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The Solar system moves at a speed of 220 km / s around the galaxy. It’s about 27,000 light years from the Galactic Centre. How long does it take for the solar system to orbit around the Milky Way?

I first calculated the circumference = $\mathrm{2 \times 3.14 \times 27,000 \times 9.4605284 \times 10^{15}\ m}$

Then, I divided the circumference by 220 km/s. However, I get $7.2 \times 10^8$

Can someone give me idea what I did wrong?

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closed as too localized by akhmeteli, Brandon Enright, Michael Brown, Emilio Pisanty, twistor59 Jun 7 '13 at 16:12

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  • $\begingroup$ Speed is 230 Km/s, not 220. $\endgroup$ – Schrödinger's Cat May 27 '13 at 8:34
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    $\begingroup$ In circumference calculation, its 10 raised to the power 15, not 5. $\endgroup$ – Schrödinger's Cat May 27 '13 at 8:37
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You've got the right idea, but, as pointed out in the comments, you've punched in the number for light years incorrectly. One light year is $9.461\times10^{15}$ meters. Also, you might not be converting km/s into m/s. Remember, all the units for a given dimension must be the same.

Since you can look up this number, I don't think I'm giving anything away by linking the answer from Wolfram|Alpha.

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  • $\begingroup$ I'm still a little confused. After dividing 1.60420716 x 10^21 by 220 km / s. How do I arrive at the answer 230 billion years; which is the answer. The website you cited does not give a clear explanation. $\endgroup$ – Kalina Kama May 27 '13 at 11:44
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    $\begingroup$ Units, units, units. $1.604\times10^{21}$ what's? And the answer you get? What unit is that in? You should find that the only missing ingredient is a conversion from one unit of time to another unit of time. $\endgroup$ – Warrick May 27 '13 at 13:11
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    $\begingroup$ @KalinaKama I cannot agree with the above point enough. For the entirety of your physics education, from this day forward, you should never, under any circumstances, write a dimensional number down without units. Failing to heed this advice will doom you to get most every calculation wrong, and it will make even your "correct" calculations useless to everyone else in the world. $\endgroup$ – user10851 May 27 '13 at 16:40

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