The SHARP/NTT stellar proper motion data now cover an interval from 1992 to 2000 and allow us to determine orbital accelerations for some of the most central stars of the Galaxy. We confirm the stellar acceleration measurements obtained by Ghez et al. with NIRC at the Keck telescope. Our analysis differs in three main points from that of Ghez et al.: (1) we combine the high-precision but shorter time-scale NIRC/Keck data with the lower precision but longer time-scale SHARP/NTT data set; (2) we statistically correct the observed accelerations for geometrical projection effects; (3) we exclude star S8 from the analysis of the amount and position of the central mass.
From the combined SHARP/NTT and NIRC/Keck data sets we show that the stars S2, and most likely S1 and S8 as well, are on bound, fairly inclined (60° < i < 80°), and eccentric (0.4 < e < 0.95) orbits around a central dark mass. The combination of both data sets results in a position of this central mass of 48+54-24 mas E and 18+42-61 mas S of the nominal radio position of Sgr A*. The mean statistically corrected enclosed mass derived from accelerations is Macc=(5±3)×106 Mo with current radial separations of S1 and S2 from Sgr A* of about 8-10 mpc. This enclosed mass estimate is derived from individual stellar orbits as close to the massive black hole at the centre of the Milky Way as currently possible. Although the uncertainties are large, this estimate is fully consistent with the enclosed mass range of (2.6 - 3.3)×106 Mo derived by Genzel et al. from radial and/or proper motion velocities of a homogenized sample of sources.
Star S8 was excluded from the analysis, since for the current proper motion velocity and radial separation from the centre we find that the measured acceleration requires orbital motion around a compact object with a mass in excess of 3×106 Mo. The data suggest either that this star was or is subject to a close interaction with a different object or that its position measurements are influenced by the emission of a different cluster star. Therefore we base the analysis of the enclosed mass solely on the available data for stars S1 and S2. We also discuss two late-type stars with projected separations from Sgr A* of about 0.5 and 1 arcsec. In addition to proper motions, these stars have known radial velocities. Orbit calculations indicate that such stars are very likely at larger physical distances from the centre and part of the larger scale central stellar cluster with a core radius of approximately 0.3 pc.
Key words: black hole physics stellar dynamics astrometry celestial mechanics Galaxy: centre infrared: general.