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Homework Help: Planet Orbits, finding radius HELPP

  1. Jan 27, 2010 #1
    Planet Orbits, finding radius HELPP!!

    1. The problem statement, all variables and given/known data
    The planet mars has a mass of 6.418*1023kg and completes an orbit around the sun in 687 days. The sun has a mass of 1.99 * 1030kg. what is the average radius of the orbit of mars?


    2. Relevant equations
    Force Gravity = G*(m1m2)/r2
    Force Centripital = mv2/r

    G = 6.67 * 10-11


    3. The attempt at a solution
    I tried plugging in the numbers into the Universal gravitaiton formula where m1 was the mass of mars * m2 which is the mass of the sun * Universal gravitation. I didn't know what to use as Force Gravity.
    with the force centripital formula, you have 2 masses. how could i go about finding the velocity of mars if i dont have the radius??
    thanks for the help
     
  2. jcsd
  3. Jan 27, 2010 #2

    rl.bhat

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    Homework Helper

    Re: Planet Orbits, finding radius HELPP!!

    G*M*m/r^2 = m*v^2/r. Or
    G*M/r= v^2.....(1)
    In the problem time T to completes an orbit around the sun is given.
    So velocity v = 2*pi*r/T...(2)
    Substitute the expression of v in eq.1 and solve for r.
     
  4. Jan 27, 2010 #3
    Re: Planet Orbits, finding radius HELPP!!

    for when i plug in equation 1, would i take the square root of the whole left side??
     
  5. Jan 27, 2010 #4

    rl.bhat

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    Re: Planet Orbits, finding radius HELPP!!

    G*M/r= v^2.....(1)
    G*M/r= (2*pi*r/T)^2.....(2)
    If you simplify, you get
    G*M*T^2= 4*pi^2*r^3.
    Convert days to seconds and solve for r.
     
  6. Jan 27, 2010 #5
    Re: Planet Orbits, finding radius HELPP!!

    I got an answer with over a billion km lol seems kinda big even for planets but whatever

    thanks alot
     
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