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Homework Help: Kepler's constant and average radius of orbit

  1. Apr 13, 2010 #1
    1. The problem statement, all variables and given/known data
    Given that Jupiter has a mass of 1.9x10^27 kg, and the sun has a mass of 1.99x10^30 kg:

    a) Calculate the value of Kepler's constant for Jupiter.

    b) If Jupiter's orbital period is 11.89 Earth years, calculate the average radius of its orbit.


    2. Relevant equations

    K = Gmp/4pi^2 = r^3/T^2
    11.89x365x24x3600 = 374963040

    3. The attempt at a solution

    For a) Kjupiter = Gmp/4pi^2
    (6.6x10^-11)(1.9x10^27)/4pi^2

    = 3.21x10^15 m^3/s^2

    b) Ksun = Gmp/4pi^2
    ksun = (6.67x10^-11)(1.99x10^30)/4pi^2

    3.36x10^18 m^3/s^2

    Ksun=r^3/T^2
    Therefore: r^3 = Ksun*T^2
    r = cubed rt. of Ksun*T^2
    r = cubed rt. of (3.36x10^18)(374963040)^2
    r = cubed rt. of 4.724068653x10^35
    r = 7.8x10^11m

    I am really unconfident about these answers, can someone tell me if I am one the right track or should give up on Physics?
    Thank you in advance.
     
  2. jcsd
  3. Jan 18, 2011 #2
    I obtained similar results. Wondering if anyone can verify if they are correct.
     
  4. Jan 18, 2011 #3
    well for (b) i guess its pretty correct

    i even confirmed it using kepler's 3rd law in its pure form

    I dont know what's kepler's constant but if you are given a straight formula so it has to be correct
     
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