Answer:
The mass of the massive object at the center of the Milky Way galaxy is [tex]3.44\times10^{37}\ Kg[/tex]
Explanation:
Given that,
Diameter = 10 light year
Orbital speed = 180 km/s
Suppose determine the mass of the massive object at the center of the Milky Way galaxy.
Take the distance of one light year to be 9.461×10¹⁵ m. I was able to get this it is 4.26×10³⁷ kg.
We need to calculate the radius of the orbit
Using formula of radius
[tex]r=\dfrac{d}{2}[/tex]
[tex]r=\dfrac{15\times9.461\times10^{15}}{2}[/tex]
[tex]r=7.09\times10^{16}\ m[/tex]
We need to calculate the mass of the massive object at the center of the Milky Way galaxy
Using formula of mass
[tex]M=\dfrac{v^2r}{G}[/tex]
Put the value into the formula
[tex]M=\dfrac{(180\times10^3)^2\times7.09\times10^{16}}{6.67\times10^{-11}}[/tex]
[tex]M=3.44\times10^{37}\ Kg[/tex]
Hence, The mass of the massive object at the center of the Milky Way galaxy is [tex]3.44\times10^{37}\ Kg[/tex]
The mass of the massive object is equal to [tex]3.44*10^37Kg[/tex]
[tex]r=\frac{d}{2} \\r= \frac{15*9.461*10^1^5}{2} = 7.09*10^1^6 m[/tex]
[tex]M= \frac{v^2*r}{g} \\M= \frac{(180*10^3)^2*7.09*10^1^6}{6.67*10^1^1} \\M= 3.44*10^3^7Kg[/tex]
Your question is incomplete. The part you forgot is "Determine the mass of the massive object at the center of the Milky Way galaxy. Give your answer in kilograms"
More information about mass in the link:
https://brainly.com/question/19694949
