Suppose that the orbit of Star S2, as described in the preceding problem, lies in a plane that is perpendicular to our line of sight. Then at periastron, when S2 is a distance 120 au from the central black hole, there will be both a transverse Doppler effect and a gravitational redshift for light from S2 to earth.

(a) Find the sum of these frequency shifts.

(b) Calculate the Schwarzschild radius (the Event Horizon radius) of the central Sgr A* black hole, and compare it with the periastron distance of S2. (The actual Event Horizon radius differs somewhat from the Schwarzschild radius because Sgr A* is undoubtedly rotating.)