Yu. N. Eroshenko 1,* 1 Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect 7a, Moscow, 117312, Russia 2 National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409, Russia * E-mail: eroshenko@inr.ac.ru The group of the fast moving S0 stars is gravitationally bound with the su- permassive black hole SgrA* in the Galactic center. Probably the orbits of S0 stars deviate from the precise ellipses and precess due to the gravitational perturbations from dim stars, stellar mass black holes or dark matter. The observational data provide only upper limits on these additional masses. Our calculation of the the Newtonian precession provides some new constraints. If the invisible mass in the Galactic center is composed by dark matter particles, it can be the source of the gamma-radiation due to annihilation. The annihi- lation limits on the invisible mass can be compared with the dynamical limits from the precession angle. In the nearest future the observations can provide the weighing of the invisible matter in the Galactic center. Keywords : Galactic center; precession; black hole; dark matter; annihilation. 1. Introduction Several high velocities stars are observed at the center of the Galaxy around supermassive black hole SgrA*. According to the parameters of their or- bits 1 and from the effect of quasiperiodic oscillations 2 the mass of SgrA* is M BH ≃ 4 × 10 6 M ⊙ . Besides SgrA*, there are additional masses such as gas, stars and their remnants, and dark matter at the center of the Galaxy. According to the fitting of the orbits of stars 1 , the mass within the orbit of the S0-2 star is no more than 3 − 4 % of M BH . This additional mass result in the de- viation of the gravitational potential from the potential of a point mass U = −GM BH /r. As a result, the orbits of stars would be unclosed and