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Homework Help: Lightyears and the surface area of a planet.

  1. Aug 30, 2007 #1
    A light year is the unit of distance that light, with a speed of 2.99792e8 m/s, travels in one year. What is the surface area of a planet whose radius is 1300 km? Answer in units of lightyears^2.

    I am wondering if my method is correct.

    SA of a sphere is 4[pi]R^2. With R = 1300, the surface area is 6.76e6[pi] km^2. Since they want this number in terms of light years, I need to first, well, convert the ratio into years. With dimension analysis (not the internet), I found that there was 31536000 seconds in one year. Setting up a proportion, that's about 9.45e15 meters in one year, or 9.45e12 km in one year. I squared that number (this is the part I am most unsure about) and then divided 6.76e6[pi] by about 8.94e25 km^2, to get 2.38e-19. But I don't think that's right, because the dimensions actually cancel, then.


  2. jcsd
  3. Aug 30, 2007 #2


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    You should divide 6.76e6[pi] km^2 by 8.94e25 km^2/lighyears^2. The units will be okay.
  4. Aug 30, 2007 #3
    Thank you!

    I forgot about km^2 being overlightyears^2.

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