Answer :
Answer:
[tex]T=2.048*10^8[/tex] years
Explanation:
Period is:
[tex]T=\frac{2*\pi}{\omega}[/tex]
The speed of the galaxy is 230 km/s. Its angular speed is given by:
[tex]\omega = \frac{V}{R}[/tex] Where R=25000 light years
Now, let N be the amount of seconds in 1 year.
[tex]R = 25000 * 3*10^8*N[/tex] This value will be in meters.
Replacing this value:
[tex]\omega = \frac{230*10^3}{75*10^{11}*N}[/tex]
[tex]\omega = \frac{3.067*10^{-8}}{N}[/tex]
Now, the period will be:
[tex]T=\frac{2*\pi}{\frac{3.067*10^{-8}}{N}}[/tex] This value is in seconds. Since we are asked to give the answer in years, we have to divide by N (amount of seconds in a year:
[tex]T=\frac{2*\pi}{\frac{3.067*10^{-8}}{N}}/N[/tex]
[tex]T=2.048*10^8[/tex] years