Black holes are difficult to observe with telescopes because they, by definition, don’t emit or reflect any light. They can be found by look- ing for other nearby objects orbit- ing them, however. Here is a dia- gram of a star in a circular orbit around a black hole. a. The period of the star’s orbit is 90 days, and its orbital radius around the black hole is observed to be 3.6 : ×10^11 m. Find the orbital velocity of the star in units of m/s. (You need to convert 90 days to seconds, first). The circumference of a circle is 2πr. b. The mass of the star is known to be 4 × 10^30 kg. Find the centripetal acceleration of the star and the strength of the gravitational force on the star. c. Find the mass of the black hole.

Black holes are difficult to observe with telescopes because they, by definition, don’t emit or reflect any light. They can be found by look- ing for other nearby objects orbit- ing them, however. Here is a dia- gram of a star in a circular orbit around a black hole. a. The period of the star’s orbit is 90 days, and its orbital radius around the black hole is observed to be 3.6 : ×10^11 m. Find the orbital velocity of the star in units of m/s. (You need to convert 90 days to seconds, first). The circumference of a circle is 2πr. b. The mass of the star is known to be 4 × 10^30 kg. Find the centripetal acceleration of the star and the strength of the gravitational force on the star. c. Find the mass of the black hole.