New observations of the stars orbiting the black hole at the Galactic Center (SgrA*) have improved the measurements. Here are the latest results from Gillessen etal. (2009) for star S0-2: period P = 15:8 yr, semimajor axis a = 1025 AU, and eccentricity e = 0:880; and for star S0-16: P = 47:3 yr, a = 2130 AU, and e = 0:963.
(a) Compute the mass (in units of solar masses) of Sgr A* implied by the new results. Do the two stars give a consistent answer?
(b) Compute the pericenter and apocenter distances (in AU) for S0-2 and S0-16.
(c) Compute the speeds (in km s^1) of S0-2 and S0-16 at pericenter and apocenter.