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Universal Gravitation Question

  1. Nov 23, 2009 #1
    1. The problem statement, all variables and given/known data

    Given: G = 6.67259 × 10^−11 Nm2/kg2
    A small Moon of a planet has an orbital period of 2.08 days and an orbital radius of 5.04 × 10^5 km.
    From these data, determine the mass of the planet. Answer in units of kg.

    2. Relevant equations

    FG=FC
    FG=Gm1m2/r^2
    FC=mv^2/r
    3. The attempt at a solution

    First step was to convert into meters/seconds:
    2.08 days to 179712 seconds
    5.04x10^5km to 5.04x10^8m

    Use v=d/t (or v=2[tex]\pi[/tex]r/T) and get a velocity of 17621.1m/s. Use Fg=Fc and simplify to Gm/r=v^2, rearrange to v^2r/G=m. I crunched out the numbers and get a mass that's nearly as large as the sun. The problem states it's a planet, so I'm assuming I'm doing something wrong...what is it?
     
  2. jcsd
  3. Nov 23, 2009 #2

    Nabeshin

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    Science Advisor

    I don't see any error in your calculation... What is your final number you get for mass? Note the mass of the sun is about 2*10^30 kg.
     
  4. Nov 24, 2009 #3
    Doh, I guess I should have done half a second of research before I posted this topic.

    For some reason I thought the earth was ....x10^10, rather than x10^24. I got an answer of something (don't have the papers by me now)x10^27, which now seems fairly reasonable.
     
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