Astronomers have observed a small, massive object at the center of our Milky Way galaxy (see Section 13.8). A ring of material orbits this massive object; the ring has a diameter of about 15 light-years and an orbital speed of about 200 km>s. (a) Determine the mass of the object at the center of the Milky Way galaxy. Give your answer both in kilograms and in solar masses (one solar mass is the mass of the sun).

4.26*10^37kg

2.14*10^7 solar mass

Explanation:

To solve this question, let us assume that the ring shaped accretion disk around the galaxy center's black hole is circular. This would permit us to use the circular orbit equation.

To find the mass of the disk, we use the formula

V = √ (Gm/r)

2*10^5 = √[6.67*10^-11 * m / (7.5 * 9.461*10^15) ]

(2*10^5) ² = 6.67*10^-11 * m / 7.096*10^16

4*10^10 * 7.096*10^16 = 6.67*10^-11 * m

m = 2.838*10^27/6.67*10^-11

m = 4.26*10^37kg

To get the mass in solar mass, we divide by mass of the sun (as instructed)

m = 4.26*10^37/1.99*10^30

m = 2.14 * 10^7 solar mass