The cover of this book shows the paths of a number of stars orbiting a massive object named Sagittarius A-Star (Sgr A* for short) at the center of our Milky Way galaxy. One of these stars, called "S2," has an orbit whose period is 16.05 years, a semimajor axis of \(970 \mathrm{au}\), and a periastron distance of \(120 \mathrm{au}\). Assuming that S2 follows a Keplerian elliptical orbit, what is its orbital

(a) eccentricity and

(b) semiminor axis?

(c) Most importantly, according to these observations what is the mass of Sgr A*, expressed as a multiple of the mass of the sun? (Note that 1 au is the average distance of the earth from the sun.)