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?

A.

The orbital speed of the clumps of matter around the black hole is equal to the ratio between the circumference of the orbit and the period of revolution:

where we have:

is the orbital speed

r is the orbital radius

is the orbital period

Solving for r, we find the distance of the clumps of matter from the centre of the black hole:

B.

The gravitational force between the black hole and the clumps of matter provides the centripetal force that keeps the matter in circular motion:

where

m is the mass of the clumps of matter

G is the gravitational constant

M is the mass of the black hole

Solving the formula for M, we find the mass of the black hole:

and considering the value of the solar mass

the mass of the black hole as a multiple of our sun's mass is

C.

The radius of the event horizon is equal to the Schwarzschild radius of the black hole, which is given by

where M is the mass of the black hole and c is the speed of light.

Substituting numbers into the formula, we find