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Using Kepler's Laws to find the mass of a star

  1. Oct 1, 2012 #1
    1. The problem statement, all variables and given/known data
    In recent years, a number of nearby stars have been found to possess planets. Suppose, the orbital radius of such a planet is found to be 4.9 1011 m, with a period of 1280 days. Find the mass of the star.


    2. Relevant equations
    T^2=4pi√((r^3)/Gm))


    3. The attempt at a solution
    (1280)^2=4pi√((4.9E11)^3/(6.67E-11)m)
    1638400=4pi√((1.17649E35)/(6.67E-11)m)
    1286796.351=√((1.17649E35)/(6.67E-11)m)
    1.655844849E12=(1.17649E35)/(6.67E-11)m)
    110.4448514m=6.67E-11
    m=6.039E-13

    I thought this was the right solution; however, I am not getting the correct answer as I am doing it online and it tells me I am doing it wrong. Am I using the wrong equation?
     
  2. jcsd
  3. Oct 1, 2012 #2
    I see at least two mistakes. The equation is wrong (c.f. Wikipedia); the period must be expressed in seconds, not days.
     
  4. Oct 1, 2012 #3

    tiny-tim

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    welcome to pf!

    hi james! welcome to pf! :smile:
    days !! :wink:
     
  5. Oct 1, 2012 #4
    I tried switching days to seconds and i got T=110592000 seconds so i changed my equation....

    (11059200)^2=4pi√((4.9E11)^3)/(6.67E-11)m)
    9.733E14=√((4.9E11)^3)/(6.67E-11)m)
    9.473E29=((4.9E11)^3)/(6.67E-11)m)
    (1.42E40)m=(4.9E11)^3
    m=8.234E-6

    I changed it to seconds, but I still don't seem to be getting the right answer.
     
  6. Oct 1, 2012 #5
    The equation is start with is wrong. I mean this one: T^2=4pi√((r^3)/Gm)) As I said. look up the correct equation.
     
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