Answer:
[tex]1.91773\times 10^{37}\ kg[/tex]
Explanation:
v = Orbital speed = 130 km/s
d = Diameter = 16 ly
r = Radius = [tex]\dfrac{d}{2}=\dfrac{16}{2}=8\ ly[/tex]
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
[tex]1\ ly=9.461\times 10^{15}\ m[/tex]
As the centripetal force balances the gravitational energy we have the following relation
[tex]\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[/tex]
Mass of the the massive object at the center of the Milky Way galaxy is [tex]1.91773\times 10^{37}\ kg[/tex]
