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Homework Help: Planet Orbit Mass Problem!

  1. Dec 2, 2009 #1
    1. The problem statement, all variables and given/known data
    A distant star has a single planet circling it in
    a circular orbit of radius 3.33 × 1011 m. The
    period of the planet’s motion about the star
    is 836 days.
    What is the mass of the star? The
    value of the universal gravitational constant
    is 6.67259 × 10−11 N · m2/kg2.
    Answer in units of kg.

    2. Relevant equations
    v = 2 π r / T
    ac = v2 / r
    Fc = mac
    Kepler's laws?

    3. The attempt at a solution
    uhhhh....have i have no idea where to start
  2. jcsd
  3. Dec 2, 2009 #2
    wait i figured it out....you use v=(gm/r)^(1/2) and substitute in 2(pi)r/T (in seconds) for v...then solve for M
    the answer i ended up with was 4.187530248*10^30
  4. Dec 2, 2009 #3


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  5. Dec 2, 2009 #4
    Well done! And your method is exactly right, Kepler's laws being unnecessary in this case, though just as useful if you know how.

    You can, of course, combined the equations to get...

    T2 = 4.π2.r3/GM

    ...and manipulated that as needed. You can see where Kepler's law comes from then, too.
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