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

Answer:

$1.91773\times 10^{37}\ kg$

Explanation:

v = Orbital speed = 130 km/s

d = Diameter = 16 ly

r = Radius = $\dfrac{d}{2}=\dfrac{16}{2}=8\ ly$

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

$1\ ly=9.461\times 10^{15}\ m$

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

$\dfrac{GMm}{r^2}=\dfrac{mv^2}{r}\\\Rightarrow M=\dfrac{v^2r}{G}\\\Rightarrow M=\dfrac{130000^2\times 8\times 9.461\times 10^{15}}{6.67\times 10^{-11}}\\\Rightarrow M=1.91773\times 10^{37}\ kg$

Mass of the the massive object at the center of the Milky Way galaxy is $1.91773\times 10^{37}\ kg$