We discuss constraints on the properties and nature of the dark mass concentration at the core of the Milky Way. We present 0".15 astrometric K-band maps in five epochs between 1992 and 1996. From these we derive improved stellar proper motions within 3" of the compact radio source Sgr A* whose infrared counterpart may have been detected, for the first time, in a deep image in June 1996. We also report λ/Δλ~35 speckle spectroscopy and show that several of the Sgr A* (IR) cluster members are likely early type stars of mass ~15 to 20 Mo. All available checks including a first comparison with high resolution maps now becoming available from other groups support our previous conclusion that there are several fast moving stars (>103 km/s) in the immediate vicinity (0.01 pc) of Sgr A*. From the stellar radial and proper motion data, we infor that a dark mass of 2.61 (±0.15stat)(±0.35stat+sys)×106 Mo) must reside within about a light week of the compact radio source. Its density must be 2.2×1012 Mopc-3 or greater. There is no stable configuration of normal stars, stellar remnants or sub-stellar entities at that density. From an equipartition argument we infor that at least 5% of the dark mass (>105 Mo) is associated with the compact radio source Sgr A* itself and is concentrated on a scale of less that 15 times the Schwarzschild radius of a 2.6×106 Mo black hole. The corresponding density is 3×1020 Mopc-3 or greater. If one accepts these arguments it is hard to escape the conclusion that there must be a massive black hole at the core of the Milky Way.
Subject headings: astrometry - stellar dynamics - Galaxy: centre - infrared: general - black holes