In 2005 astronomers announced the discovery of a large black hole in the galaxy Markarian 766 having clumps of matter orbiting around once every 27 hours and moving at 30,000 km/s. (a) How far are these clumps from the center of the black hole? (b) What is the mass of this black hole, assuming circular orbits? Express your answer in kilograms and as a multiple of our sun’s mass. (c) What is the radius of its event horizon?

Solution 39E 2r Time period (T), velocity (v) and distance (r) are related by the equation T =v . Given, period T = 27 hours = 27 × 60 × 60 s = 97,200 s 7 v = 30,000 km/s = 3 × 10 m/s (a) Therefore, the distance from equation (1), Tv r = 2 7 r = 97,200 s×3×10 m/s 2×3.14 r = 4.64 × 10 11 m 11 Therefore, the distance of the clumps from the center of the black hole is 4.64 × 10 m. GM (b) The mass can be calculated from the equation v = r ,where G is the gravitational constant and M is the mass of the black hole. Therefore, mass M = v r 7 2 11 G (3×10 ) ×4.64×10...