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The solar system is 25,000 light years from the center of our Milky Way galaxy. One light year is the distance light travels in one year at a speed of 3.0×108m/s. Astronomers have determined that the solar system is orbiting the center of the galaxy at a speed of 230 km/s.
Assuming the orbit is circular, what is the period of the solar system's orbit? Give your answer in years

Answer :

lcmendozaf

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

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