1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Gravitational Acceleration to calculate radius of Jupiter

  1. May 12, 2010 #1
    1. The problem statement, all variables and given/known data
    The moon Europa, of the planet Jupiter, has an orbital period of 3.55 days and
    an average distance from the center of the planet equal to 671,000 km. If the
    magnitude of the gravitational acceleration at the surface of Jupiter is 2.36 times greater than that on the surface of the Earth, what is the radius of Jupiter?
    (Hint: begin by calculating the rotation speed.)

    radius of orbit of Europa, rm = 671000km
    rotational period of Europa, T = 3.55 days
    Acceleration due to gravity on Jupiter = GM/r² = 2.36g
    radius of Jupiter, r = ?

    2. Relevant equations
    Rotational velocity of Europa, ω = 2π/(3.55*86400) radians/second
    Centripetal acceleration, a =rmω²

    3. The attempt at a solution

    Gravitational acceleration on Europa
    =GM/(rm)²
    =(GM/r²)*r²/(rm)²
    =(2.36g)(r/rm)²

    Equating gravitational acceleration with centripetal acceleration,
    (2.36g)(r/rm)² = rmω²
    r=(rm)³ω²/(2.36g)
    =74,038 km

    According to Google, r(Jupiter) = 71,492 km. Did I miss something?
     
  2. jcsd
  3. May 12, 2010 #2

    diazona

    User Avatar
    Homework Helper

    I don't think so, that's pretty close. You can't expect your calculation to be perfectly exact because, for example, you're implicitly assuming that Europa has a circular orbit.
     
  4. May 13, 2010 #3
    Ok. So I did all my calculations correctly? Do you get the same answer?

    Thanks for your help
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook