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?

Video transcript

welcome back everybody. We are taking a look at the first black hole ever discovered, which was cygnus X one. And we are looking at a bit of matter that is orbiting around the black hole. Now we are told that the time it takes for one total revolution is five milliseconds or 50.5 seconds. We are also told that it has an orbital speed of 1. times 10 to the eighth meters per second. And we are asked to find what the distance is between the matter and the center of the black hole. Well that distance is just going to be the radius of orbit. And we know just by our planetary equations here that our orbital speed is equal to two pi times the radius of orbit. All divided by the time it takes for one revolution, rearranging some characters around we have that our radius is equal to our orbital speed times the time it takes for one revolution. All divided by two pi. So let's plug in some numbers here We have that our radius is equal to 1.49 times eight times the time it takes a 0.5. All divided by two pi. Giving us a radius of orbit of 100 and 18.5 kilometers corresponding to answer choice B Thank you all so much for watching. Hope this video helped. We will see you all in the next one