8. Centripetal Forces & Gravitation

Astronomers have found a small, but incredibly massive object at the center of our Milky Way galaxy, and suspect it is a black hole. A cloud of gas orbits this object at $1.8\times 10^5$ m/s every 78,500 years.

a) What is the mass of this alleged black hole?

b) How large is this black hole?

(II) Astronomers using the Hubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 km/s at a distance of 60 light-years ( = 5.7 x 10¹⁷ m) from the core. Deduce the mass of the core, and compare it to the mass of our Sun.