Randall D. Knight — Newton's Theory of Gravity: Problem 55

Most galaxies, including our own Milky Way, have supermassive black holes at their centers. Recently, astronomers were able to track one star, named S2, as it orbited the black hole at the center of our galaxy. The star’s actual orbit is elliptical, but we’ll model it as a circular orbit. S2 has a period of 15 years and a radius of 1000 au, where 1 au = 1 astronomical unit is the distance of the earth from the sun. a. What is the speed of S2? Give your answer as a fraction of c, where c = the speed of light = \(3.0 \times 10^8 \text{ m/s}\). b. What is the mass of the black hole? Give your answer as a multiple of \(M_s\), where \(M_s = 1 \text{ solar mass} = 2.0 \times 10^{30} \text{ kg}\).