Question

Astronomers have observed a small, massive object at the center of our Milky Way Galaxy. A ring of material orbits this massive object; the ring has a diameter of about 16 light-years and an orbital speed of about 130 km/s. For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Black hole calculations.

Determine the mass M of the massive object at the center of the Milky Way galaxy.Take the distance of one light year to be 9.461 x 1015m.Express your answer in kilograms.

Answer 1

`1.91773* 10^(37)\ kg`

Step-by-step explanation:

v = Orbital speed = 130 km/s

d = Diameter = 16 ly

r = Radius =
`(d)/(2)=(16)/(2)=8\ ly`

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

`1\ ly=9.461* 10^(15)\ m`

As the centripetal force balances the gravitational energy we have the following relation

`(GMm)/(r^2)=(mv^2)/(r)\\\Rightarrow M=(v^2r)/(G)\\\Rightarrow M=(130000^2* 8* 9.461* 10^(15))/(6.67* 10^(-11))\\\Rightarrow M=1.91773* 10^(37)\ kg`

Mass of the the massive object at the center of the Milky Way galaxy is
`1.91773* 10^(37)\ kg`