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Radius of a planet, given the density

  1. Jan 21, 2014 #1
    Hello! I'd like to thank everyone in advance for any help I receive!

    1. The problem statement, all variables and given/known data


    In January 2006, astronomers reported the discovery of a planet comparable in size to the earth orbiting another star and having a mass of about 5.5 times the earth's mass. It is believed to consist of a mixture of rock and ice, similar to Neptune. Take mEarth=5.97×10^24kg and rEarth=6.38×10^6m.

    If this planet has the same density as Neptune (1.76 g/cm3), what is its radius expressed in kilometers?


    2. Relevant equations

    density=m/v

    volume(of a sphere)=4/3(pi)r^3

    3. The attempt at a solution

    I calculated the mass of the new planet (n) as (5.5)5.97*10^24kg=3.28*10^25kg

    I set the given density of 1.76 g/cm3 equal to the found mass of 3.28*10^22g divided by the formula for the volume of a sphere, shown below:

    1.76 g/cm3 = 3.28*10^22g/[4/3(pi)r^3]

    I simplify until I reach r^3=4.46*10^21 cm3, then take the cubic root.

    The answer I reach is 16456067.27 cm or 164.56 km (165 to three significant figures). I'm not sure why this answer is incorrect.
     
  2. jcsd
  3. Jan 21, 2014 #2

    BvU

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    From 3.28*10^25kg to 3.28*10^22g is a bit strange. 1 kg = 1000 g, so I would expect 10^28 .
    Everything else is just fine.
     
  4. Jan 21, 2014 #3
    Hi s.dyseman :smile:

    welcome to PF

    You have just gone wrong at conversions.
     
  5. Jan 21, 2014 #4
    Thanks everyone! I was able to correctly answer the problem after you pointed out my mistake.


    Thanks again
     
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