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Centripetal motion, find radius - which solution is correct?

  1. Apr 24, 2015 #1
    1. The problem statement, all variables and given/known data
    The planet Saturn will orbit the Sun every 19 Earth years (= 599 184 000 seconds). Assume Saturn travels on a circular orbit with a speed of 9 690m/s. What is the radius of the orbit of Saturn?

    I can solve this in two different ways, and get two different values. Which is the correct approach, & why?

    2. Relevant equations & attempt at solution.

    T = (2πr)/V - that is, period is 2π*radius over speed.,
    so, r = (T*V)/2π
    so, radius = 9.24 x 1011m

    However, if, the centripetal forces equals the universal law of gravitation, that is,
    Fc = Fg
    (m*v2)/r = (Gm1m2)/r2
    r = (G*msun)/v2
    r = [(6.67x10-11)(1.99x1030kg)]/(9690m/s2)
    r = 1.41 x 1012m

    So, why the difference? What applies, and what doesn't apply and why?

    Thanks!
     
  2. jcsd
  3. Apr 24, 2015 #2

    ehild

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    Homework Helper
    Gold Member

    Both of your methods are correct, but the problem maker gave wrong orbital period. It is 29 years, instead of 19.
     
  4. Apr 29, 2015 #3

    Thanks so much! I was going crazy!
     
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